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รศ.ดร.ปยะ โควินททวีวัฒน โปรแกรมวิศวกรรมโทรคมนาคม คณะวิทยาศาสตรและเทคโนโลยี มหาวิทยาลัยราชภัฏนครปฐม

การประมวลผลสัญญาณ สำหรับการจัดเก็บข้อมูลดิจิทัล เล่ม 3 : การออกแบบวงจรภาครับขั้นสูง Signal Processing for Digital Data Storage Volume III : Advanced Receiver Design สงวนลิขสิทธิ์ตามพระราชบัญญัติลิขสิทธิ์

ห้ามลอกเรียนแบบไม่ว่าส่วนใด ส่วนหนึ่งในหนังสือเล่มนี้ ไม่ว่าในรูปแบบใดๆ นอกจากจะได้รับอนุญาตเป็นลายลักษณ์อักษรจากผู้เขียนเท่านั้น

ข้อมูลทางบรรณานุกรมของหอสมุดแห่งชาติ

ปิยะ โควินท์ทวีวัฒน์ การประมวลผลสัญญาณสำหรับการจัดเก็บข้อมูลดิจิทัล เล่ม 3 : การออกแบบวงจรภาครับขั้นสูง./ ปิยะ โควินท์ทวีวัฒน์. —นครปฐม: โปรแกรมวิศวกรรมโทรคมนาคม คณะวิทยาศาสตร์และ เทคโนโลยี มหาวิทยาลัยราชภัฏนครปฐม, 2554 ISBN : 978-974-350-900-1 พิมพ์ครั้งที่ 1 สิงหาคม 2554 348 หน้า ราคา 270 บาท ผู้จัดพิมพ์ : รศ.ดร.ปิยะ โควินท์ทวีวัฒน์ พิมพ์ที่ : บริษัท เพชรเกษม พริ้นติ้ง กรุ๊ป จำกัด 18/49 ถ.ทรงพล ต.ลำพยา อ.เมือง จ.นครปฐม 73000 โทรศัพท์ : 0-3425-9758-9, 0-3425-9111 โทรสาร : 0-3425-3465

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4.8 Ã ¸ ­³ n´¤ ................................................................................................... 154

·Ê 5 ´¥ ¥²¤º qÅ n ´ ´¥ ¯ ¥­³¬Ã © Ï´Ë ............................................... 155 5.1 Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë ....................................................................................... 155 5.1.1 à ϴ§¯ m¯ ¬³ ´ ............................................................................... 157 5.1.2 Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ ................................................................. 158 5.1.3  ¯Â ¯¥qƩ©¯¥qÆ ££¶Ê ¥¶ ³¡Â©¯¥· ................................................................... 162 5.1.4  ¯Â ¯¥qƩ©¯¥qÆ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë .................................................... 167 5.2 ´¥§ § ¥² ¯ ©´£ ¥º ¥²Â ¶ ©´£¥n¯ à © Ï´Ë .......................................... 181 5.2.1 à ϴ§¯ m¯ ¬³ ´ ............................................................................... 183 5.2.2 à ϴ§¯ ¬³ ´ TA ............................................................................... 184 5.2.3 ©¶ · ´¥ ¥© ­´Ã§²Ã nÆ TA ......................................................................... 185 5.2.4 ©¶ · ´¥ ¥© ­´Ã§²Ã nÆ TA à © Ï´Ë ........................................................ 188 5.2.5 § ´¥ §¯ .............................................................................................. 189 5.2.6 ¬¥º § ´¥ §¯ ........................................................................................ 192 5.3 ¬¥º n´¤ ............................................................................................................. 193 5.4 à ¸ ­³ n´¤ ................................................................................................... 194

·Ê 6 Â Ä Ä§¤· BPMR .................................................................................. 195 6.1 Ï ´ ..................................................................................................................... 196 6.2 ©¶©³ ´ ´¥ ¯ Â Ä Ä§¤· BPMR ............................................................................ 198 6.2.1 ¬¹Ê¯ ³ ¸ ..................................................................................................... 198 6.2.2 ¥² ´¥ ³ ¸  ¶ ãm­§É ¬Ï´­¥³ BPMR ................................................... 199 6.2.3 ´¥ ¥²£©§ §¬³ ´ Å ¥² BPMR ...................................................... 201 6.3 § ¯ ¬ ¯ ¬³ ´ ³§¬q ¯ ¥² BPMR........................................................... 204 6.3.1 ´¥ Ï´§¯ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ......................................... 205 6.3.2 § ¥² ·Ê ¶ ´ Ưç qç²¥» ¥ ¯ ­³©¯m´ ........................................ 212 6.4 à ϴ§¯ ¯ ¬³ ´ ¯m´ §³ Å ¥² BPMR .................................................... 217 6.4.1 m´ ¥²£´ ¯ ¬³ ´ ³§¬q BPMR ........................................................... 218

6.4.2 m´ ¥²£´ ¯ ¬³ ´ ³§¬q BPMR ·Ê£·¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ .............. 220 6.4.3 à ϴ§¯ m¯ ¬³ ´ BPMR ·ÊÆ£m ¯ m  ¹Ê¯ ´ ©§´Ã ¬££»§ .................. 222 6.4.4 à ¥É £¶¬Â¥ ¶¬Â ¥ ³ ..................................................................................... 224 6.5 ¬¥º n´¤ ............................................................................................................. 226 6.6 à ¸ ­³ n´¤ ................................................................................................... 228

·Ê 7 ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q¬Ï´­¥³ ¥² BPMR .................... 229 7.1 ´¥qÂ É ­ ¸Ê £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ .................................................................. 230 · ·£º£Â É ª» ¤q粯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶............................................. 233 7.2 ´¥qÂ É ¬¯ £¶ ¶ Ê£ 7.2.1 £¹Ê¯ ¥´ m¯ ¬³ ´ H ............................................................................. 233 7.2.2 £¹Ê¯Æ£m ¥´ m¯ ¬³ ´ H.......................................................................... 237 7.3 ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶............................................... 238 7.4 ´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ ............................................ 239 7.5 ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ ................................................................... 240 7.6 © ¥ ¥© ­´©·Â ¯¥q ¶ ÊÅ· nÅ ¥² BPMR ................................................................. 245 7.6.1 © ¥ ¥© ­´©·Â ¯¥q ¶­ ¸Ê £¶ ¶ ......................................................................... 245 7.6.2 © ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ .¶ ......................................................................... 249 7.7 § ´¥ §¯ ......................................................................................................... 253 7.7.1 ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ ................................................................ 256 7.7.2 § ¥² ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ç²Ã ¥É £¶¬Â¥ ¶¬Â ¥ ³ .................. 257 7.7.3 ¬£¥¥ ² ¯ ¥² BPMR à © Ï´Ë ......................................................... 258 7.8 ¬¥º n´¤ ............................................................................................................. 261 7.9 à ¸ ­³ n´¤ ................................................................................................... 262

·Ê 8 Â Ä Ä§¤· HAMR ................................................................................. 263 8.1 Ï ´...................................................................................................................... 264 8.2 ­§³ ´¥Â ·¤ n¯£»§ ¯ ¥² HAMR...................................................................... 265 8.3 ¹Ë ´ à ϴ§¯ ©¶§Â§·¤£- ¯£¬ ɯ  ¶ ©´£¥n¯ ................................................. 266 8.3.1 Ä ¥Æ¡§q¯ º ­¢»£¶ ........................................................................................... 267

8.3.2 §» °¶¬Â ¯¥· ¶¬ .............................................................................................. 268 8.3.3 à ϴ§¯ ©¶§Â§·¤£- ¯£¬ ɯ ...................................................................... 270 8.3.4 à ϴ§¯ ©¶§Â§·¤£- ¯£¬ ɯ  ¶ ©´£¥n¯ .................................................. 271 8.4 ¥² HAMR à à © ¯ ................................................................................... 275 8.4.1 ´¥­´ m´ dM(x) / dx .................................................................................... 275 8.4.2 ´¥­´ m´ dM(H) / dH .................................................................................. 276 8.4.3 ´¥­´ m´ dHh / dx ........................................................................................ 277 8.4.4 ´¥­´ m´ dHd / dx ........................................................................................ 279 8.4.5 ´¥­´ m´ dHc / dT u dT / dx ........................................................................ 281 8.4.6 ´¥­´ º ª» ¤q §´ ´¥Â §·Ê¤ ¬ ´ ² x0 ....................................................... 283 8.4.7 ´¥­´ ´¥´£¶Â ¯¥q ´¥Â §·Ê¤ ¬ ´ ² a.......................................................... 284 8.5 ¥² HAMR à à © ³ Ë ...................................................................................... 285 8.6 à ϴ§¯ Æ£Ä ¥Ã ¥É ............................................................................................ 291 8.7 §³ « ²Â ´² ¯ ¥² HAMR ............................................................................. 293 8.7.1 ¥² HAMR à à © ¯ ........................................................................ 294 8.7.2 ¥² HAMR à à © ³ Ë ........................................................................... 302 8.7.3 n¯ ©¥¥²©³ Å ´¥Å nà ϴ§¯ ©¶§Â§·¤£- ¯£¬ ɯ  ¶ ©´£¥n¯ ................... 304 8.8 ¬¥º n´¤ ............................................................................................................. 305 8.9 à ¸ ­³ n´¤ ................................................................................................... 305

¡³ q ³ §¯ ´¥¶ ¸£ ´Ä  ·¤ ............................................................................ 307 ¯ Æ°Â ¯¥qÄ §¶ à  q ........................................................................ 309 ©´£¬££»§ ¯ ¬£ ´¥ (4.30) ç² (4.32) ..................................................... 311 ´¥­´ m´ ¥²£´ à ¯¡ q ¬Ï´­¥³ m¯ ¬³ ´ PR2 ................................. 313 ¥¥ ´ º ¥£ ....................................................................................................... 317 ¥¥ · ................................................................................................................. 327

·Ê 1 Ï ´ Å ·Ë ² §m´© ¸ à ϴ§¯ ´ ¶ ª´¬ ¥q ¯ m¯ ¬³ ´ ¯m´ (read channel) [1] ·ÊÅ nà ¥² ´¥ ³ ¸  ¶ ãm­§É (magnetic recording system) Å °´¥q ¶¬ qÆ ¥¡q  ¹Ê¯Å­n n»¯m´ ¥´ ¸ ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q ʸ Â É ¹Ë ´ Å ´¥ª¸ «´ m¯Æ

¯ ´ ·Ë ¤³ Æ n¯ ¶ ´¤Ã © ¶ ç² ¹Ë ´ ¯ ´¥Å n ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë (iterative

decoding) [2 – 5] Å ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q  ¹Ê¯Å­n n»¯m´  n´Å ¸

¥²Ä¤ q ¯  ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë ¸Ê Æ nÂ¥¶Ê£ Ï ´£´Å n ¥¶ Å °´¥q ¶¬ qÆ ¥¡q ¥mº Å­£mÈ [6]

 ¥´²¬´£´¥ m©¤Â ¶Ê£¬£¥¥ ² ¯ ¥² Æ n ·¤Ê ¶ ¸Ë

1.1 ¥² ´¥ ³ Â É n¯£»§ ¶ ¶ ³§ ¥² ´¥ ³ Â É n¯£»§ ¶ ¶ ³§ (digital data storage system) Å °´¥q ¶¬ qÆ ¥¡q ¬´£´¥ Ï´§¯  É

à ¢´ §É¯ Æ n ´£¥» ·Ê 1.1 [1, 5, 7] £¹Ê¯ ¶ m´©¬´¥ (message bits) » ¬m Æ ¤³ © ¥Â n´¥­³¬ à nÆ n¯ ¶ §´ (ECC encoder) Ä ¤¥­³¬ RS (Reed Solomon) [2, 8] Â É ¥­³¬ ·Ê ¶¤£Å nÅ °´¥q ¶¬ qÆ ¥¡q ´ ³ Ë n¯£»§ ·Ê n´¥­³¬Ã§n© É ² » Ï´ ´¥Â n´¥­³¬¯· ¥³ Ë ­ ¸Ê n©¤© ¥Â n´¥­³¬

£¯ »Â§ ³ (modulation encoder)  ¹Ê¯ ¥³ º ¬£ ³ ¶ ¯ n¯£»§Å­n­£´²¬£ ³ m¯ ¬³ ´ ¯

°´¥q ¶¬ qÆ ¥¡q Ä ¤¥­³¬£¯ »Â§ ³ ·Ê ¶¤£Å n ³ ³Ê©Æ ¹¯¥­³¬ RLL (run-length limited code)

[5, 9] n¯£»§Â¯´ q º ·ÊÆ n ´ © ¥Â n´¥­³¬£¯ »Â§ ³ ¹¯©m´Â É n¯£»§ ·Ê ² »  ·¤  n´Æ ³ Â É Å

¬¹Ê¯ ³ ¸ ¸Ê Â¥·¤ ³ ©m´ “ ¶ ·Ê ² » ³ ¸ (recorded bit)” ­§³ ´ ³ Ë ¶ ·Ê ² » ³ ¸ É ² »

บทนำ

¬m Æ ¤³ © ¥£¯ »Â§Â ¯¥q (modulator)  ¹Ê¯Ã § ¶ n¯£»§Å­n¯¤m»Å ¥» ¯ ¥²Ã¬Æ¡¡n ´Â ·¤ (write current waveform) çn© É n¯  n´Æ Å ­³©Â ·¤  ¹Ê¯ Ï´ ´¥Â ·¤ n¯£»§§ Æ Å ¬¹Ê¯ ³ ¸

1

บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

1

ECC encoder

message bits

modulation encoder

recorded bits

modulator

write current waveform

write head/medium/read head assembly

estimated message bits

ECC decoder

modulation decoder

reproduced bits

read channel

subsystem A

readback voltage waveform

¥» ·Ê 1.1 à ¢´ §É¯ ¯ ¥² ´¥ ³ Â É n¯£»§ ¶ ¶ ³§Å °´¥q ¶¬ qÆ ¥¡q [9, 10]

¬Ï´­¥³ ¥² © ´¥¯m´ n¯£»§ ­³©¯m´ (read head) ²¯m´ n¯£»§ ´ ¬¹Ê¯ ³ ¸ Ä ¤Â£¹Ê¯

­³©¯m´  §¹Ê¯ ·Ê£´ ¸ ¥¶Â© ·Ê£· ´¥Â §·Ê¤ à § ¬¢´ ©´£Â É Ã£m­§É (magnetization) É ²Å­n

§§³ q¯¯ £´Â É ¬³ ´ ¥» §¹Ê Ã¥ ³ Æ¡¡n ´ ·ÊÂ¥·¤ ³ ³Ê©Æ ©m´ “¬³ ´ ¯m´ §³ (readback signal)” ´ ³ Ë ¬³ ´ ¯m´ §³ ² » ¬m  n´Æ ¥²£©§ §Å m¯ ¬³ ´ ¯m´ ¸Ê ¥² ¯ n©¤ ¶ Ë ¬m© m´ È Â m © ¥ ¥¯ m´ ÏÊ´ (LPF: low-pass filter), © ¥ ³ ³©¯¤m´ (sampler ­¥¹¯

analog-to-digital converter), ¯· ©¯Æ§Â ¯¥q (equalizer), 粩 ¥ ¥© ­´¬³ §³ « q (symbol detector) Â É n Ä ¤ n¯£»§Â¯´ q º ·ÊÆ n É ² » Ï´ ´¥ ¯ ¥­³¬ n©¤© ¥ ¯ ¥­³¬£¯ »Â§ ³

(modulation decoder) 粩 ¥ ¯ ¥­³¬Ã nÆ n¯ ¶ §´ (ECC decoder) ´£§Ï´ ³  ¹Ê¯­´

m´ ¥²£´ ¯ ¶ m´©¬´¥ ·Ê n¯ ´¥ ² Ï ´£´Å n ´

1.2 à ϴ§¯ m¯ ¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q ¥² ¤m¯¤ A (subsystem A) Å ¥» ·Ê 1.1 ¬´£´¥ ì Å­n¯¤m»Å ¥» ¯ à ϴ§¯ ´ ¶ ª´¬ ¥q

Æ n ´£¥» ·Ê 1.2 [1, 10] £¹Ê¯§Ï´ ³ n¯£»§¯¶ º Ã Æ ´¥· ak {0, 1} ·Ê£· ´ ©§´ ¯ ¶  m´ ³

T ­ m ©¤ » ¬m m´ Æ ¤³ © ¥¯ º ³ q¯º £ ¶ (ideal differentiator) ·Ê£·¥» ­º ´£Â m´ ³ 1 – D £¹Ê¯ D ¹¯ ³© Ï´Â ¶ ´¥­ m © ©§´ T ­ m ©¤ Ï´Å­nÆ nÂ É §Ï´ ³ n¯£»§Â §·Ê¤ ¬ ´ ² (transition sequence) bk {–1, 0, 1} £¹Ê¯ bk = r1 ­£´¤ ¸ ´¥Â §·Ê¤ ¬ ´ ²Ã © ­¥¹¯Ã §

(positive or negative transition) ç² bk = 0 ­£´¤ ¸ Æ£m£· ´¥Â §·Ê¤ ¬ ´ ² (no transition)

´ ³ Ë §Ï´ ³ n¯£»§Â §·Ê¤ ¬ ´ ² bk ² » ¬m m´ Æ ¤³ m¯ ¬³ ´ ·Ê£· § ¯ ¬ ¯ ¯¶£ ³§¬q  m´ ³ ¬³ ´ ³§¬q §·Ê¤ ¬ ´ ² g(t) ç² » ¥ © n©¤¬³ ´ ¥ © n(t) Ï´Å­nÆ nÂ É ¬³ ´ ¯m´ §³ r(t) ¸Ê ¬´£´¥  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯

2

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

n t

ak

bk

g t

r t

aˆk

m t

H D

¥» ·Ê 1.2 à ϴ§¯ m¯ ¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q

r t

b g t kT n t

(1.1)

k

k

´ ³ Ë ·Ê© ¥¢´ ¥³ ¬³ ´ ¯m´ §³ r(t) ² » ¬m m´ Æ ¤³ © ¥ ¥¯ m´ ÏÊ´ (LPF)  ¹Ê¯ Ï´ ³ ¬³ ´ ¥ © ·Ê¯¤m» ¯ à ©´£ ·Ê ç² » Ï´ ´¥ ³ ³©¯¤m´ ©§´ ·Ê » © º£ n©¤¥² Æ ££¶Ê ¥¶ ³¡Â©¯¥· (timing recovery) [10] n¯£»§Â¯´ q º ¯ © ¥ ³ ³©¯¤m´ É ² » ¬m Æ ¤³

¯· ©¯Æ§Â ¯¥q粩 ¥ ¥© ­´¬³ §³ « q  ¹Ê¯­´§Ï´ ³ n¯£»§¯¶ º ·Ê ©¥ ²Â É ¬» ¬º aˆk (­¥¹¯ m´ ¥²£´ ¯ ak )

¬Ï´­¥³ ¥² ´¥ ³ ¸ à à © ¯ (longitudinal recording) ¬³ ´ ³§¬q §·Ê¤

¬ ´ ²­¥¹¯ ·Ê¥n» ³ ³ ³©Ê Æ ©m´¬³ ´ ³§¬q Lorentzian £·¥» ¬£ ´¥ ¹¯ [11] g t

1 1 2t / PW50

2

(1.2)

Ä ¤ ·Ê PW50 ¹¯ ©´£ ©n´ ¯ ¬³ ´ ³§¬q g(t) ©³ ϴí m ·Ê¬³ ´ ³§¬q£· ©´£¬»  É

¥¸Ê ­ ¸Ê ¯ ©´£¬» ¬» ¬º Å ² ·Ê¬³ ´ ³§¬q §·Ê¤ ¬ ´ ² ¯ ¥² ´¥ ³ ¸ à à © ³ Ë (perpendicular recording) £·¥» ¬£ ´¥ ¹¯ [12]

(1.3)

บทนำ

2t ln 2 ¬­ ­­ g t erf PW50 ®­

£¹Ê¯ ln(.) ¹¯§¯ ´¥¶ ¸£ ¥¥£ ´ ¶ (natural logarithm), PW50 ¹¯ ©´£ ©n´ ¯ ³§¬q g a t ­¥¹¯ ¯ º ³ q ¯ g(t) ©³ ϴí m ·Ê¬³ ´ ³§¬q£· ©´£¬» Â É ¥¸Ê ­ ¸Ê ¯ ©´£¬» ¬» ¬º , ç² erf(.) ¹¯¡³ q ³ n¯ ¶ §´ (error function) ¸Ê ¶ ¤´£Ä ¤

1

บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

3

¥» ·Ê 1.3 ¬³ ´ ³§¬q §·Ê¤ ¬ ´ ²¬Ï´­¥³ ´¥ ³ ¸ (a) à à © ¯ ç² (b) à à © ³ Ë

erf x

2

Q¨

x 0

2

e t dt

(1.4)

Å ¥² ´¥ ³ ¸ n¯£»§ ¯ °´¥q ¶¬ qÆ ¥¡q ©´£­ ´Ã m ¯ ´¥ ³ ¸ à ¯¥q£¯§

Ƨ q (ND: normalized recording density) ² ¶ ¤´£Ä ¤ [11] ND

PW50 T

(1.5)

¸Ê ­£´¤ ¸ ©´£­ ´Ã m ¯ ´¥ ³ ¸ n¯£»§ £¹Ê¯ T ¹¯ ´ ©§´ ¯ n¯£»§­ ¸Ê ¶ ­¥¹¯ ·ÊÂ¥·¤

³ ©m´ ¶  §§q (bit cell) Ä ¤ m´ ND ²Â É ³© m ¯ ©m´ ¥¶Â© PW50 ¬´£´¥ ³ Â É n¯£»§Æ n

·Ê ¶ ¥» ·Ê 1.3 ì § ¯ ¬ ¯ ´¥Â §·Ê¤ ¬ ´ ²¬Ï´­¥³ ´¥ ³ ¸ à à © ¯ ç²Ã

à © ³ Ë ¥² ³ ND m´ È ¸Ê ² ©m´¬³ ´ ³§¬q §·Ê¤ ¬ ´ ² ¯ ³ Ë ¬¯ à ¥¯ §º£ m© ©§´­§´¤È ¶  §§q Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ ND £· m´Â ¶Ê£ ¸Ë ­¥¹¯ §m´©¯· ³ ¤­ ¸Ê ¹¯ ´¥

à ¥ ¬¯ ¥²­©m´ ¬³ §³ « q (ISI: intersymbol interference) ²£· ©´£¥º Ã¥ £´ ¸Ë £¹Ê¯ ND £· m´Â ¶Ê£ ¸Ë  ¥´²Ä¯ ´¬ ·Ê¬³ ´ ³§¬q §·Ê¤ ¬ ´ ² ·Ê¯¤m»Å §n ³ ²£´ n¯ ­§¹Ê¯£ (overlap) ³ £· ©´£Â É Æ Æ n¬»

Å ¥ · Ê­ · ³©¯m´  §¹Ê¯ ·Ê£´ ¸ ¥¶Â© ·Ê£· ´¥Â §·Ê¤ ¬ ´ ² ¯ ¬¢´ ©´£Â É Ã£m­§É

¶ ³ ¬¯ ¥³ Ë ¬³ ´ ³§¬q¥©£ ·ÊÆ n ²Â¥·¤ ©m´ “¬³ ´ ³§¬qÆ ¶ (dibit pulse)” ­¥¹¯ § ¯

¬ ¯ Æ ¶ (dibit response) [11] ¸Ê £· m´Â m´ ³ ( »¥» ·Ê 1.2) m t g t g t T

4

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(1.6)

¥» ·Ê 1.4 ¬³ ´ ³§¬qÆ ¶ ¬Ï´­¥³ ´¥ ³ ¸ (a) à à © ¯ ç² (b) à à © ³ Ë

³ ì Å ¥» ·Ê 1.4 Ä ¤ § ¯ ¬ ¯ Æ ¶ ·Ë ² ¹¯©m´Â É ³©Ã ¯ “ m¯ ¬³ ´ (channel)” ¯ ¥² ´¥ ³ ¸ n¯£»§Å °´¥q ¶¬ qÆ ¥¡q

Ä ¤ ³©Ê Æ © ¥ ¥© ­´¬³ §³ « q Ê · ¶ ¤£Å nÅ ¥² ´¥ ³ ¸ ãm­§É ¹¯ © ¥ ¥© ­´

©·Â ¯¥q ¶ (Viterbi detector) [10, 13]  ¹Ê ¯ ´ ©´£ ³ n¯ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶ ²Â ¶Ê£ ¸Ë

à § · Ë Ï´§³ ´£ Ï´ © ­ m ©¤ ©´£ Ï´ ¯ m¯ ¬³ ´ (channel memory) ³ ³ Ë ¯· ©¯Æ§Â ¯¥q

¸ Â É ¬¶Ê Ï´Â É ·Ê n¯ Ï ´£´Å n ¹Ê¯ ¥³ ¥» ¥m´ § ¯ ¬ ¯ ¥©£ ¯ ³ Ë ¥² Å­nÂ É Æ ´£ § ¯

¬ ¯ ·Ê n¯ ´¥ ·ÊÂ¥·¤ ©m´ “ § ¯ ¬ ¯ ´¥qÂ É 1 (target response)” H(D) [10, 11, 14] ç²

m©¤§ ©´£ ³ n¯ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶Æ n Å ´ ¶ ³ ¶ ´¥qÂ É ·Ë Â¥·¤ ³ ³Ê©Æ ©m´ “ ´¥qÂ É Ã § ¯ ¬ ¯ ´ ¬m© ” ­¥¹¯ ´¥qÂ É Ã PR (partial response) Ä ¤ ´¥qÂ É Ã PR ·ÊÂ É ·Ê¤¯£¥³ Å ¥² ´¥ ³ ¸ à à © ¯ £·¥» ¬£ ´¥ ¹¯ [11] H D 1 D 1 D

n

(1.7)

ç²Å ¥² ´¥ ³ ¸ à à © ³ Ë £·¥» ¬£ ´¥ ¹¯ [14, 15] n

(1.8)

บทนำ

H D 1 D

£¹Ê¯ n ¹¯Â§ Ï´ ©  ɣ © 1

´¥qÂ É Å ´ °´¥q ¶¬ qÆ ¥¡q ­£´¤ ¸ © ¥ ¥¯ à  ¶ ¬n ·Ê£· Ï´ © Ã É (tap) n ¯¤ ç² » ¯¯ à ŭn£· § ¯ ¬ ¯  ¶ ©´£ ·Ê­£¹¯ ³ § ¯ ¬ ¯ ¯ m¯ ¬³ ´ (Æ ¶ ) Å­n£´ ·Ê¬º Ä ¤ ¥´ª ´ ´¥ ¤´¤¬³ ´ ¥ ©

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

1

บทที่

5

¥» ·Ê 1.5 § ¯ ¬ ¯  ¶ ©´£ ·Ê ¯ ´¥qÂ É Ã m´ È ¬Ï´­¥³ m¯ ¬³ ´ ´¥ ³ ¸ (a) à à © ¯ ç² (b) à à © ³ Ë

¥» ·Ê 1.5  ¥·¤  ·¤ § ¯ ¬ ¯  ¶ ©´£ ·Ê (frequency response) ¯ ´¥qÂ É Ã

m´ È Ä ¤ § ¯ ¬ ¯  ¶ ©´£ ·Ê ¯ m¯ ¬³ ´ É ¹¯ § ´¥Ã § ¡»Â¥·¤¥q (Fourier transform) ¯ ¬³ ´ ³§¬qÆ ¶ [1] Å ¬£ ´¥ (1.6) ç² ³©Â§ ·Ê¯¤m»Å  ¥¹Ê¯ ­£´¤© 夃 ¬·Ê­§·Ê¤£ [ ] ì m´¬³£ ¥²¬¶ ¶ÃÎ m§²Ã É ¯ ´¥qÂ É ³©¯¤m´  m

PR4 [1 0 –1] ­£´¤ ¸ ´¥qÂ É Ã PR4 (PR class-IV) ·Ê£·¡³ q ³ m´¤Ä¯ Å Ä Â£ D [1] ¹¯ H(D) = 1 – D2, ­¥¹¯

EEPR2 [1 4 6 4 1] ­£´¤ ¸ ´¥qÂ É Ã EEPR2 ·Ê£·¡³ q ³ m´¤Ä¯ Å Ä Â£ D ¹¯ H(D) = 1 + 4D + 6D2 + 4D3 + D4 Â É n

´ ¥» ·Ê 1.5 ©m´Â£¹Ê¯ m¯ ¬³ ´ £· m´ ND  ¶Ê£ ¸Ë ´¥qÂ É ·ÊÅ n É ©¥£· Ï´ © Ã É £´ ¸Ë (£· m´ n £´ ¸Ë )  ¹Ê¯Å­n § ¯ ¬ ¯ ¯ ´¥qÂ É £·§³ « ²Â­£¹¯ ³ § ¯ ¬ ¯ ¯ m¯ ¬³ ´ Å­n£´ ·Ê¬º ¸Ê ² m©¤ Ï´Å­n© ¥ ¥© ­´©·Â ¯¥q ¶ Ï´ ´ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ £´ ¸Ë (ª¸ «´

¥´¤§²Â¯·¤  ¶Ê£Â ¶£Æ nÅ ·Ê 3 ¯ [10])

¯ ´ ·Ë ´ ¬£ ´¥ (1.7) ç² (1.8) ©m´ m´¬³£ ¥²¬¶ ¶ Î ¯ ´¥qÂ É Ã PR º ³©

²Â É Â§ Ï´ ©  ɣ ¯¤m´ Æ¥ É ´£ n´Å n ´¥qÂ É ·Ê£· m´¬³£ ¥²¬¶ ¶ÂÎ É Â§ Ï´ © ¥¶ ¸Ê Â¥·¤ ©m´

“ ´¥qÂ É Ã GPR (generalized partial response target)” ¬£¥¥ ²¥©£ ¯ ¥² ·ÊÆ n ² · ©m´

´¥Å n ´¥qÂ É Ã PR £´ n»¬ Å ¬´£´¥ ª¸ «´Â ¶ ´¥¯¯ à ¯· ©¯Æ§Â ¯¥qç² ´¥q É

·Ê­£´² ³ m¯ ¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q Æ nÅ [10, 14, 15]

6

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

w t

ak

H D

sk

r t

q t

aˆk

¥» ·Ê 1.6 à ϴ§¯ m¯ ¬³ ´ ¯º £ ¶

1.3 à ϴ§¯ m¯ ¬³ ´ ¯º £ ¶ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 1.2 ¹¯©m´Â É “à ϴ§¯ m¯ ¬³ ´ ¬£¹¯ ¥¶ (realistic

channel model)”  ¥´²£·§³ « ² ´¥ Ï´ ´ Å §n ·¤ ³ ¥² ¥¶ ¸Ê ¥² ¯ n©¤ ¶ Ë ¬m© ·Ê¬Ï´ ³

·Ê£·¯¤m»Å ¬ ´ ³ ¤ ¥¥£ m¯ ¬³ ´ ¯m´ ¯ °´¥q ¶¬ qÆ ¥¡q [1] Å ­³© n¯ ·Ë ²¯ ¶ ´¤ “à ϴ§¯

m¯ ¬³ ´ ¯º £ ¶ (ideal channel model)” ¸Ê ¶ ¤£Å nÅ ´¥ª¸ «´Ã§²©¶Â ¥´²­q ˹ ´ ´¥

Ï´ ´ ¯ ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q  ¥´²Â É Ã Ï´§¯ ·ÊÆ£m ³ n¯ ç² m´¤ m¯ ´¥ Ï´ ©´£Â n´Å

³ ³ Ë n´¬££º ¶Å­n¥² £· ¥² © ´¥¯· ©¯Æ§Â ³ à ¬£ »¥ q (perfect equalization)

à ϴ§¯ Å ¥» 1.2 É ²¬´£´¥ § ¥» Æ nÂ É Ã Ï´§¯ m¯ ¬³ ´ ¯º £ ¶Å ¥» ·Ê 1.6 Ä ¤ §Ï´ ³ n¯£»§¯¶ º Ã Æ ´¥· ak ·Ê£· ´ ©§´ ¯ ¶  m´ ³ T ² » ¬m  n´Æ ¤³ m¯ ¬³ ´

H D

hD i i

i

£¹Ê¯ hi ¹¯ m´¬³£ ¥²¬¶ ¶ Î ³© ·Ê i ¯ m¯ ¬³ ´ ç² » §Ï´Ë ¬³ ´

(modulate) ³ ¬³ ´ ³§¬qÆ ©¶ ¬q¯º £ ¶ (ideal Nyquist pulse) q(t) = sin(St/T)/(St/T) [16] ç² » ¥ © n©¤¬³ ´ ¥ © w(t) Ï´Å­nÆ nÂ É ¬³ ´ ¯m´ §³ r t

s q t kT w t

k

(1.9)

k

Ä ¤ ·Ê sk = ak hk ¹¯ n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ ç² ¹¯ ³© Ï´Â ¶ ´¥ ¯ Ä©§» ³ (convolution operator) ´ ³ Ë ·Ê© ¥¢´ ¥³ ¬³ ´ ¯m´ §³ r(t) ² » ¬m m´ Æ ¤³ © ¥ ¥¯

บทนำ

m´ Ïʴç² » Ï´ ´¥ ³ ³©¯¤m´ ©§´ ·Ê » © º£Ä ¤¥² Æ ££¶Ê ¥¶ ³¡Â©¯¥· m¯ ²¬m n¯£»§

¯´ q º ¯ © ¥ ³ ³©¯¤m´ Æ ¤³ © ¥ ¥© ­´¬³ §³ « q ¹Ê¯ Ï´ ´¥­´§Ï´ ³ n¯£»§¯¶ º ·Ê ©¥ ²Â É ¬» ¬º

1

บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

7

1.4 ´¥ ¯ ¥­³¬Ã © Ï´Ë Ã Ï´§¯ m¯ ¬³ ´ Å ¥» ·Ê 1.2 Â É Ã Ï´§¯ ¯ “¥² ·ÊÆ£m »  n´¥­³¬ (uncoded system)” ¯¤m´ Æ¥ É ´£© ¥¢´ ¥³ ·ÊÅ n ¥¶ Å ­§´¤È ´ ¥²¤º q ²Å n ³ Ë ´¥¯· ©¯Æ§Â ³ (equalization)

 ¹Ê¯ ³ ´¥ ³ ´¥§ ¯ (distortion) ¯ m¯ ¬³ ´ ç² ´¥Â n´¥­³¬Ã nÆ n¯ ¶ §´ (error correction coding)  ¹Ê¯ ³ ´¥ ³ n¯ ¶ §´ ·Ê ¶ ¸Ë ´ m¯ ¬³ ´ Ä ¤ ³Ê©Æ ¥² ·Ê£· ´¥

Å n ´ ¥­³¬ ECC ²Â¥·¤ ©m´ “¥² ·Ê »  n´¥­³¬ (coded system)”

¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q ¥¶ ( »¥» ·Ê 1.1) ²£· ´¥Å n ´ ¥­³¬

à nÆ n¯ ¶ §´ n©¤Â m ³ ( ¸Ê ²Å n¥­³¬ RS  ¥´²¬´£´¥ à nÆ n¯ ¶ §´ ·Ê ¶ ³ ­§´¤ ¶

Æ n) §m´© ¹¯ ¶ m´©¬´¥ ² » ¬m  n´Æ ¤³ © ¥Â n´¥­³¬Ã nÆ n¯ ¶ §´ 粩 ¥Â n´¥­³¬£¯ »Â§ ³

É ²Æ nÂ É §Ï´ ³ n¯£»§¯¶ º ak Å ¥» ·Ê 1.2 ´ ³ Ë ·Ê© ¥¢´ ¥³ §Ï´ ³ n¯£»§¯¶ º ·Ê ¥© ­´ Æ n aˆk Å ¥» ·Ê 1.2 É ² » ¬m Æ ¤³ © ¥ ¯ ¥­³¬£¯ »Â§ ³ 粩 ¥ ¯ ¥­³¬Ã nÆ n¯ ¶ §´  ¹Ê¯Å­nÆ nÂ É m´ ¥²£´ ¯ ¶ m´©¬´¥ ·Ê ² Ï ´Æ Å n ´ Æ n ´¥ Ï´ ´ ¯ ¥² ´¥ ¥²£©§ §

¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q Å §³ « ² ·Ë ¶¤£Å n ³ Ë Ã m¯ · ¸ ³ º ³ ¸Ê ¹¯©m´Â É ´¥ ¥²£©§

§Ã ´  ·¤© (one-way processing) ³Ê ¹¯© ¥ ¥© ­´¬³ §³ « q ² Ï´ ´ Â É ¯¶¬¥² ´ © ¥ ¯ ¥­³¬ ECC

¯¤m´ Æ¥ É ´£ ´ ©¶ ³¤ [2 – 5] ì Å­nÂ­É ©m´ “ ´¥ ¯ ¥­³¬Ã © Ï´Ë (iterative

decoding)” ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ © ¥ ¥© ­´¬³ §³ « q粩 ¥ ¯ ¥­³¬ ECC

¬´£´¥ m©¤Â ¶Ê£¬£¥¥ ²¥©£ ¯ ¥² Æ nÂ É ¯¤m´ £´ °´¥q ¶¬ qÆ ¥¡q Ê·Å n¥² ´¥ ¥²£©§ §

¬³ ´ à © Ï´Ë ²£·Ä ¥ ¬¥n´ ´£¥» ·Ê 1.7 Ä ¤£· ´¥Â ¶Ê£© ¥Â n´¥­³¬Ã © Ï´Ë (iterative

encoder) 粩 ¥ ¯ ¥­³¬Ã SISO2 (soft-input soft-output)  n´Æ Å ¥² ¯ ´ ·Ë © ¥

¥© ­´¬³ §³ « q Ê·Å nÅ ¥² ¤m¯¤ A ² n¯  §·Ê¤ ´ © ¥ ¥© ­´©·Â ¯¥q ¶Â É © ¥ ¥© ­´ à SISO Ä ¤ ·Ê© ¥Â n´¥­³¬Ã © Ï´Ë É ¹¯© ¥Â n´¥­³¬Ã nÆ n¯ ¶ §´ ¥²Â¢ ­ ¸Ê 3 ¸Ê ¶ ¤£

Å n¥­³¬ LPDC (low-density parity-check code) [17]  ¥´²Â É ¥­³¬ ECC ·Ê£·¬£¥¥ ²£´ ¬º

[2, 5] (ª¸ «´¥´¤§²Â¯·¤  ·Ê¤©¥­³¬ LPDC Æ nÅ ·Ê 4)

³ º ³ ·Ë °´¥q ¶¬ qÆ ¥¡q ¥mº Å­£mÈ Æ n Ï´Â ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë £´Å n ´ çn©

( ´£¥» ·Ê 1.7) ¸Ê ²£· ´¥Ã§  §·Ê¤ m´©¬´¥Ã ¯¡ q (soft information) [2] ¥²­©m´ © ¥

2

3

© ¥ ¥© ­´Ã SISO 粩 ¥ ¯ ¥­³¬Ã SISO ² Ï´ ´ Ä ¤Å n n¯£»§¯¶ º ·ÊÂ É m´©¬´¥Ã ¯¡ q (soft information) ç²Å­n n¯£»§Â¯´ q º ·ÊÂ É m´©¬´¥Ã ¯¡ q m ³ (ª¸ «´¥´¤§²Â¯·¤ Æ nÅ ·Ê 2 – 3) ¥­³¬ Reed Solomon Æ£m ¶¤£ Ï ´£´Å nÅ ´¥ ¯ ¥­³¬Ã © Ï´Ë ³ ³ Ë °´¥q ¶¬ qÆ ¥¡q ÊÅ· n¥² ´¥ ¥²£©§ § ¬³ ´ à © Ï´Ë ¸ Ï´Â É n¯  ¶Ê£© ¥Â n´¥­³¬Ã © Ï´Ë (iterative encoder)  n´Æ Å ¥²

8

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 1.7 à ¢´ §É¯ ì ´¥ Ï´ ´ ¯ ¥² ´¥ ¥²£©§ §¬³ ´ à © Ï´Ë ¯ °´¥q ¶¬ qÆ ¥¡q

¥© ­´Ã SISO 粩 ¥ ¯ ¥­³¬Ã SISO Ä ¤ ·Ê© ¥ ¥© ­´Ã SISO ·ÊÅ n ³ ´¥ ¯

¥­³¬Ã © Ï´Ë ¬´£´¥ ³ ´Æ n ´ ¯³§ ¯¥¶ ¸£ BCJR [18] ­¥¹¯ SOVA (soft-output Viterbi algorithm) [19] (ª¸ «´¥´¤§²Â¯·¤ Æ nÅ ·Ê 2 – 3) Å ² ·Ê© ¥ ¯ ¥­³¬Ã SISO ·ÊÅ n

¯ ¥­³¬ n¯£»§ ·Ê »  n´¥­³¬ n©¤¥­³¬ LDPC ² ³ ´£´ ´ ¯³§ ¯¥¶ ¸£ ´¥ m´ m´©¬´¥ (message passing algorithm) [17] (ª¸ «´¥´¤§²Â¯·¤ Æ nÅ ­³© n¯ ·Ê 4.4.4)

´¥ Ï´ ´ ¯  ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë Â¥¶Ê£ ´ © ¥ ¥© ­´Ã SISO Ï´ ´¥

¥© ­´ n¯£»§ ·ÊÆ n¥³ çn©¬m §§³ q Ê·Æ n ( ¸Ê Â É m´©¬´¥Ã ¯¡ q) Æ ¤³ © ¥ ¯ ¥­³¬Ã

SISO ´ ³ Ë © ¥ ¯ ¥­³¬Ã SISO É ²¬m §§³ q Ê·Æ n ´ ´¥ ¯ ¥­³¬ n¯£»§ §³ Æ Å­n© ¥ ¥© ­´Ã SISO  ¹Ê¯Å nÅ ´¥ ¥© ­´ n¯£»§Å­£m¯· ¥³ Ë ­ ¸Ê ¥² © ´¥ ·Ë ² Ï´Â ¶ ´¥Æ

Â¥¹Ê¯¤È ¥² ³ Ê ¥ ´£ Ï´ © ¥¯ (iteration) ¯ ´¥© Ï´Ë ·Ê Ï´­ © ¥ ¯ ¥­³¬Ã SISO

¸ ²¬m n¯£»§Â¯´ q º ·ÊÆ nÆ ¤³ © ¥ ¯ ¥­³¬£¯ »Â§ ³ 粩 ¥ ¯ ¥­³¬ RS  ¹Ê¯ Ï´ ´¥ ¯ ¥­³¬

n¯£»§ m¯Æ ­£´¤Â­ º

´ ¥» ·Ê 1.7 ² ©m´£· ´¥Å n ´ ³ Ë ¥­³¬ RS ç²¥­³¬ LDPC ¯¤m´ Æ¥ É ´£Å ´

¶ ³ ¶ ©m´ [20] £¹Ê¯£· ´¥Å n ´ ¥­³¬ LPDC Å ´¥ ¯ ¥­³¬Ã © Ï´Ë Ã§n© ɯ´ ²Æ£m Ï´Â É

n¯ Å n¥­³¬ RS ÉÆ n ³ ³ Ë n»Å n¬´£´¥ §¹¯ Å n ´ ¥­³¬ RS ç²¥­³¬ LDPC ¥m©£ ³ ­¥¹¯Å n¥­³¬

LDPC  ·¤ ¯¤m´  ·¤© ɤ³ Å­n¬£¥¥ ² ·ÊÅ §n ·¤ ³

บทนำ

1.5 ¹Ë ´ ç² Ï´ª³ q Ê · m ´¬ Å Å ­³© n¯ ·Ë ²¯ ¶ ´¤ ¹Ë ´ ç² Ï´ª³ q Ê· m´¬ Å ·Ê ·Ê¤© n¯ ³ ´¥ ¯ ¥­³¬Ã © Ï´Ë Â ¹Ê¯Å­n n»¯m´  n´Å ©´£­£´¤ ¯ ϴ­§m´ ·Ë m¯ ª¸ «´Â ¹Ë ¯­´Å ·Ê 2 – 4

1

บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

9

1.5.1 ´¥ ³ ¬¶ Å Ã °´¥q ç²Ã ¯¡ q © ¥¢´ ¥³ ¯ ¥² ¬¹Ê¯¬´¥ ¶ ¶ ³§ © ¥ ¥© ­´Ã§²© ¥ ¯ ¥­³¬¬´£´¥ §¹¯ Å n ´ Æ n ³Ë ´¥ ³ ¬¶ Å Ã °´¥q (hard decision) ç² ´¥ ³ ¬¶ Å Ã ¯¡ q (soft decision) £¹Ê¯

´¥ ³ ¬¶ Å Ã °´¥q ¹¯ ´¥­´ m´ ¥²£´ ¯ ¶ n¯£»§­¥¹¯¬³ §³ « q (symbol) ·ÊÆ n

´ © ¥ ¥© ­´­¥¹¯ © ¥ ¯ ¥­³¬ Ä ¤ §§³ q ·ÊÆ n ²Â¥·¤ ©m´ “ m´©¬´¥Ã °´¥q (hard

information)”  m n´© ¥ ¥© ­´Æ n¥³ n¯£»§ ·Ê£· m´Â m´ ³ 0.9 ɯ´ ² ³ ¬¶ Å ©m´ ¶ n¯£»§

·Ê¬m £´ ´ © ¥¢´ ¬m ¹¯ ¶ 1

´¥ ³ ¬¶ Å Ã ¯¡ q ¹¯ ´¥­´ m´ ©´£ m ´Â ¹Ê¯ ¹¯ (reliability) ¯ ¶ n¯£»§­¥¹¯¬³ §³ « q

·ÊÆ n ´ © ¥ ¥© ­´­¥¹¯© ¥ ¯ ¥­³¬Ä ¤¯´ª³¤ n¯£»§ ·Ê© ¥¢´ ¥³ £· ³ Ë ­£ ç² §§³ q Ê·

Æ n ²Â¥·¤ ©m´ “ m´©¬´¥Ã ¯¡ q (soft information)” ³©¯¤m´  m n´© ¥ ¯ ¥­³¬Å­n §§³ q Â É m´©¬´¥Ã ¯¡ q Ê·£· m´£´ Éì ©m´ m´ ¥²£´ ¯ ¶ n¯£»§­¥¹¯¬³ §³ « q Ê·Æ n ´ © ¥ ¯ ¥­³¬ ·Ë£· ©´£ m ´Â ¹Ê¯ ¹¯­¥¹¯ ©´£Â É Æ Æ n Ê · ² » n¯ ¬»

¬Ï´­¥³ ¥² ¬¹Ê¯¬´¥Ã Æ ´¥· ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§ ²©³ ´ “¯³ ¥´¬m© ©¥ ²

Â É Ã §¯ ´¥¶ ¸£ (LLR: log-likelihood ratio)” ³Ê ¹¯ n´ Ï´­ Å­n x {0, 1} Â É ³©Ã ¥ ¬mº£Æ ´¥· ³ ³ Ë m´ LLR ¯ x ¶ ¤´£Ä ¤

p x 1 ¬­ ­­ M x ln p x 0 ®­­

(1.10)

£¹Ê¯ ln(.) ¹¯§¯ ´¥¶ ¸£ ¥¥£ ´ ¶ (natural logarithm) ç² p(x) ¹¯¡³ q ³ ©´£­ ´Ã m ©´£ m ´ ²Â É (pdf: probability density function) ¯ x ¯ ´ ·Ë m´¬³£ »¥ q (absolute value) ¯ M x ¹¯ m´©¬´¥Ã ¯¡ q­¥¹¯ m´ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§ x ç²Â ¥¹Ê¯ ­£´¤ ¯ M x

É ¹¯ m´©¬´¥Ã °´¥q ­¥¹¯ m´ ¥²£´ ¯ ¶ n¯£»§ x ³Ê ¹¯ £ ¦1, if M x p 0 xˆ ¦ ¤ ¦ ¦ ¥0, if M x 0

(1.11)

1.5.2 ¯³ ¥´¬m© ©¥ ²Â É Ã §¯ ´¥¶ ¸£ ¯³ ¥´¬m© ©¥ ²Â É Ã §¯ ´¥¶ ¸£ (LLR) ¹¯Â É Â£ ¥¶ (metric) ­¥¹¯ ³© ·©Ë ³ m´©¬´¥ ·ÊÅ n£´

Å ¯³§ ¯¥¶ ¸£ m´ È ·ÊÅ nÅ ¥² © ´¥ ¯ ¥­³¬Ã © Ï´Ë Â m ¯³§ ¯¥¶ ¸£ BCJR, SOVA, ç²

LDPC Â É n Å ­ ³ ¬¹¯ ·Ë ²Å n¬³ §³ « q M x à m´ LLR ¯ ¶ n¯£»§ x {0, 1} ¸Ê

10

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

8

Log-likelihood ratio (LLR)

6 4 2 0 -2 -4 -6 -8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p(a = +1)

¥» ·Ê 1.8 m´ LLR ¯ ¶ n¯£»§ a £¹Ê¯Â ·¤ ³ ©´£ m ´ ²Â É p(a = +1)

É ¹¯ m´§¯ ´¥¶ ¸£ ¥¥£ ´ ¶ ¯ ª«¬m© ¥²­©m´ ©´£ m ´ ²Â É ¯ ¶ 1 ç² ¶ 0 ´£ ·Ê ¶¤´£Å ¬£ ´¥ (1.10)

¬Ï´­¥³ ¥² ¬¹Ê¯¬´¥ ·ÊÅ n n¯£»§¯¶ º Æ ´¥·Ã  ¶ ³©Ë ³Ê ¹¯ a {–1, 1} m´ LLR

² ¶ ¤´£Ä ¤

p a 1 ¬­ ­­ M a ln p a 1 ®­­

(1.12)

¸Ê ¶ ¤£Å n£´ Å ¯³§ ¯¥¶ ¸£ ´¥ ¯ ¥­³¬ (decoding algorithm)  ¥´²Â ¥¹Ê¯ ­£´¤ ¯ m´ M a

·Ë ¬´£´¥ Ï ´£´Å nÂ É m´ ¥²£´ ¯ ¶ n¯£»§ a (­¥¹¯ m´©¬´¥Ã °´¥q ) Æ n ³ · Å Ï´ ¯

 ·¤© ³ ´ ¯ M a ÉÅ nÂ É ³© ¯ ¸ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§ a (­¥¹¯ m´©¬´¥Ã ¯¡ q)

¥» ·Ê 1.8 ì m´ LLR ¯ ¶ n¯£»§ a £¹Ê¯Â ·¤ ³ ©´£ m ´ ²Â É p(a = +1) Ä ¤ M a £· m´ Â É © £¹Ê¯ p(a = +1) > 0.5 ³Ê ¹¯ ¶ n¯£»§ a £· ©´£ m ´Â ¹Ê¯ ¹¯ ·Ê ²Â É ¶ 1 £´ ©m´ ¶ –1

£´ ©m´ ¶ 1 ¯ ´ ·Ë n´ p(a = +1) = 0.5 É ² Ï´Å­n M a 0 ¸Ê ­£´¤ ©´£©m´ ¶ n¯£»§ a

บทนำ

ç² M a £· m´Â É § £¹Ê¯ p(a = +1) < 0.5 ³Ê ¹¯ ¶ n¯£»§ a £· ©´£ m ´Â ¹Ê¯ ¹¯ ·Ê ²Â É ¶ –1 £·Ä¯ ´¬ ·Ê ²Â É Æ n ³ Ë ¶ 1 ç² ¶ –1 n©¤ ©´£ m ´ ²Â É Â m´ ³

 ¹Ê ¯ ´ p(a = +1) = 1 – p(a = –1) ³ ³ Ë ¬£ ´¥ (1.12) ³ ¥» Å­£mÆ n É

1

บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

11

e

M a

p a 1

(1.13)

1 p a 1

ç² p a 1

p a 1

e

M a

1 e e

1

M a

1 e

M a

1 e

M a

M a

1

M a

1 e

e

e

M a / 2

e

e

M a / 2

e

M a / 2

M a / 2

M a / 2

e

M a / 2

(1.14)

(1.15)

´ ¬£ ´¥ (1.14) ç² (1.15) ¬¥º Æ n©m´¬Ï´­¥³ C {–1, +1} ²Æ n©m´ p a C

CM a / 2

e e

M a / 2

e

M a / 2

(1.16)

1.5.3 n¯£»§Â¯´ q º à ¯¡ q ¯ m¯ ¬³ ´ ¶ ´¥ ´¥² ¬¹Ê¯¬´¥Ã Æ ´¥· £¹Ê¯ ¶ n¯£»§ x {0, 1} » ¬m Æ ¤³ © ¥Â n´ m» (mapper)  ¹Ê¯

à § Å­nÂ É ¶ n¯£»§ u {–1, 1} çn©¬m m´ m¯ ¬³ ´ ·ÊÆ£m£·­ m ©¤ ©´£ Ï´ ¸Ê Ï´Å­n¬³ ´ ·Ê© ¥¢´ ¥³ Æ n¥³ £· m´Â m´ ³ y = u + n £¹Ê¯ n ¹¯¬³ ´ ¥ ©  ´¬q¬· ´©Ã © (AWGN: additive white Gaussian noise) ·Ê£· m´Â §·Ê¤Â m´ ³ ª» ¤qç² ©´£Ã ¥ ¥©  m´ ³ V2

¶ ¤´£¡³ q ³ ©´£­ ´Ã m ©´£ m ´ ²Â É Ã £·Â ¹Ê¯ Æ (conditional probability

density function) p y | x ¹¯¡³ q ³ ©´£­ ´Ã m ©´£ m ´ ²Â É ¯ ³©Ã ¥¬mº£ y £¹Ê¯ Ï´­ m´ x £´Å­n Å ´ §³ ³ n´ Ï´­ m´ y £´Å­n É ²Æ n©m´ p y | x ·ÊÂ É ¡³ q ³ ¯ ³©Ã ¥ x ² » Â¥·¤ ©m´ “¡³ q ³ ©¥ ²Â É (likelihood function)” [4]

Å ´ ¶ ³ ¶ m¯ ·Ê© ¥¢´ ¥³ ²Æ n¥³ n¯£»§ y ©´£ m ´ ²Â É ¯² ¶¥¶¯¯¥¶ (a priori

probability) ¯ x ²£· m´Â m´ ³ p x 1 ç² p x 0 ¯¤m´ Æ¥ É ´£­§³ ´ ·Ê© ¥¢´ ¥³ Æ n¥³ n¯£»§ y ©´£ m ´ ²Â É p x 1 | y ç² p x 0 | y ²Â §·Ê¤ Â É ©´£ m ´ ²Â É ¯²Ä ¬  ¯¥¶¯¯¥¶ (APP: a posteriori probability) ç² ´ ¯  ¬q (Bayes’ rule) Ï´Å­nÆ n©m´ p x i | y p x i ; y / p y

p y | x i p x i / p y

12

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(1.17)

³ ©´£­ ´Ã m ©´£ m ´ ²Â É ¥m©£ (joit pdf) ¥²­©m´ £¹Ê¯ i {0, 1} ç² p a ; b ¹¯¡³ q ³©Ã ¥¬mº£ a ç² b ³ ³ Ë m´ LLR ¯ ¶ n¯£»§ x £¹Ê¯ Ï´­ m´ y £´Å­n ² ¶ ¤´£Ä ¤ p x 1| y ¬­ ­­ M x | y ln p x 0 | y ®­­

(1.18)

´ ¯  ¬q ²Æ n©m´ p x 1| y ¬­ p y | x 1 ¬­ p x 1 ¬­ ­­ ln ­­ ln ­­ ln p x 0 | y ®­­ p y | x 0 ®­­ p x 0 ®­­

(1.19)

Lc y M x

£¹Ê¯ Lc ¹¯ n¯£»§Â¯´ q º à ¯¡ q ¯ m¯ ¬³ ´ ¸Ê ¹¯Â É m´©¬´¥Ã ¯¡ q ·Ê¬¯ §n¯

³ ¶ n¯£»§ x ·ÊÆ n£´ ´ n¯£»§ y ç² M x Â¥·¤ ©m´ “ m´©¬´¥¯² ¶¥¶¯¯¥¶ (a priori information)”

¹¯ m´©¬´¥ ·Ê ·Ê¤© ³ ¶ n¯£»§ x m¯ ·Ê© ¥¢´ ¥³ Æ n¥³ n¯£»§ y Ä ¤Å ¥ · Ê·© ¥¢´ ¥³ Æ£m£·

m´©¬´¥¯² ¶¥¶¯¯¥¶ É ² Ï´­ Å­n M x 0

Ä ¤ ³©Ê Æ m´ Lc Å ¬£ ´¥ (1.19) ²Â¥·¤ ©m´ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ m¯ ¬³ ´ (channel

reliability) ¸Ê ¸Ë ³ §³ « ² ¯ m¯ ¬³ ´ ³©¯¤m´  m Å ¥ · Ê· nk ¹¯¬³ ´ ¥ ©

AWGN É ²Æ n©m´

p y | x 1 ¬­ p y | u 1 ¬­ ­­ w ln ­­ ln p y | x 0 ®­­ p y | u 1 ®­­

2 1 exp 2T 2 y 1

ln 2 1 exp 2T 2 y 1

¬­­­­ 2 y ­

®­­­ T 2

(1.20)

³Ê ¹¯ Lc 2 / T 2

บทนำ

1.5.4 © ¥ ¯ ¥­³¬Ã SISO © ¥ ¯ ¥­³¬Ã SISO (soft-input soft-output) ¹¯© ¥ ¯ ¥­³¬ n¯£»§ ·Ê Ï´ ´ ³ m´©¬´¥

à ¯¡ q Ä ¤ ²¥³ n¯£»§¯¶ º ·ÊÂ É m´©¬´¥Ã ¯¡ q n´£´ ¥²£©§ § ç²Å­n n¯£»§Â¯´ q º Â É m´©¬´¥Ã ¯¡ q

1

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13

nk uk

xk \0,1^

Ma x k

yk

\o1^

Mp x k

xˆk

M xk | y

¥» ·Ê 1.9 ¥² ¬¹Ê¯¬´¥ ¶ ¶ ³§ ·ÊÅ n© ¥ ¯ ¥­³¬Ã SISO

¶ ´¥ ´¥² ¬¹Ê¯¬´¥Å ¥» ·Ê 1.9 £¹Ê¯§Ï´ ³ n¯£»§ xk {0, 1} » ¬m Æ ¤³ © ¥Â n´¥­³¬

(encoder) 粩 ¥Â n´ m» (mapper)  ¹Ê¯Å­nÆ nÂ É §Ï´ ³ n¯£»§ uk {–1, 1} ´ ³ Ë © ¥ ¯ ¥­³¬ à SISO ² Ï´ ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¬³ ´ yk = uk + nk Ä ¤ ·Ê nk ¹¯¬³ ´ ¥ ©

AWGN Ä ¤¯´ª³¤ ©´£ m©¤Â­§¹¯ ´ §Ï´ ³ n¯£»§ Ma x k £¹Ê¯ Ma x k ¹¯ m´ LLR à ¯² ¶¥¶¯¯¥¶

(a priori LLR) ¯ ¶ n¯£»§ xk ³Ê ¹¯ p x k 1 ¬­ ­­ Ma xk ln p x k 0 ®­­

(1.21)

¸Ê ­£´¤ ¸ m´©¬´¥ ·Ê ·Ê¤© ³ ¶ n¯£»§ xk m¯ ·Ê© ¥¢´ ¥³ ²Æ n¥³ §Ï´ ³ n¯£»§ y ­¥¹¯ n¯£»§ yk

³ Ë ­£ ( ³Ê ¹¯Â É ¯¶¬¥² ´ y) Å Ï´ ¯  ·¤© ³ n´© ¥¢´ ¥³ Æ£m£· m´©¬´¥¯² ¶¥¶¯¯¥¶ É ²

Ï´­ Å­n Ma xk 0 ¬Ï´­¥³ º m´ k ¸Ê ­£´¤ ©´£©m´ ¶ n¯£»§ xk º ³©£· ©´£ m ´ ²Â É ·Ê ²

 ¶ ¸Ë  m´ ³

´ ³ Ë © ¥ ¯ ¥­³¬Ã SISO ²Å­n n¯£»§Â¯´ q º Â É m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶

(a posteriori LLR) ¯ ¶ n¯£»§ xk ³Ê ¹¯

p x k 1| y ¬­ ­­ Mp xk ln p x k 0 | y ®­­

(1.22)

Ä ¤ ·Ê m´ ¥²£´ ¯ ¶ n¯£»§ xk ¬´£´¥ ­´Æ n ´ ´¥¬m m´ Mp x k m´  n´Æ ¤³ © ¥ ¥© ­´ · Â¥¶Ê£Â §·Ê¤ (threshold detector) ´£ ©´£¬³£ ³ q ³ ·Ë £ ¦1, if Mp x k p 0 xˆk ¦ ¤ ¦ ¦ ¥0, if Mp x k 0

­£´¤Â­ º

14

¬Ï´­¥³ m´ LLR ¯ ¶ n¯£»§ x ³Ê ¹¯ M x Å ­ ³ ¬¹¯Â§m£ ·Ë ² ¶ ¤´£ ³ ·Ë

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(1.23)

n´ m´ LLR £· ©³ ­n¯¤ (subscript) Â É ´¥´£¶Â ¯¥q a  m Ma x ²­£´¤ ¸ m´ LLR à ¯² ¶¥¶¯¯¥¶ (a priori LLR) ¯ ¶ n¯£»§ x

n´ m´ LLR £· ³©­n¯¤Â É ´¥´£¶Â ¯¥q p  m Mp x ²­£´¤ ¸ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ (a posteriori LLR) ¯ ¶ n¯£»§ x

1.6 ¬¥º n´¤ Å ·ËÆ n¯ ¶ ´¤Ã Ï´§¯ m¯ ¬³ ´ ¯m´ ·ÊÅ nà ¥² ´¥ ³ ¸  ¶ ãm­§É ( ³ Ë Ã Ï´§¯ m¯ ¬³ ´ ¬£¹¯ ¥¶ Å ¥» ·Ê 1.2 ç²Ã Ï´§¯ m¯ ¬³ ´ ¯º £ ¶Å ¥» ·Ê 1.6)  ¹Ê¯Å­n n»¯m´ ¬´£´¥ Ï ´Ã Ï´§¯ ·ËÆ Å nÅ ´¥©¶Â ¥´²­q¥² ´¥ ¥²£©§¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q

 ¹Ê ¯ ´ °´¥q ¶¬ qÆ ¥¡q ¥mº Å­£mÈ ·Ê£· Ï´­ m ´¤Å n¯ §´ ²Å n ¶ ´¥ ¯ ¥­³¬Ã

© Ï´Ë (iterative decoding)  ¥´²¬´£´¥ m©¤Â ¶Ê£¬£¥¥ ² ¯ ¥² Æ n ·¤Ê¶ ¸Ë ³ ³ Ë Å ·Ë

¸ Æ n¯ ¶ ´¤Ã © ¶ ç² ¹Ë ´ ¯  ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë ¥©£ ³ Ë ©´£­£´¤ ¯ SISO ©´£ m ´ ²Â É ¯² ¶¥¶¯¯¥¶ ©´£ m ´ ²Â É ¯²Ä ¬Â ¯¥¶¯¯¥¶ m´©¬´¥Ã ¯¡ q 粯³ ¥´¬m© ©¥ ²Â É Ã §¯ ´¥¶ ¸£ (LLR) Â É n  ¹Ê¯Â ¥·¤£ ©´£ ¥n¯£ ¯ n»¯m´ m¯ ·Ê ²ª¸ «´­§³ ´¥

Ï´ ´ ¯ © ¥ ¥© ­´Ã§²© ¥ ¯ ¥­³¬Ã SISO ¸Ê ²¯ ¶ ´¤ m¯Æ Å ·Ê 2 – 4

1.7 Ã ¸ ­³ n´¤ 1.

¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ¥² ´¥ ³ Â É n¯£»§ ¶ ¶ ³§Å °´¥q ¶¬ qÆ ¥¡q Å ¥» ·Ê 1.1

2.

Å nÄ ¥Ã ¥£ SCILAB ©´ ¥» m¯Æ ·Ë (http://home.npru.ac.th/piya/webscilab ­¥¹¯ http://www.scilab.org)

2.1) ¬³ ´ ³§¬q §·Ê¤ ¬ ´ ² m´ ND m´ È ´£¥» ·Ê 1.3 2.2) § ¯ ¬ ¯ Æ ¶ m´ ND m´ È ´£¥» ·Ê 1.4 ì ©m´ § ´¥Ã § ¡»Â¥·¤¥q ¯ § ¯ ¬ ¯ Æ ¶ m(t) Å ¬£ ´¥ (1.6) ¯ ¥² ´¥ ³ ¸ à à © ¯ £· m´Â m´ ³

บทนำ

3.

M 8 exp \ Q 8 ND^ 1 exp \ j 2Q8^

ç² ¯ ¥² ´¥ ³ ¸ à à © ³ Ë £· m´Â m´ ³

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บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

15

M 8

¦£ Q 282 ND 2 ¦²¦ T exp ¦¤ » 1 exp \ j 2Q8^

¦¦ jQ8 ln 16 ¦¼¦ ¥

£¹Ê¯ exp{.} ¹¯¡³ q ³ § · Ë Ï´§³ , : = fT ¹¯ ©´£ ·Êà ¯¥q£¯§Æ§ q (normalized frequency), f ¹¯ ©´£ ·Ê£·­ m ©¤Â É Â°¶¥ q, | x | ¹¯ m´¬³£ »¥ q ¯ x, ç² j 1

4.

´ § ´¥Ã § ¡»Â¥·¤¥q ¯ § ¯ ¬ ¯ Æ ¶ Å n¯ 3 ©´ ¥» § ¯ ¬ ¯  ¶ ©´£ ·Ê ¯

5.

¯ ¶ ´¤ ©´£Ã m´ ¥²­©m´ à ϴ§¯ m¯ ¬³ ´ ¬£¹¯ ¥¶ Å ¥» ·Ê 1.2 ç²Ã Ï´§¯

6.

¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ¥² ´¥ ¥²£©§ §¬³ ´ à © Ï´Ë ¯ °´¥q ¶¬ qÆ ¥¡q Å

m¯ ¬³ ´ m´ ND m´ È Å ¥» ·Ê 1.5 Ä ¤Å nÄ ¥Ã ¥£ SCILAB m¯ ¬³ ´ ¯º £ ¶Å ¥» ·Ê 1.6

¥» ·Ê 1.7

7.

¯ ¶ ´¤ ©´£­£´¤ ¯ m´©¬´¥Ã ¯¡ q (soft information)

8.

¯ ¶ ´¤ ©´£­£´¤ ¯ ¯³ ¥´¬m© ©¥ ²Â É Ã §¯ ´¥¶ ¸£ (LLR: log-likelihood ratio)

9.

¯ ¶ ´¤ ©´£­£´¤ ¯ m´ LLR à ¯² ¶¥¶¯¯¥¶ ç² m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶

10. ¯ ¶ ´¤ ©´£­£´¤ ¯ © ¥ ¥© ­´Ã SISO 粩 ¥ ¯ ¥­³¬Ã SISO

16

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

·Ê 2 ¥­³¬Â ¯¥qÄ Å ³ º ³ ¥­³¬Ã nÆ n¯ ¶ §´ [2 – 5] £·Å­n§¹¯ Å n ´ Ï´ © £´ ´£§³ « ² ´¥Å n ´ ¯

à m§² ´ ¥²¤º q Ä ¤ ³©Ê Æ ´ ¥²¤º q Ê · n¯ ´¥ ©´£¬´£´¥ Å ´¥Ã nÆ n¯ ¶ §´ ¬» É ² n¯ Å n© ¥Â n´¥­³¬Ã§² ¯ ¥­³¬ ·Ê£· ©´£ ³ n¯ ¬» £´  m ³ ©¶ · ´¥Ã n ³ ­´¯¤m´ m´¤ É ¹¯

´¥Å n ´¥Â n´¥­³¬Ã m¯ ³ (concatenated coding) ¸Ê Â É ´¥Â n´¥­³¬ n¯£»§Ä ¤Å n© ¥Â n´¥­³¬

£´ ©m´­ ¸Ê © ¥£´ m¯ ³ à ¯ º ¥£­¥¹¯Ã ´ Ä ¤¯´ª³¤ ©´£ m©¤Â­§¹¯ ¯ © ¥¯¶  ¯¥q §·¡Â©¯¥q (interleaver) ´ ³ Ë n¯£»§ ·Ê »  n´¥­³¬ É ² » Ï´ ´¥ ¯ ¥­³¬ n©¤© ¥ ¯ ¥­³¬Ã m§²

³© ¸ ãn©m´ §§³ q ÊÆ· n ´ ©¶ · ´¥ ·Ë ¹¯©m´Â É Ã Â­£´² ·Ê¬º à ¥¯ (sub-optimal) à m©¶ · ´¥

·Ë ² ¥² · ¥² ¯£¥²­©m´ ©´£¬´£´¥ Å ´¥Ã nÆ n¯ ¶ §´ ç² ©´£ ³ n¯ ¯ ¥² © ´¥

 n´¥­³¬Ã§² ¯ ¥­³¬

 ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë (iterative decoding) [2, 3] ¹¯Â É Â ¶ ·Ê¬´£´¥

m©¤§ ¯³ ¥´ n¯ ¶ §´ ¯ ¶ (BER: bit-error rate) ¯ ¥² Å­n n¯¤§ ©m´Â ¶£Æ n ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¥­³¬Â ¯¥qÄ (turbo code) [3] ¹¯Â É ³©¯¤m´ ¯ ´¥ ¯ ¥­³¬Ã © Ï´Ë ¸Ê Å ³ º ³

Æ n£· ´¥ Ï ´£´Å nÅ ­§´¤ ´ ¥²¤º q Æ nà m ¥² Ä ¥ª³ q §¹Ê¯ ·Ê ç²¥² ¬¹Ê¯¬´¥ m´ ´©Â ·¤£ Â É n ¯ ´ ·Ë ­§³ ´¥Â ¯¥qÄ (turbo principle) ·ÊÅ nÅ ´¥ ¯ ¥­³¬ n¯£»§Ã  ¯¥qÄ ¤³

¬´£´¥ Ï ´£´ ¥²¤º qÅ n ³ ¥² © ´¥¯· ©¯Æ§Â ³ (equalization) Æ n Ä ¤ ²Â¥·¤  ¶ ·Ë ©m´ “¯· ©¯Æ§Â ³ à  ¯¥qÄ (turbo equalization)” [21] ¸Ê ¹¯Â É ¥² © ´¥ ¯ ¥­³¬Ã Å ¯ · ·ÊÆ£mÆ nÅ n ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë

·Ë ²Â¥¶Ê£ n ¯ ¶ ´¤¥­³¬ ¯ Ä©§» ³ 粯³§ ¯¥¶ ¸£ BCJR [18] ¸Ê ¹¯Â É ¬m© ¬Ï´ ³

¯ ¥­³¬Â ¯¥qÄ Â ¹Ê¯Å­n n»¯m´  n´Å  ¶ ´¥Â n´¥­³¬Ã§² ´¥ ¯ ¥­³¬Ã © Ï´Ë ·ÊÅ nÅ ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q

บทนำ รหัสเทอรโบ

© Ï´Ë ·ÊÆ n Ï´£´Å n ¥¶ Å °´¥q ¶¬ qÆ ¥¡q ¥mº Å­£mÈ Ã§n© [6] ¸Ê £·¬£¥¥ ² · ©m´°´¥q ¶¬ qÆ ¥¡q

21

บทที่ บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

17

2.1 ¥­³¬ ¯ Ä©§» ³ ¥­³¬Ã nÆ n¯ ¶ §´ ­¥¹¯¯´ Â¥·¤ ©m´ ¥­³¬Ã nÆ n¯ ¶ §´ à n´ ­ n ´ (FEC: forward error-

correction code) ¶ ¤£ Ï ´£´Å nÅ ³ ´¥ ³ ¬³ ´ ¥ © ç² n¯ ¶ §´ ·Ê ¶ ´ m¯ ¬³ ´ Ä ¤ ³©Ê Æ ¥­³¬Ã nÆ n¯ ¶ §´ ¬´£´¥ à m ¯¯ Æ nÂ É ¬¯ à ¹¯ ¥­³¬ §É¯ (block code) ç² ¥­³¬ ¯ Ä©§» ³ (convolutional code) [2] ¯ ´ ·Ë ¤³ £·¥­³¬ ECC à ŭ£m Ê·¯´ª³¤Â ¶

´¥ ¯ ¥­³¬Ã © Ï´Ë Â m ¥­³¬Â ¯¥qÄ [3] ç²¥­³¬ LDPC [17] Â É n ¸Ê £·¬£¥¥ ²Â n´

Å §n ©´£ º m¯ ¬³ ´ ¯ à ¯ 4 (Shannon’s channel capacity) £´ ©m´¥­³¬ ¯ Ä©§» ³ Å ­³© n¯ ·Ë ²¬¥º ­§³ ´¥ Ï´ ´ ¯ ¥­³¬ ¯ Ä©§» ³  ¥´²Â É ¶ Ë ¬m© ·Ê¬Ï´ ³ ¯ ¥­³¬Â ¯¥qÄ ¸Ê ² §m´© m¯Æ Å ­³© n¯ ·Ê 2.3

2.1.1 ´¥Â n´¥­³¬ © ¥Â n´¥­³¬ ¯ Ä©§» ³ (convolutional encoder) ²Å nÂ¥ ¶¬Â ¯¥qà §¹Ê¯ (shift register) ç² © ¥ © à £¯ ºÄ§¬¯ 5 (modulo-2 adder) Å ´¥Â n´¥­³¬ n¯£»§ Ä ¤ ² Ï´ ´¥Â n´¥­³¬§Ï´ ³

n¯£»§¯¶ º (input data sequence) ­ ¸Ê º ç²Å­n§Ï´ ³ n¯£»§Â¯´ q º Ï´ © £´ ©m´­¥¹¯Â m´ ³

­ ¸Ê º Ä ¤ ·Ê n´© ¥Â n´¥­³¬ ¯ Ä©§» ³  n´¥­³¬ n¯£»§¯¶ º 1 ¶ çn© Ï´Å­n ¶ n¯£»§Â¯´ q º

Ï´ © n ¶ ì ©m´© ¥Â n´¥­³¬ ¯ Ä©§» ³ ·Ë £·¯³ ¥´¥­³¬ (code rate)  m´ ³ R 1/ n ¥» ·Ê

2.1 ì ³©¯¤m´ © ¥Â n´¥­³¬ ¯ Ä©§» ³ ·Ê£·¯³ ¥´¥­³¬ R = 1/2 £¹Ê¯ D ¹¯ ³© Ï´Â ¶ ´¥­ m © ©§´­ ¸Ê ­ m ©¤ (unit delay operator) ¸Ê Å nà ¥ ¶¬Â ¯¥qà §¹Ê¯ Å ´ ¶ ³ ¶© ¥Â n´¥­³¬

¯ Ä©§» ³ ²Â ·¤ à n©¤ ­º ´£ ³© Ï´Â ¶ (generator polynomial) ¸Ê £·¥» ¬£ ´¥ ¹¯ [1] N

G D gi D i i 0

(2.1)

£¹Ê¯ P ¹¯ Ï´ © ­ m ©¤ ©´£ Ï´ ¯ © ¥Â n´¥­³¬ ¯ Ä©§» ³ (­¥¹¯ Ï´ © Â¥ ¶¬Â ¯¥qà §¹Ê¯ )

ç² gi = 1 n´ ¶ n¯£»§¯¶ º ·Ê » ­ m © ©§´Æ i ­ m ©¤ £· § m¯ ´¥Â ¶ ¯ ¶ n¯£»§Â¯´ q º

©§´ ³ º ³ ³©¯¤m´  m © ¥Â n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.1 ( ) £· ­º ´£ ³© Ï´Â ¶ ¹¯ G D ¡¢G1 D , G2 D ¯°± ¡1 D , 1 D 2 ¯° ¢ ±

4 5

18

»¥´¤§²Â¯·¤ Â¥¹Ê¯ ©´£ º m¯ ¬³ ´ (channel capacity) Æ nÅ ­³© n¯ ·Ê 5.1.3 ¯ [1] n´Å­n ¹¯ ³© Ï´Â ¶ ´¥ © à £¯ ºÄ§¬¯ ³ ³ Ë 0 0 = 0, 0 1 = 1, 1 0 = 1, ç² 1 1 = 0

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(2.2)

yk1 xk yk2

¥» ·Ê 2.1 ( ) © ¥Â n´¥­³¬ ¯ Ä©§» ³ , ( ) © ¥Â n´¥­³¬ ¯ Ä©§» ³ à £·¥² , ç² ( ) © ¥Â n´¥­³¬ ¯ Ä©§» ³ à £·¥² ©·¤  ¶

£¹Ê¯ ¹¯ ³© Ï´Â ¶ ´¥ © à £¯ ºÄ§¬¯ , G1(D) ¹¯ ­º ´£ ³© Ï´Â ¶ ¯ n¯£»§Â¯´ q º yk1 ,

G2(D) ¹¯ ­º ´£ ³© Ï´Â ¶ ¯ n¯£»§Â¯´ q º yk2 , ç²£·­ m ©¤ ©´£ Ï´ P = 2 ­ m ©¤ ¯ ´ ·Ë © ¥Â n´¥­³¬ ¯ Ä©§» ³ à £·¥² (systematic convolutional encoder)

¹¯© ¥Â n´¥­³¬ ¯ Ä©§» ³ ·Ê Ï´Å­n n¯£»§Â¯´ q º ­ ¸Ê º £· m´Â m´ ³ n¯£»§¯¶ º ´£ ·Êì Å

¥» ·Ê 2.1 ( ) ¸Ê £· ­º ´£ ³© Ï´Â ¶ ¹¯ ¡1, 1 D 2 ¯° ¬Ï´­¥³ © ¥Â n´¥­³¬ ¯ Ä©§» ³ à £·¥² ¢ ± ·Ê£· ´¥ n ¯ §³ n©¤ ²Â¥·¤ ©m´© ¥Â n´¥­³¬ ¯ Ä©§» ³ à £·¥² ©·¤  ¶ (recursive systematic convolutional encoder) ´£¥» ·Ê 2.1 ( ) ¸Ê £· ­º ´£ ³© Ï´Â ¶ ¹¯ ¡1, 1/ 1 D 2 ¯° Ä ¤ ³Ê©Æ ¢ ± © ¥Â n´¥­³¬ ¯ Ä©§» ³ à £·¥² ©·¤  ¶ ²Â É ·Ê ¶¤£Å n ´ £´ ©m´© ¥Â n´¥­³¬ ¯ Ä©§» ³ à ¯¹Ê È [2]

Ä ¤ ³Ê©Æ ´¥©¶Â ¥´²­q¥­³¬ ¯ Ä©§» ³ ²¯´ª³¤Â ¥¹Ê¯ ¬ ´ ² Ï´ ³ (FSM: finite state

machine) ¸Ê Â É Ã Ï´§¯ ·Êì Å­nÂ­É ¸ ´¥Â §·Ê¤ à § ¯ n¯£»§¯¶ º , ¬ ´ ²Â¥¶Ê£ n

­³© n¯ ·Ê 4.3.1 ¯ [10]) ¥» ·Ê 2.2 ( n´¤) ì  ¥¹Ê¯ ¬ ´ ² Ï´ ³ ¯ © ¥Â n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.1 ( ) ¸Ê £· ³ Ë ­£ 2P = 4 ¬ ´ ² ¹¯ 00, 01, 10 ç² 11 Ä ¤ ·Ê¬n §» ª¥ ²Ã¬

รหัสเทอรโบ

(start state), ¬ ´ ² m¯Æ (next state), ç² n¯£»§Â¯´ q º ¯ ¥² (ª¸ «´¥´¤§²Â¯·¤ Æ nÅ

¬n ´ ´¥Â §·Ê¤ ¬ ´ ² ç² m´ x / y 1y 2 ·Ê¯¤m» ¶ ³ ¬n §» ª¥ ²Å nà m´ n¯£»§¯¶ º ¶ x

ç² n¯£»§Â¯´ q º ¶ y1 ç² y2 ¯ ´ ·Ë à ¢´  ¥§§¶¬ (trellis diagram) ¸Ê Å nì ´¥

 §·Ê¤ ¬ ´ ²Å à m§² m© ©§´ ɬ´£´¥ Å n¯ ¶ ´¤ ´¥ Ï´ ´ ¯ ¥­³¬ ¯ Ä©§» ³ Æ n m ³ ¥» ·Ê 2.2 ( ©´) ì à ¢´  ¥§§¶¬ ¯ © ¥Â n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.1 ( ) ³Ê ¹¯Ã ¢´

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

2

บทที่

19

¥» ·Ê 2.2 à ¢´  ¥¹Ê¯ ¬ ´ ² Ï´ ³ ç²Ã ¢´  ¥§§¶¬ ¯ ¥» ·Ê 2.1 ( )

 ¥§§¶¬Å ¥²¤² ·Ê k ²Ã¬ ´¥Â §·Ê¤ ¬ ´ ² ·ÊÂ É Æ Æ n ³ Ë ­£ ¯ © ¥Â n´¥­³¬ ´ ¬ ´ ²­ ¸Ê ©§´ k Æ ¤³ ¯· ¬ ´ ²­ ¸Ê ©§´ k + 1 Ä ¤ m´ ·Ê¯¤m» ¶ ³ ¬n §» ª¥ É ¹¯ m´ x / y 1y 2 ·Ê¯¤m»

Å Â ¥¹Ê¯ ¬ ´ ² Ï´ ³ ³Ê ¯  ¹Ê ¯ ´ ¬n ´ (path) ·Ê ¶ Æ ´£Ã ¢´  ¥§§¶¬ ²­£´¤ ¸ º ¯ ¬n ¬´ ´ (branch) ·Ê ¥² ¯ n©¤­ ¸Ê ¬n ¬´ ´ m¯­ ¸Ê ¥²¤² ³ ³ Ë Ï´¥­³¬ (codeword)

º Ï´ (­¥¹¯ n¯£»§Â¯´ q º ¯ © ¥Â n´¥­³¬ ¯ Ä©§» ³ ) ² n¯ ¬¯ §n¯ ³ ¬n ´ ·ÊÂ É Æ n ·¤

­ ¸Ê  ·¤© (unique path) Å Ã ¢´  ¥§§¶¬ ( »¥» ·Ê 2.5) ³©¯¤m´ ·Ê 2.1 ì ³ Ë ¯ ´¥Â n´¥­³¬ ¯ © ¥  n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.1 ( ) £¹Ê¯ ¶ n¯£»§ ¯¶ º ¹¯ {x0, x1, x2, x3} = {1 0 1 1}

©¶ · Ï´

¥» ·Ê 2.1 ( ) ì Å­£mÆ n ´£¥» n´ ©´£¹¯

¸Ê £¹Ê¯ Ï ´ ¶ n¯£»§ {xk} £´Â n´¥­³¬ n©¤© ¥Â n´¥­³¬

Y1 X

D

S1

D

S2 Y2

¯ Ä©§» ³ ²£· ³ Ë ¯ ´¥ Ï´ ´ ³ ·Ë ³ Ë ·Ê­ ¸Ê

Ï´­ Å­n¬ ´ ² ¯ Â¥ ¶¬Â ¯¥qà §¹Ê¯ ³ Ë ­£ ³Ê ¹¯ S1 ç² S2 £· m´Â É 0

( Ï´Å­nÂ É ¬ ´ ² 00) Ä ¤ ³ Ë ¯ ·Ë Â É Â ·¤ ´¥Â ¥·¤£ ©´£ ¥n¯£ ¯ © ¥Â n´

¥­³¬Ã§²¤³ Æ£m£· ´¥ n ¯ ¶ n¯£»§Â n´Æ

20

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

Â¥¶Ê£ n ¯ ¶ Ã¥ ¸Ê £· m´Â É 1 ( ³Ê ¹¯ x0 = 1)  n´¬m»© ¥ É Ï´Å­n m´ Y1 = X S1

³ Ë ·Ê¬¯

= 1 0 = 1 ç² Y2 = X S2 = 1 0 = 1 ¸Ê ¹¯ n¯£»§Â¯´ q º ·ÊÆ n ´ ´¥Â n´¥­³¬ ¯ ¶ Ã¥ ³Ê ¯

³ Ë ·Ê¬´£

Â¥¶Ê£ n ¯ ¶ ·Ê¬¯ ¸Ê £· m´Â É 0  n´¬m»© ¥ m´ m´ È Å © ¥ É ²Â§¹Ê¯ Æ ­ ¸Ê ¶

³ Ë ­£ ( ©§´ ·Ë S1 = 1 ç² S2 = 0) Ï´Å­n m´ Y1 = X S1 = 0 1 = 1

ç² Y2 = X S2 = 0 0 = 0 ¸Ê ¹¯ § ·ÊÆ n ´ ´¥Â n´¥­³¬ ¯ ¶ ·Ê¬¯ ³ Ë ·Ê¬Ê·

Â¥¶Ê£ n ¯ ¶ ·Ê¬´£ ¸Ê £· m´Â É 1  n´¬m»© ¥ m´ m´ È Å © ¥ É ²Â§¹Ê¯ Æ ­ ¸Ê ¶

³ Ë ­£ ( ©§´ ·Ë S1 = 0 ç² S2 = 1) Ï´Å­n m´ Y1 = X S1 = 1 0 = 1

ç² Y2 = X S2 = 1 1 = 0 ¸Ê ¹¯ § ·ÊÆ n ´ ´¥Â n´¥­³¬ ¯ ¶ ·Ê¬´£ ³ Ë ·Ê­n´

Â¥¶Ê£ n ¯ ¶ ·Ê¬Ê· ʸ £· m´Â É 1  n´¬m»© ¥ m´ m´ È Å © ¥ É ²Â§¹Ê¯ Æ ­ ¸Ê ¶ ³ Ë ­£ ( ©§´ ·Ë S1 = 1 ç² S2 = 0) Ï´Å­n m´ Y1 = X S1 = 1 1 = 0 ç² Y2

= X S2 = 1 0 = 1 ¸Ê ¹¯ § ·ÊÆ n ´ ´¥Â n´¥­³¬ ¯ ¶ ·Ê¬Ê· ³ Ë ·Ê­

¬³  ©m´¬ ´ ² ¯ © ¥Â n´¥­³¬ ¯ Ä©§» ³ Æ£mÆ n §³ Æ ¬m»¬ ´ ²Â¥¶Ê£ n ·Ê É

ª» ¤q­£ ( ¯ ·Ë ¯¤m»Å ¬ ´ ² 11) n©¤Â­ º ·Ë ¸ n¯ £· ´¥Â ¥·¤£ ¶ ­´ (tail

bit) ·Ê­£´²¬£¯· 2 ¶  ¹Ê¯ ¥³ © ¥Å­n §³ Æ ¬m»¬ ´ ² ·Êª» ¤q ³ Ë ­£ ¥² ©

´¥Â n´¥­³¬ ¸ ²Â¬¥É ¬£ »¥ q ³ Ë ¬º n´¤

´¥Â§¹¯ m´ ¯ ¶ ­´ £·­§³ ´¥ m´¤È ¹¯Å­n ¶ ´¥ ´ »©m´ ¶ n¯£»§Å ·Ê£· § Ï´Å­n

m´Å Â¥ ¶¬Â ¯¥qà §¹Ê¯ Â É ª» ¤q ³ Ë ­£ ¸Ê Å ·Ê ·Ë ²Æ n©m´Å­n n¯ ¶ 0 ¬¯ ¶

 n´Æ Å © ¥ É ² Ï´Å­n© ¥Â n´¥­³¬ §³ Æ ¬m»¬ ´ ² 00 ¯· ¥³ Ë ¸Ê ¹¯©m´¬¶ Ë ¬º

¥² © ´¥Â n´¥­³¬ Ä ¤ ¶ ­´ ³©Ã¥ ²Å­n n¯£»§Â¯´ q º Â É Y1 = 1 ç² Y2

= 1 Å ² ·Ê ¶ ­´ ³© ·Ê¬¯ ²Å­n n¯£»§Â¯´ q º Â É Y1 = 0 ç² Y2 = 1

³©¯¤m´ ´¥Â n´¥­³¬ ·ÊÆ n¯ ¶ ´¤£´ ·Ë ì Å ¥» ·Ê 2.3 ¸Ê n´ Ï ´£´Ã¬ Å ¥» ¯ à ¢´ ´¥Â §·Ê¤ ¬ ´ ² É ²£·§³ « ² ´£¥» ·Ê 2.4 ­¥¹¯ n´ Ï ´£´Ã¬ Å ¥» ¯ à ¢´  ¥§§¶¬ É ²£·§³ « ²

รหัสเทอรโบ

´£¥» ·Ê 2.5 ¸Ê ²Â­É Æ n©m´¥» ·Ê 2.3 – 2.5 Å­n §§³ q m´ ³

¯ ´ ·Ë ´¥Â n´¥­³¬ ¯ Ä©§» ³ ¤³ ¬´£´¥ Ï´Æ nÄ ¤Å n ´¥Ã § D (D transform) [1]

 m ³ ³Ê ¹¯ n¯£»§Â¯´ q º ·ÊÆ n ´ © ¥Â n´¥­³¬ ¯ Ä©§» ³ ²£· m´Â m´ ³ Yi D Gi D X D

(2.3)

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

2

บทที่

21

¥» ·Ê 2.3 ³ Ë ¯ ´¥Â n´¥­³¬ ¯ Ä©§» ³ Å ³©¯¤m´ ·Ê 2.1

xk / yk1yk2

¥» ·Ê 2.4 à ¢´ ´¥Â §·Ê¤ ¬ ´ ²Å ³©¯¤m´ ·Ê 2.1

£¹Ê¯ Yi D

yD k

i k

k

¹¯ § ´¥Ã § D ¯ n¯£»§Â¯´ q º yki ¬Ï´­¥³ i \1, 2^ , Gi(D)

¹¯ ­º ´£ ³© Ï´Â ¶ ¯ n¯£»§Â¯´ q º yki , ç² X D k xk D k ¹¯ § ´¥Ã § D ¯ n¯£»§¯¶ º  m ´ ³©¯¤m´ ·Ê 2.1 (¥» ·Ê 2.1 ( )) ²Æ n©m´ X D 1 D 2 D 3 ç² Gi D

Â É Æ ´£¬£ ´¥ (2.2) ³ ³ Ë n¯£»§Â¯´ q º ·ÊÆ n ´ ´¥Â n´¥­³¬ ³ Ë ¬¯ º \yk1 , yk2 ^ £· m´Â m´ ³

22

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 2.5 à ¢´  ¥§§¶¬Å ³©¯¤m´ ·Ê 2.1 (ì ¬n ´ ·ÊÂ É Æ Æ n ·¤ ­ ¸Ê  ·¤© ¯ Ï´¥­³¬)

Y1 D G1 D X D 1 D 1 D 2 D 3

1 D 2 D 3 D D 3 D 4

1 D D 2 D 4

Y2 D G2 D X D 1 D 2 1 D 2 D 3

1 D 2 D 3 D 2 D 4 D 5

1 D 3 D 4 D 5

³Ê ¹¯ \y 10 , y11 , y12 , y31 , y 14 , y51 ^ \1 1 1 0 1 0^ ç² \y 02 , y12 , y 22 , y32 , y 42 , y52 ^ \1 0 0 1 1 1^ ¸Ê ¥ ³ n¯£»§Â¯´ q º ·ÊÆ n ´£¥» ·Ê 2.3 – 2.5 ³©¯¤m´ ·Ê 2.2 ¶ ´¥ ´© ¥Â n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.6 ¸Ê £· ­º ´£ ³© Ï´Â ¶ Å ¥» ¯ §

Â¥·¤ ©m´ ­º ´£ n ¯ §³ (feedback polynomial) ç² g2 Â¥·¤ ©m´ ­º ´£ n ¯ n´ ­ n ´ (feed-

forward polynomial) ­¥¹¯Å ­ ³ ¬¹¯ ´ §m£¯´ ì ­º ´£ ³© Ï´Â ¶ Å ¥» ¯ ª«¬m© Å Ä Â£ D ¹¯

g 2 D

g1 D

1 D 3 1 D D 2 D 3

ì à ¢´  ¥¹Ê¯ ¬ ´ ² Ï´ ³ ¥n¯£ ³ Ë Â n´¥­³¬ ¶ n¯£»§

11011100 ( ¶ n¯£»§ n´ n´¤¬º ¹¯ n¯£»§ ³©Ã¥ ·Ê ² »  n´¥­³¬) ©¶ · Ï´

à ¢´  ¥¹Ê¯ ¬ ´ ² Ï´ ³ ¯ © ¥Â n´¥­³¬ ¯ Ä©§» ³ ·Ëì Å ¥» ·Ê 2.7 ¬Ï´­¥³ ´¥

 n´¥­³¬ ¶ n¯£»§ 11011100 Å­n Ï´ ´£ ³ Ë ¯ m´ È §n´¤ ³ ³©¯¤m´ ·Ê 2.1 ³Ê ¹¯Â¥¶Ê£ n ² เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

รหัสเทอรโบ

´ à ¹¯ (g1, g2) = (17, 11) ­¥¹¯£· m´Â m´ ³ (001111, 001001) Š§ ´ ¬¯ Ä ¤ ·Ê g1

2

บทที่

23

g 2 D

g1 D

1 D 3 1 D D 2 D 3

¥» ·Ê 2.6 © ¥Â n´¥­³¬ ¯ Ä©§» ³ ·Ê£· ­º ´£ ³© Ï´Â ¶ Å ¥» ¯ § ´ à ¹¯ (g1, g2) = (17, 11)

100 0/0 0/0

001

000

0/1

1/0

1/1

010

1/1

1/0

0/1

1/0

0/1

0/1

1/1

101

1/0

110

111 1/1

011

0/0 0/0 ¶ n¯£»§¯¶ º / ¶ n¯£»§Â¯´ q º

à ¶ n¯£»§¯¶ º ·£ Ê · m´Â É 0 à ¶ n¯£»§¯¶ º ·£ Ê · m´Â É 1

¥» ·Ê 2.7 à ¢´  ¥¹Ê¯ ¬ ´ ² Ï´ ³ (FSM) ¯ © ¥Â n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.6

Ï´­ Å­n¬ ´ ² ¯ Â¥ ¶¬Â ¯¥qà §¹Ê¯ ³ Ë ­£ £· m´Â É 0 ´ ³ Ë É Ï´ ´¥ n ¯ n¯£»§Â n´Æ Å

© ¥ ·§² ¶ çn© Ï´ © ­´ n¯£»§Â¯´ q º ¯ © ¥Â n´¥­³¬ ·§² ³© £¹Ê¯ n ¯ ¶ n¯£»§¯¶ º  n´ Æ Å © ¥Â n´¥­³¬ ¥ çn© ÉÅ­n n¯ ¶ ­´ ¯· Ï´ © ­ ¸Ê ¥² ³Ê Ï´Å­nÂ¥ ¶¬Â ¯¥qà §¹Ê¯

³ Ë ­£ £· m´Â É 0 ­£¹¯  ¶£

­´ Ï´ » n¯ ²Æ n©m´ ¶ ­´ ·Ê n¯ n ¯  n´Æ Å © ¥Â n´¥­³¬ ¹¯ 111 ç² §§³ q Ê·Æ n

´ ´¥Â n´¥­³¬ ¹¯ 10101110001

24

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

xk

z k \z 00z 10 , z10z11 ,..., z k0z k1 ^

xk

\z z ^ \x y ^ 0 1 k k

yk

k k

x k / x k yk

xk 0

xk 1

¥» ·Ê 2.8 ( ) © ¥Â n´¥­³¬ ¯ Ä©§» ³ ç² ( ) à ¢´  ¥§§¶¬

2.1.2 ´¥ ¯ ¥­³¬ Å ´ ¶ ³ ¶ n¯£»§ ·Ê »  n´¥­³¬ n©¤¥­³¬ ¯ Ä©§» ³ ¬´£´¥ Ï´ ´¥ ¯ ¥­³¬ n¯£»§Æ n n©¤© ¥

¯ ¥­³¬ ·Ê¬¥n´ ´ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [13] ­¥¹¯ ·ÊÂ¥·¤ ©m´© ¥ ¥© ­´©·Â ¯¥q ¶ Å ·Ê ·Ë ²Ã¬ ³©¯¤m´ ´¥ ¯ ¥­³¬ n¯£»§ ·Ê »  n´¥­³¬ n©¤¥­³¬ ¯ Ä©§» ³ ³ m¯Æ ·Ë

³©¯¤m´ ·Ê 2.3 ¶ ´¥ ´© ¥Â n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.8 ( ) ¸Ê £·Ã ¢´  ¥§§¶¬ ´£¥» ·Ê

2.8 ( ) n´¬££º ¶©m´§Ï´ ³ n¯£»§ zk ¹¯¬¶Ê ·Ê© ¥ ¯ ¥­³¬ n¯ ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¥­³¬§Ï´ ³ ©¶ · Ï´

Ï´­ Å­n (u, q) à ´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² u Æ ¬ ´ ² q ç²Â£ ¥¶ ¬´ ´

(branch metric) ¥²¤² ·Ê k ¶ ¤´£Ä ¤

2

Sk u ,q z k0 x k u , q z k1 y k u ,q

รหัสเทอรโบ

n¯£»§ zk = {11 01 10 11 00}

2

Ä ¤ ·Ê x k u , q ç² y k u , q ¹¯ ¶ n¯£»§ xk ç² yk ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² (u, q) ¯ ´ ·Ë Ï´­ Å­n£ ¥¶ ¬n ´ (path metric) ¬ ´ ² q ·Ê©§´ k + 1 ² ¶ ¤´£Ä ¤

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

2

บทที่

25

0

2

2

0

2

2

2

1

0

2

1

0

0

\z k ^

11

\xˆk ^

1

0

0

01

2

0

10

0

2

1

11 1

0 ¶ ­´

00 0

¥» ·Ê 2.9 à ¢´  ¥§§¶¬Ã¬ ´¥ ´¥ ¯ ¥­³¬ n¯£»§ zk = {11 01 10 11 00}

'k 1 q min \'k u Sk u , q ^ u

³ ³ Ë ³ Ë ¯ ´¥ ¯ ¥­³¬ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶¬¥º Æ n ³ ·Ë 1)

¬Ï´­¥³ à m§²¥²¤² ·Ê k ¬Ï´­¥³ à m§²¬ ´ ² q Ï´ © ­´ m´Â£ ¥¶ ¬´ ´ Sk u , q ¯ º ¬n ¬´ ´ ·Ê£´ ¸ ¬ ´ ² q §¹¯ ¬n ¬´ ´ ·Ê£· m´Â£ ¥¶ ¬n ´ n ¯¤¬º ¥³ ¥º m´Â£ ¥¶ ¬n ´ ¯ ¬ ´ ² q ·Ê©§´ k + 1 ³Ê ¹¯ 'k 1 q

( Ï´ Ï´Ë ¥ º ¬ ´ ² q) ( Ï´ Ï´Ë ¥ º ¥²¤² ·Ê k)

2)

¯ ¥­³¬ n¯£»§¯¶ º xk ´ ¬n ´ ·Ê£·Â£ ¥¶ ¬n ´ n ¯¤¬º

¥» ·Ê 2.9 ì ³ Ë ¯ ´¥ ¯ ¥­³¬ n¯£»§ ´£Ã ¢´  ¥§§¶¬ ¸Ê ²Ã¬  ´²Â¬n ´ ·Ê¤³ £·

·©¶ ¯¤m» (survivor path) ·Ê£´ ¸ à m§²¬ ´ ² Ä ¤ m´ ·Ê¯¤m» ¶ ³ à m§²Â¬n ¬´ ´ ¹¯ m´Â£ ¥¶ ¬´ ´

Sk u , q ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² (u, q) ³ Ë È Ã§² ³©Â§ ·Ê¯¤m» ¥ Ä­ ¯ à m§²¬ ´ ²

¹¯ m´Â£ ¥¶ ¬n ´ 'k q ´ ¥» ²Æ n©m´© ¥ ¯ ¥­³¬ ¯ Ä©§» ³ ²Å­n m´ ¥²£´ ¯ ¶ n¯£»§ Ë ¯ ´¥ ¯ ¥­³¬ n¯£»§ ¯ © ¥ ¥© ­´ ¯¶ º xk Â É xˆk \1, 0,1,1^ ¬Ï´­¥³ ¥´¤§²Â¯·¤ ³ ©·Â ¯¥q ¶¬´£´¥ ª¸ «´Æ nÅ ·Ê 4 ¯ [10]

26

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¯¤m´ Æ¥ É ´£ n´ Ï ´¥­³¬ ¯ Ä©§» ³ £´Å nÂ É ¬m© ¥² ¯ Å ¥­³¬Â ¯¥qÄ É ²Æ£m¬´£´¥

Å n© ¥ ¥© ­´©·Â ¯¥q ¶Å © ¥ ¯ ¥­³¬Â ¯¥qÄ Æ n  ¥´²© ¥ ¯ ¥­³¬Â ¯¥qÄ Ï´ ´ Ä ¤Å n m´©¬´¥ à ¯¡ q ¯ ¶ n¯£»§Â m´ ³ Ë (à m© ¥ ¥© ­´©·Â ¯¥q ¶ ²Å­n §§³ qÂ É m´©¬´¥Ã °´¥q ­¥¹¯

m´ ¥²£´ ¯ ¶ n¯£»§) ³ ³ Ë © ¥ ¯ ¥­³¬Â ¯¥qÄ ·ÊÅ n ¯ ¥­³¬ n¯£»§ ·Ê »  n´¥­³¬ n©¤¥­³¬

¯ Ä©§» ³ ² n¯ Â É © ¥ ¥© ­´ ·Ê¬¥n´ ´ ¯³§ ¯¥¶ ¸£ BCJR [18] ­¥¹¯ SOVA (soft-output Viterbi algorithm) [19]  m´ ³ Ë ¸Ê ²¯ ¶ ´¤ m¯Æ Å ­³© n¯ ·Ê 2.2 ç² ·Ê 3 ´£§Ï´ ³

2.2 ¯³§ ¯¥¶ ¸£ BCJR © ¥ ¥© ­´©·Â ¯¥q ¶ [1, 13] ¹¯© ¥ ¥© ­´Ã ©¥ ²Â É ¬» ¬º ­¥¹¯© ¥ ¥© ­´Ã ML (maximum-likelihood) ·ÊÅ nÅ ´¥ ¯ ¥­³¬ n¯£»§ ·Ê »  n´¥­³¬ n©¤¥­³¬ ¯ Ä©§» ³ Ä ¤ n¯£»§

¯´ q º ·ÊÆ n ²Â É m´ ¥²£´ ¯ §Ï´ ³ n¯£»§ ·Ê n¯ ´¥ ¥© ­´ ­¥¹¯¯´ §m´©Æ n©m´© ¥ ¥© ­´

à ML ² Ï´Å­n n¯ ¶ §´ ¯ §Ï´ ³ n¯£»§£· m´ n ¯¤¬º à mÆ£mÆ n¥³ ¥² ³ ©m´ ¶ n¯£»§Ã m§² ¶

·Ê¯¤m»Å §Ï´ ³ n¯£»§ ³ Ë Â É ¶ n¯£»§ ·Ê · Ê·¬º ³Ê ¹¯© ¥ ¥© ­´Ã ML Æ£mÆ n Ï´Å­n ¶ n¯£»§ à m§² ¶ £· n¯ ¶ §´ n ¯¤¬º

¯ ´ ·Ë© ¥ ¥© ­´©·Â ¯¥q ¶Æ£m¬´£´¥ Ï ´£´Å nÅ ¥² ¯ ¥­³¬ n¯£»§Ã © Ï´Ë Æ n

 ¥´²¥² ·Ë ²£· ´¥Ã§  §·Ê¤ m´©¬´¥Ã ¯¡ q¥²­©m´ © ¥ ¥© ­´Ã§²© ¥ ¯ ¥­³¬Ã nÆ n¯ ¶ §´ ³ ³ Ë ¥² ¯ ¥­³¬ n¯£»§Ã © Ï´Ë ² n¯ Å n© ¥ ¥© ­´ ©´£ m ´ ²Â É ¯²Ä ¬

 ¯¥¶¯¯¥¶¬» ¬º ­¥¹¯Â¥·¤ ©m´ “© ¥ ¥© ­´Ã MAP (maximum a posteriori probability)”

Ä ¤© ¥ ¥© ­´Ã MAP ¬´£´¥ ¥³ ¥² ³ Æ n©m´ ¶ n¯£»§Ã m§² ¶ ·Ê ¥© ­´Æ nÂ É ¶ n¯£»§ ·Ê · ʬ · º (­¥¹¯ ¶ n¯£»§Ã m§² ¶ £· n¯ ¶ §´ n ¯¤¬º )

Å ¬m© ·Ë ²¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ BCJR [18]  ¥´²Â É ¯³§ ¯¥¶ ¸£ ·ÊÅ n

Å ´¥¬¥n´ © ¥ ¥© ­´Ã MAP ¸Ê ¯³§ ¯¥¶ ¸£ ·Ë Æ n » ¶ n ç² ³ ´ ¸Ë Ä ¤ Bahl, Cock,

Jelinek, ç² Raviv  ¹Ê¯Å nÅ ´¥ ¥© ­´ m´ ©´£ m ´ ²Â É ¯²Ä ¬Â ¯¥¶¯¯¥¶ (APP: a posteriori

probability) ¬» ¬º ¯ ¬³ ´ ·Ê m´ m¯ ¬³ ´ ·Ê£· ´¥Ã ¥ ¬¯ ¥²­©m´ ¬³ §³ « q (ISI)

รหัสเทอรโบ

ç²£·¬³ ´ ¥ ©  ´¬q¬· ´©Ã © (AWGN)

2.2.1 à ϴ§¯ ¯ m¯ ¬³ ´ ç²Ã ¢´  ¥§§¶¬ ¶ ´¥ ´Ã Ï´§¯ ¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 £¹Ê¯¬³ ´ ·Ê© ¥¢´ ¥³ Æ n¥³ (­¥¹¯¬³ ´ ·Ê n¯ ´¥ ¯ ¥­³¬) §Ï´ ³ ·Ê k ¹¯

2

บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

27

nk N 0, T 2

ak

H D

O

rk

yk

a h

i k i

nk

i 0

¥» ·Ê 2.10 à ϴ§¯ m¯ ¬³ ´

Zk u

Hk u , q

Bk u

Bk 1 q

Zk 1 q

Ck u

Ck 1 q

k 1

yl k \yl ^0

L O 1

yl k \yl ^k 1

yk

¥» ·Ê 2.11 ´¥Â §·Ê¤ ¬ ´ ² (u, q) Å ¥²¤² ·Ê k ¯ à ¢´  ¥§§¶¬ O

yk ai hk i nk

(2.4)

i 0

£¹Ê¯ ak A ¹¯ n¯£»§¯¶ º ¶ ·Ê » §¹¯ £´ ´  ¯ º ³©¯³ «¥ A ( m ¥² Æ ´¥· ²Æ n A = {0, 1} ­¥¹¯ {–1, 1}), H (D )

O

hD k 0 k

k

¹¯ m¯ ¬³ ´ ·ÊÆ£m m¯Â ¹Ê ¯ (discrete

Î ³© ·Ê k ¯ m¯ ¬³ ´ , O ¹¯­ m ©¤ ©´£ Ï´ ¯ m¯ ¬³ ´ , channel), hk ¹¯ m´¬³£ ¥²¬¶ ¶

nk ¹¯ AWGN ·Ê£· m´Â §·Ê¤Â m´ ³ ª» ¤qç² ©´£Ã ¥ ¥©  m´ ³ V2 ­¥¹¯Â ·¤ à n©¤ nk a

Ư 0, T2 , rk ¹¯ n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ , ç² L ¹¯ ©´£¤´© ¯ §Ï´ ³ n¯£»§¯¶ º

{ak} Ä ¤ ³©Ê Æ n¯£»§­ ¸Ê   ¯¥q ²£· L = 4096 ¶ n´¬££º ¶©m´© ¥¢´ ¬m Æ n Ï´ ´¥¬m §Ï´ ³

n¯£»§¯¶ º a = <a 0 ,..., a L 1 > Ï´ © L ¶ Ä ¤ ¶ n¯£»§Ã m§² ¶ £· m´ ·ÊÂ É Æ Æ n¯¤m»¢´¤Å

 A ç²Æ£m£· ´¥¬m n¯£»§Å È Å m© ©§´ ·Ê k < 0 ç² k > L – 1 ³ ³ Ë ´ ¬£ ´¥ (2.4) L O 1

¬³ ´ ·Ê© ¥¢´ ¥³ Æ n¥³ ³ Ë ­£ Å ¥» ¯ ©  ¯¥q ¹¯ y \yl ^0

¢y 0 ,..., y L O 1 ¯±

¥» ·Ê 2.11 ì à ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ hk £¹Ê¯ Zk w <ak 1 , ak 2 ,..., ak O > ¹¯¬ ´ ² (state) ©§´ k (­¥¹¯ m´ ·Ê¯¤m»Å Â¥ ¶¬Â ¯¥qà §¹Ê¯ ³ Ë ­£ ©§´ k), Q A

28

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

O

¹¯ Ï´ © ¬ ´ ² ³ Ë ­£ ·ÊÂ É Æ Æ n, ¥²¤² ·Ê k (k-th stage) ¹¯ §mº£ ¯ ¬n ¬´ ´ (branch) ·Ê

Â É Æ Æ n ³ Ë ­£ ¥²­©m´ ©§´ k ç²Â©§´ k + 1, ç² (u, q) ¹¯¬³ §³ « q Ê·Å nà ´¥Â §·Ê¤

¬ ´ ² (transition) ´ ¬ ´ ² u Æ ¤³ ¬ ´ ² q n´Å­n¬ ´ ²Ã m§²¬ ´ ² ¹¯¬ ´ ² 0 ¸ ¬ ´ ²

Q – 1 Ä ¤ ·Ê¬ ´ ² 0 ­¥¹¯ Zk w <0, 0,..., 0> ²Å nà ¬ ´ ²©m´  §m´ (idle state) ¬Ï´­¥³ k d 0 ç² k t L + Q – 1 ³ ³ Ë ¯´ §m´©Æ n©m´¥» ·Ê 2.11 ì ¥²¤² ·Ê k ¯ à ¢´  ¥§§¶¬ ¸Ê

¬¯ §n¯ ³ ¶ n¯£»§¯¶ º §Ï´ ³ ·Ê k (­¥¹¯ ak), n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ §Ï´ ³ ·Ê k (­¥¹¯

rk), ç² n¯£»§ ·Ê© ¥¢´ ¥³ Æ n¥³ §Ï´ ³ ·Ê k (­¥¹¯ yk)

2.2.2 © ¥ ¥© ­´Â­£´² ·Ê¬º Å ´ ¶ ³ ¶© ¥ ¥© ­´Ã MAP ¹¯©m´Â É © ¥ ¥© ­´Â­£´² ·Ê¬º (optimal detector)

 ¥´²Â É © ¥ ¥© ­´ n¯£»§ ·Ê¬´£´¥ ¥³ ¥² ³ Æ n©m´ ©´£ m ´ ²Â É ¯ n¯ ¶ §´ ¯ ¶ n¯£»§ à m§² ¶ £· m´ n ¯¤¬º ³©¯¤m´  m Å ´¥ ³ ¬¶ Å ¶ n¯£»§§Ï´ ³ ·Ê k (­¥¹¯ ak) © ¥ ¥© ­´Ã

MAP ² Ï´ © ­´ m´ ©´£ m ´ ²Â É ¯²Ä ¬Â ¯¥¶¯¯¥¶ (APP) ­¥¹¯ Pr <ak | y > ¸Ê ­£´¤ ¸ m´

©´£ m ´ ²Â É ¯ ¶ n¯£»§ ak £¹Ê¯ Ï´­ §Ï´ ³ n¯£»§ y £´Å­n ¬Ï´­¥³ à m§² ¶ n¯£»§ ak ´ ³ Ë

²Â§¹¯ m´ ak ·Ê Ï´Å­n Pr <ak | y > £· m´¬» ¬º © ¥ ¥© ­´Ã MAP ² Ï´Â ¶ ´¥§³ « ² ·Ë Æ

Â¥¹Ê¯¤È ¥ n¯£»§ L ¶ Å ´ ¶ ³ ¶ m´ Pr <ak | y > Ï´ © Æ nÄ ¤ m´¤ n´ ¥´ m´ ©´£ m ´ ² Â É ¯ ´¥Â §·Ê¤ ¬ ´ ²Ã ¯²Ä ¬Â ¯¥¶¯¯¥¶ Pr ¢ Zk u ; Zk 1 q | y ¯± ¬Ï´­¥³ º ´¥Â §·Ê¤ ¬ ´ ² (u, q) Å Ã ¢´  ¥§§¶¬

¯³§ ¯¥¶ ¸£ BCJR ¹¯Â É ³ Ë ¯ ©¶ · Ê·£· ¥²¬¶ ¶¢´ £´ Å ´¥­´ m´ ©´£ m ´ ²Â É ¯

´¥Â §·Ê¤ ¬ ´ ²Ã ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¸Ê Ï´Æ n m´¤Ä ¤ ´¥ ³ ¥» Pr ¢ Zk u ; Zk 1 q | y ¯± ¬Ï´­¥³ ´¥Â §·Ê¤ ¬ ´ ² ©§´ k ¯¯ Â É 3 ¬m© ³ ·Ë k 1

1) ¬m© ·Ê­ ¸Ê ¸Ë ¯¤m» ³ n¯£»§ ·ÊÆ n¥ ³ ³ Ë ­£ Å ¯ · ³Ê ¹¯ yl k \yl ; l k ^ \yl ^0 2) ¬m© ·Ê¬¯ ¸Ë ¯¤m» ³ n¯£»§ ·ÊÆ n¥³ Å ³ º ³ ³Ê ¹¯ yk

´ ¯  ¬q (Bayes’ rule) m´ Pr ¢ Zk u ; Zk 1 q | y ¯± ³ ¥» Å­£mÆ n É

รหัสเทอรโบ

L O 1

3) ¬m© ·Ê¬´£ ¸Ë ¯¤m» ³ n¯£»§ ·ÊÆ n¥ ³ ³ Ë ­£ Å ¯ ´ ³Ê ¹¯ yl k \yl ; l k ^ \yl ^k 1

Pr ¢ Zk u ; Zk 1 q | y ¯± p Zk u ; Zk 1 q ; y / p y

p Zk u ; Zk 1 q ; yl k ; yk ; yl k / p y

p yl k |Zk u ; Zk 1 q ; yl k ; yk p Zk u ; Zk 1 q ; yl k ; yk / p y

(2.5)

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29

£¹Ê¯ p x ¹¯¡³ q ³ ©´£­ ´Ã m ©´£ m ´ ²Â É (pdf: probability density function) ¯ x ´ º ¬£ ³ ¶ ¯ £´¥q ¯¡ (Markov property) [4] ¯ à ϴ§¯  ¥¹Ê¯ ¬ ´ ² Ï´ ³ ¸Ê §m´©©m´

¬Ï´­¥³ m¯ ¬³ ´ Å È m´©¬´¥Â ·Ê¤© ³ n¯£»§ ¯ ¬ ´ ² ·Ê©§´ k + 1 ²Â n´£´Ã ·Ê m´©¬´¥  ·Ê¤© ³ n¯£»§ ¯ ¬ ´ ² ·Ê©§´ k ¥©£ ³ Ë m´ yk ç² yl k ³ ³ Ë ¬£ ´¥ (2.5) § ¥» Æ nÂ É Pr ¢ Zk u ; Zk 1 q | y ¯± p yl k |Zk 1 q p Zk u ; Zk 1 q ; yl k ; yk / p y

p yl k |Zk 1 q p Zk 1 q ; yk | Zk u ; yl k p Zk u ; yl k / p y

(2.6)

Å Ï´ ¯  ·¤© ³ ¯´ª³¤ º ¬£ ³ ¶ ¯ £´¥q ¯¡Â ¹Ê¯ ³ ¥» ¬£ ´¥ (2.6) É ²Æ nÂ É Pr ¢ Zk u ; Zk 1 q|y ¯±

p Zk u ; yl k p Zk 1 q ; yk | Zk u p yl k |Zk 1 q

p y

Bk u qHk u ,q qCk 1 q / p y

(2.7)

¸Ê ²Â­É Æ n©m´ ´¥´£¶Â ¯¥q Bk u ¹¯ m´ ©´£ m ´ ²Â É ¬Ï´­¥³ ¬ ´ ² u ©§´ k ¸Ê ¸Ë ¯¤m» ³ n¯£»§ ·ÊÆ n¥³ Å ¯ · yl k , ´¥´£¶Â ¯¥q Ck 1 q ¹¯ m´ ©´£ m ´ ²Â É ¬Ï´­¥³ ¬ ´ ² q ©§´

k + 1 ¸Ê ¸Ë ¯¤m» ³ n¯£»§ ·ÊÆ n¥³ Å ¯ ´ rl ! k , ç² ´¥´£¶Â ¯¥q Hk u , q ¹¯ m´ ©´£ m ´ ²Â É ¯ ´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² u ©§´ k Æ ¤³ ¬ ´ ² q ©§´ k + 1 ¸Ê ¸Ë ¯¤m» ³ n¯£»§Å

³ º ³ yk ( » ´¥´£¶Â ¯¥q m´ È Å ¥» ·Ê 2.11) Ä ¤ ³Ê©Æ ´¥´£¶Â ¯¥q Bk u ç² Ck 1 q Â¥·¤ ©m´ £ ¥¶ ¬ ´ ² (state metric) ç² ´¥´£¶Â ¯¥q Hk u ,q Â¥·¤ ©m´Â£ ¥¶ ¬´ ´ (branch metric) n´ Ï´­ Å­n Sa ¹¯Â ¯ ´¥Â §·Ê¤ ¬ ´ ² (u, q) ·ÊÂ É Æ Æ n ³ Ë ­£ ·Ê¬¯ §n¯ ³

¶ n¯£»§ a ³ ³ Ë m´ ©´£ m ´ ²Â É ¯²Ä ¬Â ¯¥¶¯¯¥¶ Pr <ak a | y > ­´Æ n ´ Pr <ak a | y >

u ,q Sa

Pr ¢ Zk u ; Zk 1 q | y ¯±

1 Bk u Hk u , q Ck 1 q

p y u ,q S

(2.8)

a

¬£ ´¥ (2.8) ­´Æ n m´¤ £¹Ê¯ ¥´ m´ B k u , Hk u , q ç² Ck 1 q ¬Ï´­¥³ º ´¥Â §·Ê¤ ¬ ´ ²

u ,q ç² º ¥²¤² ·Ê k

30

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

2.2.3 ´¥ Ï´ © ­´ m´ ´¥´£¶Â ¯¥q ¯ ¯³§ ¯¥¶ ¸£ BCJR ´¥´£¶Â ¯¥q ¯ ¯³§ ¯¥¶ ¸£ BCJR ´£¬£ ´¥ (2.8) ³Ê ¹¯ Hk u , q , Bk u , Ck 1 q ç² p y ¬´£´¥ Ï´ © ­´Æ n ³ ·Ë

´¥­´ m´Â£ ¥¶ ¬´ ´ Hk u , q ¬Ï´­¥³ m¯ ¬³ ´ AWGN ¯³§ ¯¥¶ ¸£ BCJR ²Ã m´ ´ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [13] ¥ ·Ê©m´¯³§ ¯¥¶ ¸£ BCJR ² Ï´ ´¥

Ï´ © ¬¯ ¬n ´ ¹¯

1) ¬n ´ n´ ­ n ´ (forward pass) Ä ¤Â¥¶Ê£ Ï´ © m´ m´ È ³ Ë Ã m n¯£»§ ·ÊÆ n¥³ ³©Ã¥ Æ n´ ­ n ´ ¸ n¯£»§ ³©¬º n´¤

2) ¬n ´ ¤n¯ §³ (backward pass) Ä ¤Â¥¶Ê£ Ï´ © m´ m´ È ³ Ë Ã m n¯£»§ ·ÊÆ n¥³ ³©¬º n´¤ ¤n¯ §³ £´ ¸ n¯£»§ ³©Ã¥

¯ ´ ·Ë£ ¥¶ ¬´ ´ ¯ ¯³§ ¯¥¶ ¸£ BCJR Ï´ © Æ n ´ Hk u , q p Zk 1 q ; yk | Zk u

p yk | Zk u ; Zk 1 q p Zk 1 q | Zk u

(2.9)

¬Ï´­¥³ m¯ ¬³ ´ à AWGN ¬³ ´ ·ÊÆ n¥³ ¹¯ yk rk nk £¹Ê¯ nk ~ Ư 0, T2 ¹¯ ¬³ ´ ¥ ©  ´¬q¬· ´©Ã © n´ Ï´­ Å­n aˆ u , q ç² rˆ u , q ¹¯ ¶ n¯£»§¯¶ º ç² n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² u , q ´£§Ï´ ³ ³ ³ Ë q Ã¥ ´ ©´£¹¯ ¯ ¬£ ´¥ (2.9) £· m´Â m´ ³ £ 1 ² 2¦ ¦ exp ¤ 2 yk rˆ u , q » ¦ ¦ ¦ 2T ¦ ¥ ¼ 2QT 1

2

(2.10)

£¹Ê¯ exp(.) ¹¯¡³ q ³ § · Ë Ï´§³ (exponential function) ç² q Ê·¬¯ ´ ©´£¹¯ ¯ ¬£ ´¥

(2.9) ¹¯

รหัสเทอรโบ

p yk | Zk u ; Zk 1 q

p Zk 1 q | Zk u p ak aˆ u ,q ; Zk u / p Zk u

p Zk u | ak aˆ u , q

p ak aˆ u , q

/ p Zk u

2

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31

p Zk u p ak aˆ u ,q

/ p Zk u

p ak aˆ u , q

(2.11)

Å ´ ¶ ³ ¶ m´ ©´£ m ´ ²Â É Å ¬£ ´¥ (2.11) ²Â¥·¤ ©m´ ©´£ m ´ ²Â É ¯² ¶¥¶¯¯¥¶ (a priori

probability) ¯ ¶ n¯£»§ ak ´ ³ Ë Ã m´¬£ ´¥ (2.10) ç² (2.11) § Å ¬£ ´¥ (2.9) ² Æ n©m´Â£ ¥¶ ¬´ ´ ¯ ¯³§ ¯¥¶ ¸£ BCJR £· m´Â m´ ³ Hk u , q

£ 1 ² 2¦ ¦ exp ¤ 2 yk rˆ u , q »q p ak aˆ u ,q

¦ ¦ ¦ 2T ¦ ¥ ¼ 2QT 1

2

(2.12)

¸Ê ² ©m´Â£ ¥¶ ¬´ ´ ¯ ¯³§ ¯¥¶ ¸£ BCJR £· q p ak aˆ u , q

 ¶Ê£ ¸Ë £´ ´ £ ¥¶ ¬´ ´ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [4] Å ¥ · Ê· ¶ n¯£»§ ak º ³©£·Ä¯ ´¬Â ¶ ¸Ë  m´ ³ m´ ©´£ m ´ ²Â É ¯² ¶¥¶¯¯¥¶ p ak a ²Â É m´ ³© ·ÊÆ£m ¸Ë ³ m´ a ³ ³ Ë Å ¥ · ·Ë£ ¥¶ ¬´ ´ ¯ ¯³§ ¯¥¶ ¸£

BCJR ²£· m´Â m´ ³ £ ¥¶ ¬´ ´ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ¯¤m´ Æ¥ É ´£Å ¥ · Ê· ¶ n¯£»§ ak à m

§² ³©£·Ä¯ ´¬Â ¶ ¸Ë Æ£m m´ ³  ¥´² ² ³ Ë n´ ¥´ n¯£»§Â ·Ê¤© ³ ak à m§² ³©§m© ­ n ´ É ² m©¤ Ï´Å­n ´¥ ¯ ¥­³¬ n¯£»§£· ©´£ » n¯ £´ ¤¶Ê ¸Ë

´¥­´ m´Â£ ¥¶ ¬ ´ ² Bk u ç² Ck 1 q

£ ¥¶ ¬ ´ ² Bk u ç² Ck 1 q Å ¬£ ´¥ (2.7) Ï´ © ­´Æ n m´¤Ä ¤¯´ª³¤ º ¬£ ³ ¶ ¯ £´¥q ¯¡Ã§²Â ¶ ©·¤  ¶ (recursive) ³ ·Ë ´ ¬£ ´¥ (2.7) ²Æ n©m´ Bk u p Zk u ; yl k

³ ³ Ë Bk 1 q p Zk 1 q ; yl k 1

p Zk 1 q ; yk ; yl k

Q 1

p Z

k 1

q ; yk ; Zk u ; yl k

k 1

q ; yk | Zk u ; yl k p Zk u ; yl k

u 0

Q 1

p Z u 0

32

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(2.13)

Q 1

p Z

k 1

q ; yk | Zk u p Zk u ; yl k

u 0

Q 1

H

k

(2.14)

u ,q Bk u

u 0

Å Ï´ ¯  ·¤© ³ ´ ¬£ ´¥ (2.7) ²Æ n©m´ (2.15)

Ck 1 q p yl k | Zk 1 q

³ ³ Ë Ck u p yl k 1 | Zk u

p yl k ; yk | Zk u

Q 1

p y

l k ;

yk ; Zk 1 q | Zk u

q 0

Q 1

p y

l k |yk ;

Zk 1 q ; Zk u p yk ; Zk 1 q | Zk u

q 0

Q 1

p y

l k

| Zk 1 q p yk ; Zk 1 q | Zk u

q 0

Q 1

C

k 1

(2.16)

q Hk u ,q

´¥ Ï´­  ¹Ê¯ Æ Â¥¶Ê£ n ¯ Bk u ç² Ck 1 q

¯³§ ¯¥¶ ¸£ BCJR ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ë ²¬££º ¶©m´¬£ ´¥ (2.15) ç² (2.16) Â¥¶Ê£ Ï´ ´¥ Ï´ ©

Ä ¤Å n ¹Ê¯ Æ Â¥¶Ê£ n (initial condition) ¯ £ ¥¶ ¬ ´ ² Bk u ç² Ck 1 q ³ ·Ë £ ¦1, u 0 B 0 u ¦ ¤ ¦ ¦ ¥0, else

ç²

£¦1, q 0 CL O q ¦¤ ¦¦¥0, else

(2.17)

รหัสเทอรโบ

q 0

2

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33

¸Ê Å n ³ ¥ · Ê· º ¬n ¬´ ´ (branch) Å Ã ¢´  ¥§§¶¬Â¥¶Ê£ n ·Ê¬ ´ ² Z0 0 ç²£· ´¥ ³ ³ Å­n º ¬n ¬´ ´Å à ¢´  ¥§§¶¬¬¶ Ë ¬º ·Ê¬ ´ ² ZL O 0 ³Ê ¹¯ º ¬n ¬´ ´Å m© ´¥Â©·¤  ¶ à n´ ­ n ´ (forward recursion) n¯ ¬¶ Ë ¬º ·Ê¬ ´ ² ZL O 0 ç² º ¬n ¬´ ´ Å m© ´¥Â©·¤  ¶ à ¤n¯ §³ (backward recursion) n¯ ¬¶ Ë ¬º ·Ê¬ ´ ² Z0 0 ¯¤m ´ Æ¥ É ´£Å ¥ · Ê· Æ £m £· ´¥ ³ ³ Å­n º ¬n ¬´ ´Å à ¢´  ¥§§¶ ¬ ¬¶Ë ¬º ·Ê

¬ ´ ² ZL O 0 É ¶ ¤£ Ï´­ Å­n m´Â¥¶Ê£ n ¯ £ ¥¶ ¬ ´ ² CL O q £· m´Â m´ ³ £ ¥¶ ¬ ´ ² B L O q ³Ê ¹¯ CL O q B L O q

(2.18)

¬Ï´­¥³ º ¬ ´ ² q {0, 1, …, Q – 1}  ¥´²¯³§ ¯¥¶ ¸£ BCJR Æ£m£· ©´£¥n»Â ·Ê¤© ³ n¯£»§

©´£ m ´ ²Â É ¯ à m§²¬ ´ ² ©§´ L O

´¥­´ m´ p y

Å ´ ¶ ³ ¶ m´ p y ·ÊÅ nÅ ´¥ Ï´ © ­´ m´ ©´£ m ´ ²Â É ¯²Ä ¬Â ¯¥¶¯¯¥¶ Pr <ak | y > ´£ ¬£ ´¥ (2.8) ¬´£´¥ §² ¶ Ë Æ n  ¹Ê ¯ ´ p y £· m´ ·Ê¬Ï´­¥³ º ©§´ k ³ ³ Ë ¥² © ´¥ ­´ m´¬» ¬º ¯ Pr <ak | y > ¸ ¤³ Å­n §§³ q m´Â ¶£ ¯¤m´ Æ¥ É ´£Å ·Ê ·Ë ²Ã¬ ©¶ ·­´ m´ p y

³ ·Ë

 ¹Ê ¯ ´ §¥©£ ¯ ©´£ m ´ ²Â É Ã £·Â ¹Ê¯ Æ ¯ º ­ º ´¥ q n¯ £· m´Â m´ ³ ­ ¸Ê

¬£¯ ³ ³ Ë ´ ¬£ ´¥ (2.7) ²Æ n©m´ Q 1 Q 1

u 0 q 0

Pr ¢ Zk u ; Zk 1 q|y ¯±

Q 1 Q 1

B u Hk u ,q Ck 1 q ¬­ k ­­­ 1 p y

® q 0

(2.19)

u Hk u ,q Ck 1 q

(2.20)

u 0

³Ê ¹¯ Q 1 Q 1

p y

B

k

u 0 q 0

´ ¬£ ´¥ (2.16) ²Æ n©m´ p y

Q 1

B u 0

34

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

k

u Ck u

(2.21)

¬£ ´¥ (2.21) ì Å­nÂ­É ©m´ § » ¯ m´ Bk u ç² Ck u ¯ º ¬ ´ ² u ¢´¤Å à ¢´  ¥§§¶¬ ²£· m´Â m´ ³ º ©§´ k ¸Ê £· m´Â m´ ³ m´ p y  ¥´² ² ³ Ë ´ ¬£ ´¥ (2.17) Ï´Å­nÆ n ©´£¬³£ ³ q©m´ (2.22)

p y C0 0 B L O 0

2.2.4 ¯³§ ¯¥¶ ¸£ BCJR ¬Ï´­¥³ ¶ n¯£»§Ã Æ ´¥· Å ¥ · Ê· ¶ n¯£»§¯¶ º Â É Ã Æ ´¥· ³Ê ¹¯ ak \ 1,1^ m´ ©´£ m ´ ²Â É ¯²Ä ¬Â ¯¥¶¯¯¥¶ Pr <ak a | y > Å ¬£ ´¥ (2.8) ² » Ï´­ n©¤ m´ Pr <ak 1 | y > 1 Pr <ak 1 | y > ­¥¹¯

m´¯³ ¥´¬m© Pr <ak 1 | y > / Pr <ak 1 | y > ¸Ê Å Ä Â£ §¯ ´¥¶ ¸£ (logarithm domain)  ·¤ Æ nÂ É Pr <ak 1 | y > ¬­ ­­ M p ak ln Pr <ak 1 | y >®­

(2.23)

£¹Ê¯ M p ak ¹¯ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ³ ³ Ë ´ ¬£ ´¥ (2.8) ²Æ n©m´

Bk u Hk u ,q Ck 1 q ¬­­ ­­ u ,q S1 ­­ M p ak ln ­ B k u Hk u ,q Ck 1 q ­­ ­ u ,q S ®­

(2.24)

1

¯³§ ¯¥¶ ¸£ BCJR ¬Ï´­¥³ ¶ n¯£»§Ã Æ ´¥· ²Å n¬£ ´¥ (2.24) Å ´¥ Ï´ © ­´ m´

LLR ¬Ï´­¥³ à m§² ¶ n¯£»§ ·Ê¬m £´ ´ © ¥¢´ ¬m ¸Ê m´ M p ak ² » Ï ´£´Å nÅ ´¥ ³ ¬¶ Å ­´ m´ ¥²£´ ¯ ¶ n¯£»§ ak ·Ê Ï´Å­n ©´£ m ´ ²Â É ¯ n¯ ¶ §´ £· m´ n ¯¤¬º Ä ¤¯´ª³¤ £¦1, if M p ak p 0 aˆk ¦¤ ¦¦ 1, if M p ak 0 ¥

(2.25)

¯ ´ ·Ë m´ ©´£ m ´ ²Â É ¯² ¶¥¶¯¯¥¶ p ak a ¬Ï´­¥³ a \o1^ ¤³ £· ©´£¬³£ ³ q

รหัสเทอรโบ

´¥ ³ ¬¶ Å ³ ·Ë

³ ¡³ q ³ ©¥ ²Â É Ã §¯ ´¥¶ ¸£ ³ ·Ë ( »¬£ ´¥ (1.6)) p ak a

exp a Ma ak / 2

exp Ma ak / 2 exp Ma ak / 2

(2.26)

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บทที่

35

£¹Ê¯ p ak 1 ¬­ ­­ Ma ak ln p ak 1 ®­

(2.27)

¹¯ m´ LLR à ¯² ¶¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ¯¤m´ Æ¥ É ´£Â ¹Ê ¯ ´ ³©¬m© Å ¬£ ´¥ (2.26) £· m´

 m´ ³ ¬Ï´­¥³ º ´¥Â §·Ê¤ ¬ ´ ² (u, q) Å Ã ¢´  ¥§§¶¬ ³ ³ Ë ¸ ¬´£´¥ Å n m´ ©´£ m ´ ²Â É ¯² ¶¥¶¯¯¥¶

a M a ¬ p ak a exp a k ­­­ 2 ®­

(2.28)

Å ´¥­´ m´Â£ ¥¶ ¬´ ´ ¯ ¯³§ ¯¥¶ ¸£ BCJR Å ¬£ ´¥ (2.12) Æ n ³Ê ¹¯ Hk u , q

aˆ u , q Ma ak ¬­ ² 2¦ ¦£ 1 ­­ exp ¤ 2 yk rˆ u , q »q exp ¦¥¦ 2T ¦¼¦ 2 ®­ 2QT2 1

(2.29)

2.2.5 ¬¥º ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ £ ¸ BCJR ­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ BCJR ¬¥º Â É ³ Ë ¯ m´ È Æ n ´£¥» ·Ê 2.12

2.2.6 n¯¬³  ¯ ¯³§ ¯¥¶ ¸£ BCJR ´¥ Ï ´¯³§ ¯¥¶ ¸£ BCJR ·Ê¯ ¶ ´¤Å ¥» ·Ê 2.12 Æ Å n ´ ¥¶ Å ´ ¶ ³ ¶ Ï´Â É ² n¯ Ï´ ´¥

¯¥q£¯§Æ§Â ³ (normalization) [22] m´Â£ ¥¶ ¬ ´ ² Bk u ç² Ck u ¬Ï´­¥³ º ¬ ´ ²

u ç² º ©§´ k  ¹Ê¯­§· §·Ê¤ ³ ­´Â¥¹Ê¯ n ¯¤Â ¶ Â É Â ¶ ³©Â§ (numerical underflow) Å

Ä ¥Ã ¥£ ¯£ ¶©Â ¯¥q §m´© ¹¯Å à m§²Â©§´ k ·Ê Ï´ ´¥ Ï´ © ­´ m´ B k u ç² Ck u £¹Ê¯

Æ n m´ Bk u ç² Ck u ´£¬£ ´¥ (2.14) ç² (2.16) ¬Ï´­¥³ º ¬ ´ ² u çn© ÉÅ­n Ï´ ´¥ ¯¥q£¯§Æ§Â ³ m´Â£ ¥¶ ¬ ´ ² ³ Ë ¬¯ ´£ ©´£¬³£ ³ q ³ ·Ë Bk u

Bk u

B i

k

i

ç²

Ck u

Ck u

C i

(2.30)

i k

 ¹Ê¯Å­n §¥©£ ¯ Bk u ¬Ï´­¥³ º u £· m´Â m´ ³ ­ ¸Ê ç²Å­n §¥©£ ¯ Ck u ¬Ï´­¥³ º u £· m´Â m´ ³ ­ ¸Ê ´ ³ Ë ¸ Â¥¶Ê£ Ï´ © ­´ m´ Bk u ç² Ck u Š©§´ k ³ Æ

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¯³§ ¯¥¶ ¸£ BCJR 1. Ï´­ m´Â¥¶Ê£ n £ ¥¶ ¬ ´ ² ¢B 0 0 , B 0 1 , !, B 0 Q 1 ¯± <1, 0, !, 0> 2. ´¥Â©·¤  ¶ à n´ ­ n ´ (forward recursion) ¬Ï´­¥³ k 0,1, !, L O 1 ¬Ï´­¥³ q 0,1, !,Q 1 Ï´ © ­´ m´ Hk u , q ´£¬£ ´¥ (2.29) ¬Ï´­¥³ º u ·Ê Ï´Å­n (u, q) Â É ¥¶ Ï´ © ­´ m´ B k 1 q ´£¬£ ´¥ (2.14) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ q) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ k) 3. Ï´­ m´Â¥¶Ê£ n £ ¥¶ ¬ ´ ²6 ¢ CL O 0 , CL O 1 , !, CL O Q 1 ¯± <1, 0, !, 0> 4. ´¥Â©·¤  ¶ à ¤n¯ §³ (backward recursion) ¬Ï´­¥³ k L O 1, L O 2, !, 0 ¬Ï´­¥³ u 0,1, !,Q 1 Ï´ © 7­´ m´ Hk u , q ´£¬£ ´¥ (2.29) ¬Ï´­¥³ º q ·Ê Ï´Å­n (u, q) Â É ¥¶ Ï´ © ­´ m´ Ck u ´£¬£ ´¥ (2.16) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ u) Ï´ © ­´ m´ M p ak ´£¬£ ´¥ (2.24) ³ ¬¶ Å ­´ m´ ak ´£¬£ ´¥ (2.25) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ k) ¥» ·Ê 2.12 ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ BCJR

 ¥´²¬´£´¥ ¥³ ¥² ³ Æ n©m´ ¶ n¯£»§Ã m§² ¶ ²£· n¯ ¶ §´ n ¯¤¬º ¯¤m´ Æ¥ É ´£Å ´ ¶ ³ ¶ 6

£¹Ê¯¬££ ¶©m´£· ´¥ ³ ³ Å­n º ¬n ¬´ ´Å à ¢´  ¥§§¶¬¬¶ Ë ¬º ·Ê¬ ´ ² Z L O 0 £¶ ² ³ Ë Ã§n© n¯ Ï´­

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m´Â¥¶Ê£ n ¯ CL O q ´£¬£ ´¥ (2.18) 7

m´Â£ ¥¶ ¬´ ´ Hk u , q ·Ê Ï´ © Æ nÅ m© ´¥Â©·¤  ¶ à ¤n¯ §³ ²£· m´Â m´ ³ m´Â£ ¥¶ ¬´ ´ ·Ê Ï´ © Æ nÅ m© ´¥Â©·¤  ¶ à n´ ­ n ´ à m Ê· Ï´ ´¥ Ï´ © m´Â£ ¥¶ ¬´ ´Å­£m¯· ¥³ Ë Å m© ´¥Â©·¤  ¶ à ¤n¯ §³ É ¹Ê¯ § Ï´ © ­ m ©¤ ©´£ Ï´ (memory) ·Ê n¯ Å nÅ ´¥Â É m´Â£ ¥¶ ¬´ ´Å m© ´¥Â©·¤  ¶ à n´ ­ n ´

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

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37

¯³§ ¯¥¶ ¸£ BCJR Æ£m ¶¤£ Ï ´£´Å n ¥¶ Å ¶ ¥²£©§ §¬³ ´ ¯ ´ ¥²¤º q m´ È Æ n  ¥´²

¯³§ ¯¥¶ ¸£ BCJR Å n ¥³ ¤´ ¥Å ´¥ Ï´ © ¬» 粯m¯ Æ­© m¯ m´ ©´£Ã ¥ ¥© ¯ ¬³ ´

¥ © ­¥¹¯ V2 [23, 24] ¸Ê n¯ Å nÅ ´¥­´ m´ Hk u ,q ´£¬£ ´¥ (2.29) §m´© ¹¯ ´¥Å n ´ Å ¥² ¥¶ ²Æ£m¬´£´¥ ¥´ m´ V2 ·Êà n ¥¶ Æ n ( Ï´Æ nà m ·¤ ´¥Å n ¶ m´ È Å ´¥­´ m´

¥²£´ ¯ V2  m´ ³ Ë ) ³ ³ Ë n´ V2 £· m´Æ£m » n¯ É ² Ï´Å­n m´ ´¥´£¶Â ¯¥q m´ È ¯ ¯³§ ¯¥¶ ¸£

BCJR £· m´ ¶  ·¤ Ë ³ Ë ­£ ¸Ê ¬m §Å­n¬£¥¥ ² ¯ © ¥ ¥© ­´Ã MAP n¯¤§ £´ ³ ³ Ë

³ ©¶ ³¤ ¸ Æ n ³ ´¯³§ ¯¥¶ ¸£ m´ È Â m Max-Log-MAP, Log-MAP ç² SOVA ¸Ê £·¬£¥¥ ² Å §n ·¤ ­¥¹¯Â ·¤  m´¯³§ ¯¥¶ ¸£ BCJR à mÅ n ¥³ ¤´ ¥Å ´¥ Ï´ © n ¯¤ ©m´Ã§²Æ£m¯m¯ Æ­©

m¯ m´ V2 [24] ¸ Ï´Å­n¬´£´¥ Ï ´Æ Å n ¥¶ Å ¶ ¥²£©§ §¬³ ´ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ (Å ·Ê 3 ²¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯³§ ¯¥¶ ¸£ m´ È Â­§m´ ·Ë)

³©¯¤m´ ·Ê 2.4 ´ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 n´ Ï´­ Å­n§Ï´ ³ n¯£»§¯¶ º ak = {1, –1, 1}, m¯ ¬³ ´ H D 1 0.5D , ¬³ ´ ¥ © nk = {–0.1, 0.3, –0.2, –0.1} Ë ¯ ´¥ ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ ¸Ê £· ©´£Ã ¥ ¥©  m´ ³ T2 1 / 2Q ì ³ BCJR (¬££º ¶©m´¥² Æ£m ¥´ m´©¬´¥¯² ¶¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ) ©¶ · Ï´

n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ rk ­´Æ n ´ rk ak hk {r0 , r1 , r2 , r3 } {1, 0.5, 0.5, 0.5}

£¹Ê¯ * ¹¯ ³© Ï´Â ¶ ´¥ ¯ Ä©§» ³ (convolution operator) ç² yk rk nk {0.9, 0.2, 0.3, 0.6} {y 0 , y1 , y 2 , y3 }

´ ³ Ë Å­n¬¥n´ à ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ H D 1 0.5D ¸Ê ²Æ n ´£¥» ·Ê 2.13 Ä ¤ £· ³ Ë ­£ ¬¯ ¬ ´ ² ¹¯ ¬ ´ ² (a) 粬 ´ ² (b)

´¥ ¯ ¥­³¬ n¯£»§ ¯ ¯³§ ¯¥¶ £ ¸ BCJR £·¥´¤§²Â¯·¤ ³ ·Ë

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¥¶ ´£Ã ¢´  ¥§§¶¬Å ¥» ·Ê 2.13 ¸Ê ²Æ n

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

a k 1 ak 1

¥» ·Ê 2.13 à ¢´  ¥§§¶¬¬Ï´­¥³ m¯ ¬³ ´ H(D) = 1 + 0.5D £¹Ê¯ n¯£»§¯¶ º ¹¯ ak {r1}

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Å­n Ï´ ´¥ ¯¥q£¯§Æ§Â ³ ´£¬£ ´¥ (2.30) ²Æ n

รหัสเทอรโบ

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3. ¥²¤² ·Ê 1 (£¹Ê¯ k = 1) ¯³§ ¯¥¶ ¸£ BCJR ¥³ n¯£»§ y1 = –0.2 £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ ³ ·Ë

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^qexp 12 0 ®­­­­ x 0.0049 เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

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39

\

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Å­n Ï´ ´¥ ¯¥q£¯§Æ§Â ³ ´£¬£ ´¥ (2.30) ²Æ n B1 a 0.7537 / 0.7537 0.0001 x 0.9999 B1 b 0.0001/ 0.7537 0.0001 x 0.0001

4. ¥²¤² ·Ê 2 ç² 3 (£¹Ê¯ k = {2, 3}) ¯³§ ¯¥¶ ¸£ BCJR ¥³ n¯£»§ y2 = 0.3 ç² y3 = 0.6 £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ ç² ¥³ m´Â£ ¥¶ ¬ ´ ² B k 1 q ¬Ï´­¥³ q {a, b}

 m  ·¤© ³ ³ ©¶ · ´¥ ·Ê¯ ¶ ´¤Å ³ Ë ¯ ·Ê 2 ç² 3 ¸Ê ²Æ n m´ Hk u ,q ç² B k 1 q

´£ ·Êì Å ¥» ·Ê 2.14 Ä ¤ m´ ·Ê¯¤m» ¶ ³ ¬n ¬´ ´Ã m§²Â¬n ¹¯ m´ Hk u ,q ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² (u, q) ³ Ë È Ã§² ³©Â§ ·Ê¯¤m» ¥ Ä­ ¯ à m§²¬ ´ ²Ã¬ ¸ m´ £ ¥¶ ¬ ´ ² B k u ç² Ck u Å ¥» ª«¬m© ³ ·Ë Bk u

Ck u

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

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5. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬ ´ ² C4 u B 4 u ¬Ï´­¥³ u {a, b} ³Ê ¹¯ ç²

C4 a 0.2214

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´¥Â©·¤  ¶ à ¤n¯ §³ 6. ¥²¤² ·Ê 3 (£¹Ê¯ k = 3) ¯³§ ¯¥¶ ¸£ BCJR ¥³ n¯£»§ y3 = 0.6 £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ É ²Æ n

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รหัสเทอรโบ

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บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

41

C3 b H 3 b , a C 4 a H 3 b , b C4 b

0.0223 0.2214 0.0785 0.7786 0.066057

Å­n Ï´ ´¥ ¯¥q£¯§Æ§Â ³ ´£¬£ ´¥ (2.30) ²Æ n C3 a 0.75454 / 0.75454 0.066057 x 0.9195 C3 b 0.066057 / 0.75454 0.066057 x 0.0805

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n¯£»§¯¶ º ç² m¯ ¬³ ´ ¸ Ï´Å­n£· n¯£»§Å­£m ¶Ê£ ¸Ë £´ ¯¤m´ Æ¥ É ´£ m´ M p a3 ¯´ Ï ´

£´Å n ¥²Ä¤ qÅ ¥² © ´¥ ¯ ¥­³¬Ã © Ï´Ë Æ n 7. ¥²¤² ·Ê 2 (£¹Ê¯ k = 2) ¯³§ ¯¥¶ ¸£ BCJR ¥³ n¯£»§ y2 = 0.3 £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ É ²Æ n

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

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0.00004 0.9195 0.8819 0.0805 0.07103 C2 b H 2 b , a C3 a H 2 b ,b C3 b

0.1339 0.9195 0.0108 0.0805 0.12399

Å­n Ï´ ´¥ ¯¥q£¯§Æ§Â ³ ´£¬£ ´¥ (2.30) ²Æ n C2 a 0.07103 / 0.07103 0.12399 x 0.3642 C2 b 0.12399 / 0.07103 0.12399 x 0.6358

´ ³ Ë Ï´ ´¥ Ï´ © ­´ m´ M p a 2 ´£¬£ ´¥ (2.24) ³Ê ¹¯ B a H 2 a ,b C3 b B 2 b H 2 b , b C3 b ¬­ ­­ M p a 2 ln 2 B 2 a H 2 a ,a C3 a B 2 b H 2 b , a C3 a ®­ 0.9999 0.8819 0.0805 0.0001 0.0108 0.0805 ¬­ ­­ ln 0.9999 0.00004 0.9195 0.0001 0.1339 0.9195 ®­

 ¹Ê ¯ ´ M p a 2 0 ³ ³ Ë ¯³§ ¯¥¶ ¸£ BCJR ² ¯ ¥­³¬ ¶ n¯£»§ a2 Æ nÂ É aˆ2 1 8. ¥²¤² ·Ê 1 ç² 0 (£¹Ê¯ k = {1, 0}) ¯³§ ¯¥¶ ¸£ BCJR ¥³ n¯£»§ y1 = –0.2 ç² y0 = 0.9

รหัสเทอรโบ

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£´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ ç² ¥³ m´Â£ ¥¶ ¬ ´ ² Ck u ¬Ï´­¥³ u {a, b}

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เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

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43

M p a 0 18.28

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Æ nÂ É \aˆ0 , aˆ1 , aˆ2 ^ \1, 1,1^ ¸Ê ¥ ³ ¶ n¯£»§ {ak} ·Ê¬m £´ ´ © ¥¢´ ¬m ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ BCJR

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n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ rk ­´Æ n ´ rk ak hk {r0 , r1 , r2 , r3 , r4 } {1, 1, 0, 1, 1}

ç² yk rk nk {1.2, 0.7, 0.2, 0.5, 0.7} {y 0 , y1 , y 2 , y3 , y 4 }

´ ³ Ë Å­n¬¥n´ à ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ H D 1 D 2 ¸Ê ²Æ n ´£¥» ·Ê 2.15 Ä ¤ £· ³ Ë ­£ ¬·Ê¬ ´ ² ¹¯ ¬ ´ ² (a), (b), (c) ç² (d)

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\M p a0 , M p a1 , M p a 2 , M p a3 , M p a 4 ^ \4.778, 27.646, 4.778, 12.566, 4.525^

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

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¥» ·Ê 2.16 ´¥ Ï´ © ¢´¤Å ¯³§ ¯¥¶ ¸£ BCJR Å ³©¯¤m´ ·Ê 2.5

รหัสเทอรโบ

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บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

45

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46

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

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2.3.1 © ¥Â n´¥­³¬Â ¯¥qÄ © ¥Â n´¥­³¬Â ¯¥qÄ £·Ä ¥ ¬¥n´ ´£¥» ·Ê 2.18 Ä ¤§Ï´ ³ n¯£»§¯¶ º x k ² » n ¯  n´Æ Å Ã m§² ¯ q ¥² ¯ ¤m¯¤ ¯ © ¥Â n´¥­³¬Â ¯¥qÄ ³ Ë ¬´£¬m© ¹¯ ¬m© ·Êà § §Ï´ ³ n¯£»§ x k Å­nÂ É §Ï´ ³ n¯£»§ x k , yk1 ç² yk2 ´£§Ï´ ³ ( ³Ê ¹¯© ¥Â n´¥­³¬Â ¯¥qÄ ·Ë £·¯³ ¥´¥­³¬Â m´ ³ 1/3) ´ ¥» ·Ê 2.18 ² ©m´§Ï´ ³ n¯£»§ yk1 Æ n ´ ´¥ n ¯ §Ï´ ³ n¯£»§ x k  n´Æ Å © ¥Â n´¥­³¬¤m¯¤­£´¤Â§ 1

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2

8

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»¥´¤§²Â¯·¤  ·Ê¤© ³ © ¥¯¶  ¯¥q§·¡Â©¯¥qÆ nÅ ­³© n¯ ·Ê 2.3.4

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

47

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© ¥Â n´¥­³¬¤m¯¤ ·Ê¢´ ¬m Ä ¤ ² Ï´ ´ ¬³£ ³ q ³ [18]

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48

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

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เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

2

บทที่

49

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7) ³ Ë ¯ ·Ê 1 – 6 ¹¯Â É ´¥ ¯ ¥­³¬Â ¯¥qÄ ¥ ­ ¸Ê ¥¯ ¬Ï´­¥³ ´¥ ¯ ¥­³¬Â ¯¥qÄ Å

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x k M2ext xk ²Â §·Ê ¤ Æ Â ¹Ê ¯ ´ m ´ M2ext xk ²Â É m ´ Å­£m Ê· Æ n ´ ´¥ ¯ ¥­³ ¬

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50

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

·Ê ¶ ´ ¹Ë n¯ ¶ §´ (error floor) [2, 4] n ¯¤§ Æ n Å ´ ¶ ³ ¶© ¥¯¶  ¯¥q§·¡Â©¯¥q Ê·£·

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เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

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X1

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X3

X4

X5

X6

X7

X8

X9

X10

X11

X12

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X15

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X17

X18

X19

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n¯ Ï´­ S » Å n ¹Ê¯¥³ ¥¯ ©m´ n¯ ¶ §´ ·Ê ¶ ³ ­§´¤ ¶ ·Ê£· ©´£¤´© n ¯¤ ©m´ S

à £Â ¶ § ² » Ï´Å­n ¥² ³ ¥² ´¤Æ ¯¤m»Å ϴí m m´ È ¯ §Ï´ ³ n¯£»§ Å ´ ¶ ³ ¶ m´ S n¯

£· m´ n ¯¤ ©m´¥´ ·Ê¬¯ ¯ N/2 [28] ç²Ä ¤ ³Ê©Æ ¯³ ¥´ ¤´¤ ¯ © ¥¯¶  ¯¥q§·¡Â©¯¥qà ·Ë ²£· m´£´ ©m´ S ¬£¯

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SNR ÏÊ´ à m ²£·¬£¥¥ ² n ¯¤ ©m´© ¥¯¶  ¯¥q§·¡Â©¯¥qà ¬mº£Â ·¤£Â£¹Ê¯ Ï´ ´ ·Ê m´ SNR ¬»

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52

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

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» ¥ © n©¤¬³ ´ ¥ © nk N 0, T 2 £¹Ê¯ V2 = N0/(2T) ² » ¬m Æ ¤³ © ¥ ·£³§ ¶

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เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

รหัสเทอรโบ

¯³ ¥´ n¯ ¶ §´ ¯ ¶ (BER: bit-error rate) ç²Â¬n à x ¹¯ m´¯³ ¥´¬m© §³ ´ ¯ ¶

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¥» ·Ê 2.23 ¬£¥¥ ² ¯ ¥²  ¯¥qÄ ·Ê¥² ³ Eb/N0 m´ È

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à y ¹¯ m´ BER ç²Â¬n à x ¹¯ Ï´ © ¥¯ ¯ ´¥ ¯ ¥­³¬Ã © Ï´Ë ¸Ê Â­É Æ n ³ Â

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à m¯¯ º ¥£ (serial concatenated turbo code) ¸Ê Â É ¹Ë ´ ¯ ¯· ©¯Æ§Â ³ à  ¯¥qÄ (turbo equalization) ·Ê ²¯ ¶ ´¤ m¯Æ Å ­³© n¯ ·Ê 2.4

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54

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

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2) m´©¬´¥Ã ¯¡ q M1 wk ² » ¬m Æ ¤³ © ¥¯¶  ¯¥q§·¡Â©¯¥q ³ ( Q 1 )  ¹Ê¯¬§³ ϴí m

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M2ext wk ¸Ê Ï´­ n ´ ·ÊÂ É m´©¬´¥¯² ¶¥¶¯¯¥¶ ¯ §Ï´ ³ n¯£»§ wk Ä ¤ ²Å­n n¯£»§Â¯´ q º  É

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3) Ï´ © ­´ m´ m´©¬´¥Â¯ q ¥¶ ¶ M1ext uk M1 uk M2ext uk £¹Ê¯ M2ext uk ¹¯ m´©¬´¥ ¯ q ¥¶ ¶ ¯ ¶ n¯£»§ uk ·ÊÆ n ´ © ¥ ¯ ¥­³¬¢´¤ ¯ (outer decoder)

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

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4) © ¥ ¯ ¥­³¬¢´¤ ¯ ² Ï´ ´ Ä ¤Å n m´©¬´¥Â¯ q ¥¶ ¶ M1ext uk ç²Å­n n¯£»§Â¯´ q º Â É m´©¬´¥Ã ¯¡ q ¯ ¶ ·Ê »  n´¥­³¬ M2 uk ç² ¯ ¶ m´©¬´¥ M x k [31] 5) Ï´ © ­´ m´ m´©¬´¥Â¯ q ¥¶ ¶ M2ext uk M2 uk M1ext uk ·ÊÆ n ´ © ¥ ¯ ¥­³¬ ¢´¤ ¯ 6) m´©¬´¥Â¯ q ¥¶ ¶ M2ext uk ² » ¬m Æ ¤³ © ¥¯¶  ¯¥q§·¡Â©¯¥q ( Q )  ¹Ê¯¬§³ ϴí m ¯ n¯£»§Å­nÂ É m´©¬´¥Â¯ q ¥¶ ¶ ¯ ¶ n¯£»§ wk ­¥¹¯ M2ext wk ¸Ê ² » Ï ´Æ Å nÅ © ¥ ¯ ¥­³¬¢´¤Å ¬Ï´­¥³ ´¥ ¯ ¥­³¬Å ¥¯ ³ Æ 7) ³ Ë ¯ ·Ê 1 – 6 ¹¯Â É ´¥ ¯ ¥­³¬Â ¯¥qÄ Ã m¯¯ º ¥£ ¥ ­ ¸Ê ¥¯ ¬Ï´­¥³ ´¥

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ECC encoder

Interleaver

sk

Mapper

zk

Channel

nk

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Equalizer/ Detector

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Equalizer / SISO equalizer Demapper

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Interleaver

Deinterleaver ECC decoder

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ECC decoder

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เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

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©¶ · ´¥ ·Ë Ï´Æ n ¥¶ n´ m¯ ¬³ ´ £· Ï´ © Ã É (tap) Æ£m£´  ¥´² ²£· § m¯ Ï´ © ¬ ´ ²

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o ³ Ë ¯ ·Ê¬¯ ¹¯ ´¥ ¯ ¥­³¬ n¯£»§Ã ©¥ ²Â É ¬» ¬º (ML: maximum-likelihood) ­¥¹¯Ã ¯²Ä ¬Â ¯¥¶¯¯¥¶¬» ¬º (MAP: maximum a posteriori)

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­¥¹¯Æ nÂ É m´©¬´¥Ã ¯¡ q ¯ ¶ n¯£»§ sk ­¥¹¯ M sk ¸Ê ¸Ë ¯¤m» ³ ¥²Â¢ ¯ © ¥ ¥© ­´ (detector) ·ÊÅ n  m n´Å nÂ É © ¥ ¥© ­´©·Â ¯¥q ¶ É ²Æ n §§³ qÂ É sˆk à m n´Å n Â É © ¥ ¥© ­´ BCJR É ²Æ n §§³ qÂ É M sk Â É n ­§³ ´ ³ Ë © ¥ ¥© ­´ ²¬m §§³ q Ê·Æ nÆ ¤³ © ¥Â n´ m» ³ (de-mapper), © ¥¯¶  ¯¥q§·¡Â©¯¥q ³ (deinterleaver) 粩 ¥ ¯ ¥­³¬Ã nÆ n¯ ¶ §´ (ECC decoder)  ¹Ê¯­´ m´ ¥²£´ ¯ §Ï´ ³ n¯£»§ xk

­¥¹¯ xˆk

à ·Ê¬´£ (© ¥¢´ ¥³ C) Â É Ä ¥ ¬¥n´ ¯ ¥² © ´¥¯· ©¯Æ§Â ³ à  ¯¥qÄ (turbo equalization) §m´© ¹¯Å ´ ¶ ³ ¶Ã © ¶ ´ n´  ¯¥qÄ ( ·ÊÅ n© ¥ ¯ ¥­³¬¤m¯¤¬¯ © ¥

Ï´ ´¥Ã§  §·Ê¤ m´©¬´¥Ã ¯¡ q ¹Ê¯Å n ¯ ¥­³¬ n¯£»§) ¬´£´¥ Ï ´£´Å n ³ ¯· ©¯Æ§Â ³ Æ n m ³ ¸Ê  ¶ ·Ë ²Â¥·¤ ©m´¯· ©¯Æ§Â ³ à  ¯¥qÄ Ã§²© ¥¢´ ¥³ ·ÊÅ n ´  ¶ ·Ë

²Â¥·¤ ©m´ “¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ (turbo equalizer)” [21] Ä ¤¥² ·Ë ¬´£´¥ ¶ ´¥ ´ Æ n©m´Â É ¥­³¬Â ¯¥qÄ Ã m¯¯ º ¥£ ·Ê£· m¯ ¬³ ´ Ï´­ n ´ ·ÊÂ É ¥­³¬¢´¤Å (inner code) 粩 ¥Â n´¥­³¬ ECC Ï´­ n ´ ·ÊÂ É ¥­³¬¢´¤ ¯ (outer code) ¯ ´ ·Ë Ä ¥ ¬¥n´ ¯

© ¥ ¯ ¥­³¬ ²Â­£¹¯ ³ Ä ¥ ¬¥n´ ¯ © ¥ ¯ ¥­³¬Â ¯¥qÄ Ã m¯¯ º ¥£Å ¥» ·Ê 2.25

¤ ©n  ·¤ © ¥ ¯ ¥­³¬¢´¤Å ²Â §·Ê¤ Â É ¯· ©¯Æ§Â ¯¥qà SISO (SISO equalizer) ³ ì Å ¥» ·Ê 2.26 ­¥¹¯Â ·¤ Å­£mÆ nÂ É ¥» ·Ê 2.27

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

M x k

zk

Q 1 0

Q ¥» ·Ê 2.27 Ä ¥ ¬¥n´ ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ

nk xk

Q

ak

1 1 D 2

1 D 2

zk

¥» ·Ê 2.28 © ¥¢´ ¬m (¬Ï´­¥³ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ )

n¯ · ¯ Ä ¥ ¬¥n´ ·Ë ¹¯¥­³¬ ECC ·ÊÅ nÆ£m Ï´Â É n¯ Â É ¥­³¬Â ¯¥qÄ Â ¹Ê¯ Å­n¥² £·

¬£¥¥ ² ·Ê · ³©¯¤m´  m ´ ©¶ ³¤Å [33] Æ nì Å­nÂ­É ©m´¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ¬´£´¥

Ï´ ´ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ ¬Ï´­¥³ m¯ ¬³ ´ à PR-IV ·ÊÅ n© ¥Â n´¥­³¬ m¯ (precoder)

·Ê£·¥» ­º ´£ 1 / 1 D 2 ç²Å n¥­³¬ ¯ Ä©§» ³ Â É ¥­³¬ ECC ¯¤m´ Æ¥ É ´£°´¥q ¶¬ qÆ ¥¡q

¥mº Å­£mÈ ·ÊÅ n¥² ¯ ¥­³¬Ã © Ï´Ë ² ¶ ¤£Å n¥­³¬ LDPC [5, 8, 17] Â É ¥­³¬ ECC  ¥´²

£·¬£¥¥ ²¬» ¬º ( »¥´¤§²Â¯·¤ Å ·Ê 4)

n¯ ©¥¥²©³ ¯· ©¯Æ§Â ¯¥qà SISO Â É ¹Ê¯ ´  ¶ ·ÊÅ nÂ¥·¤ © ¥ ¥© ­´ ·Ê¬´£´¥ Å­n n¯£»§ ¯´ q º Â É m´©¬´¥Ã ¯¡ qÆ n ( ¹Ê¯ Ï ´£´Å nÅ ¥² © ´¥ ¯ ¥­³¬Ã © Ï´Ë ) à m¯· ©¯

Ƨ ¯¥qÂ É © ¥ ·Ê Ï´­ n ´ ·Ê ¥³ ¥» ¥m´ ¯ ¬³ ´ Å­nÂ É Æ ´£ § ¯ ¬ ¯ ´¥qÂ É (target

response) ´ ³ Ë É ² Ï ´ ´¥qÂ É ·Ë£´Å n¬¥n´ à ¢´  ¥§§¶¬¬Ï´­¥³ ¥© ­´ n¯£»§Ä ¤Å n¯· ©¯ ­ ³ ¬¹¯Â§m£ ·Ë ²Å­n ©´£¬Ï´ ³ ³ ´¥ Ï´ ´ ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Â ¥´²Â É

¯ q ¥² ¯ ­§³ ¬Ï´­¥³ °´¥q ¶¬ qÆ ¥¡q ÊÅ· n¥² ¯ ¥­³¬Ã © Ï´Ë Å ·Ê 5 ²Ã¬ Å­n­É

¬£¥¥ ²Ã§² ¥²Ä¤ q ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ¸Ê ¬´£´¥ Ï ´£´ ¥²¤º qÅ nà n ³ ­´ n´

รหัสเทอรโบ

Ƨ ¯¥qà SISO [5, 8]

m´ È Æ n  m Æ ££¶Ê ¥¶ ³¡Â©¯¥· (timing recovery) [34 – 36] ç² ´¥ ¥© ­´Ã§²Ã nÆ ©´£ ¥º ¥²Â ¶ ©´£¥n¯ (TA: thermal asperity) [37] Â É n

2

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2.4.1 ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ¶ ´¥ ´¥² ¬¹Ê¯¬´¥ ¶ ¶ ³§ ·Ê£·¯³ ¥´¥­³¬Â m´ ³ 8/9 Å ¥» ·Ê 2.28 £¹Ê¯ ¶ m´©¬´¥ xk ´ 3636

¶ m¯­ ¸Ê   ¯¥q Ê·£· ´ ©§´Â m´ ³ T »  n´¥­³¬ n©¤© ¥Â n´¥­³¬ ¯ Ä©§» ³ à £·¥² 3 4 ©·¤  ¶ ·Ê£·¯³ ¥´¥­³¬ R = 1/2 ç²£· ­º ´£ ³© Ï´Â ¶ ¹¯ ¡1, 1 D D 4D ¯° ´ ³ Ë É ² » ¬m  n´ 1 D D ¢ ± Æ ¤³ © ¥Â ´² (puncturer) [2]  ¹Ê¯Â ¶Ê£¯³ ¥´¥­³¬ ´ 1/2 Â É 8/9 Ä ¤ ³ ¶ ´¥¶ ¶Ë (parity bit) ¶ Ë Ï´ © 7 ¶ Å º È 8 ¶ ( ³©¯¤m´  m ¶ ´¥ ´© ¥Â n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.8 ( )

¶ ´¥¶ · É ¹¯ ¶ n¯£»§ yk ³Ê ¯ )  ¹Ê¯ Ï´Å­nÆ nÂ É §Ï´ ³ n¯£»§ ´ 4095 ¶ m¯­ ¸Ê   ¯¥q

´ ³ Ë ¸ ¬m m¯Æ ¤³ © ¥Â n´ m»Ã§²© ¥¯¶  ¯¥q§·¡Â©¯¥qà ¬mº£ S ·Ê£· S = 16 É ²Æ nÂ É §Ï´ ³

n¯£»§ ak çn© ɬm m¯Æ ¤³ © ¥Â n´¥­³¬ m¯ ·Ê£·¥» ­º ´£Â m´ ³ 1 / 1 D 2 ç² m¯ ¬³ ´ PR-IV ·Ê£·¥» ­º ´£ ¹¯ 1 – D2 N 0, T

¬³ ´ ·Ê© ¥¢´ ¥³ Æ n¥³ ¹¯§Ï´ ³ n¯£»§ zk ¸Ê » ¥ © n©¤¬³ ´ ¥ © nk a

2

£¹Ê¯ V2 = N0/(2T) ² » Ï´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ·Ê£·

Ä ¥ ¬¥n´ ´£¥» ·Ê 2.27  ·¤ à m ¶Ê£© ¥Â ´² ³ (depuncturer)  n´Æ Å ¥² ·Ê n´ ´Â n´ ¯ © ¥ ¯ ¥­³¬¢´¤ ¯ ç²Â ¶Ê£© ¥Â ´² (puncture) ¯· ­ ¸Ê © ¥ ·Ê n´ ´¯¯ ¯ © ¥

¯ ¥­³¬¢´¤ ¯ ¯ ´ ·Ë¯· ©¯Æ§Â ¯¥qà SISO 粩 ¥ ¯ ¥­³¬Ã SISO ²¬¥n´ £´

´ ¯³§ ¯¥¶ ¸£ BCJR Ä ¤Ã ¢´  ¥§§¶¬ ·ÊÅ nÅ ¯· ©¯Æ§Â ¯¥qà SISO ²¬¥n´ £´ ´ ´¥q É

·ÊÂ É §¥©£ ¯ © ¥Â n´¥­³¬ m¯ ç² m¯ ¬³ ´ [33]

¥» ·Ê 2.29 ì ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Å ¥» ¯ BER ¬Ï´­¥³ à m§²

¥¯ ¯ ´¥© Ï´Ë (iteration) Ä ¤ ·Ê m´ BER à m§² m´ ·ÊÆ n£´ ´ ´¥ n ¯ n¯£»§¯¶ º  n´Æ Å

¥² ­§´¤È   ¯¥q (1   ¯¥q£· 3636 ¶ ) ¥² ³ Ê £· n¯ ¶ §´ ¯ ¶ (bit error)  ¶ ¸Ë

Ï´ © £´ ©m´ 1000 ¶ ¥¯ ·Ê 10 ¯ ´¥ ¯ ¥­³¬Ã © Ï´Ë ¯ ´ ·Ë “0.5 iteration” ­£´¤ ¸ ¬£¥¥ ² ·Ê n´ ´¯¯ ¯ ¯· ©¯Æ§Â ¯¥qà SISO Å ² ·Ê¤³ Æ£m£· ´¥ Ï´ ´ Ã

© Ï´Ë (¯´ ¶ ´¥ ´Æ n©m´Â É ¬£¥¥ ² ¯ ¥² ·ÊÆ£m »  n´¥­³¬ (uncoded system) ÉÆ n) ´ ¥»

²Â­É Æ n©m´¥² £·¬£¥¥ ² · ¸Ë £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë ¸ ¥² ³ Ec /N0

­ ¸Ê ·Ê Ï´Å­n¬£¥¥ ² ¯ ¥² Â¥¶Ê£ ·Ê ²Æ£m£· ´¥Â §·Ê¤ à § ³©¯¤m´  m n´¥² Å n ´¥© Ï´Ë

Ï´ © 7 ¥¯ ³ ³ Ë Â£¹Ê¯ Ec /N0 > 5.5 dB ©m´¬£¥¥ ² ¯ ¥² Â¥¶Ê£ ·Ê ( ³Ê ¹¯¥²  ¶ ¹Ë n¯ ¶ §´ )

¥» ·Ê 2.30 ì ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Å ¥» ¯³ ¥´ n¯ ¶ §´ ¯

  ¯¥q (SER: sector error rate)  ·¤ ³ Ec /N0 ³Ê ¹¯ n´¢´¤­ ¸Ê   ¯¥q£· n¯ ¶ §´

¯ ¶  ¶ ¸Ë £´ ©m´­¥¹¯Â m´ ³ ­ ¸Ê ¶ É ¹¯©m´£· n¯ ¶ §´ ¯   ¯¥q ¶ ¸Ë ´ ¥» ² ©m´

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 2.29 ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Å ¥» ¯ BER  ·¤ ³ Ec /N0

¥² £· m´ SER § n ¯¤§ £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë ¸ m´ Ec /N0 ­ ¸Ê ¸Ê Ï´Å­n

รหัสเทอรโบ

¥» ·Ê 2.30 ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Å ¥» ¯ SER  ·¤ ³ Ec /N0

¬£¥¥ ² ¯ ¥² Â¥¶Ê£ ·Ê ¯ ´ ·Ë¥» ·Ê 2.31 ì ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Å ¥» ¯ SER  ·¤ ³ Ï´ © ¥¯ ¯ ´¥© Ï´Ë ¸Ê ©m´ ¥² ³ Ec /N0 ­ ¸Ê £¹Ê¯ Ï´ ©

¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë ¥² É ²£· m´ SER § n ¯¤§ ¸ Ï´ © ¥¯ ¯ ´¥© Ï´Ë ­ ¸Ê

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บทที่

61

¥» ·Ê 2.31 ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Å ¥» ¯ SER  ·¤ ³ Ï´ © ¥¯ ¯ ´¥© Ï´Ë

 m ·Ê Ec /N0 = 5.5 dB ¥² ²£·¬£¥¥ ² · ¸Ë Â¥¹Ê¯¤È ¸ ¥¯ ·Ê 7 ¯ ´¥© Ï´Ë ´ ³ Ë

¥² ²£·¬£¥¥ ² ·Ê ãn©m´ Ï´ © ¥¯ ¯ ´¥© Ï´Ë ²Â ¶Ê£ ¸Ë É ´£

´ § ´¥ §¯ ¬¥º Æ n©m´ ¥² ·ÊÅ n ´¥ ¯ ¥­³¬ n¯£»§Ã © Ï´Ë ­¥¹¯Â¥·¤ ©m´¥²

·Ê »  n´¥­³¬ (coded system) ²£·¬£¥¥ ² · ©m´¥² ·ÊÆ£m »  n´¥­³¬Â¬£¯ ³ ³ Ë ¸ Â É Â­ º § ·Ê Ï´Æ£°´¥q ¶¬ qÆ ¥q¡Å ³ º ³ ¸ Â¥¶Ê£ Ï ´¥² ´¥ ¯ ¥­³¬ n¯£»§Ã © Ï´Ë (Å ¥» ¯ ¯· ©¯ Ƨ ¯¥qà  ¯¥qÄ ) £´Å nÅ ¶ m¯ ¬³ ´ ¯m´

2.5 ¬¥º n´¤ ¥­³¬Â ¯¥qÄ ¹¯Â É ¥­³¬Ã nÆ n¯ ¶ §´ (ECC) ·Ê£·¬£¥¥ ²¬» £· ©´£ ³ n¯ Æ£m£´ ç²Å n

Â É £´ ¥ ´ ¬Ï´­¥³ ´¥ ¶ m¯¬¹Ê¯¬´¥ ¯ ¥² Ä ¥ª³ q §¹Ê¯ ·Ê¤º ·Ê¬´£ (3G: third generation) Ä ¤ ´¥Â n´¥­³¬Â ¯¥qÄ ²Å n© ¥Â n´¥­³¬ ¯ Ä©§» ³ £´ ©m´­ ¸Ê © ¥£´ m¯ ³ à ¯ º ¥£­¥¹¯ à ´ Ä ¤¯´ª³¤ ©´£ m©¤Â­§¹¯ ¯ © ¥¯¶  ¯¥q§·¡Â©¯¥q Å ² ·Ê ´¥ ¯ ¥­³¬Â ¯¥qÄ ²

Å n© ¥ ¯ ¥­³¬ BCJR £´ ©m´­ ¸Ê © ¥ ( m´ ³ Ï´ © © ¥Â n´¥­³¬ ·ÊÅ n) Ï´ ´¥Ã§  §·Ê¤

m´©¬´¥Ã ¯¡ q Ê ¸ ³ ç² ³ ¯ ´ ·Ë ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¥­³¬Â ¯¥qÄ ·Ë ¹¯Â É ´¥ ¯ ¥­³¬Ã © Ï´Ë (iterative decoding) ¸Ê ¬´£´¥ Ï ´£´ ¥²¤º qÅ n ³ ¥² © ´¥¯· ©¯Æ§Â ³

Æ nÄ ¤ ²Â¥·¤ ©m´¯· ©¯Æ§Â ³ à  ¯¥qÄ (turbo equalization) ¸Ê ¹¯Â É ¥² © ´¥ ¯ ¥­³¬

à © Ï´Ë ·ÊÆ n Ï´£´Å n ¥¶ Å °´¥q ¶¬ qÆ ¥¡q ¥mº Å­£mÈ

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

³ ³ Ë Å ·Ë ¸ Æ n¯ ¶ ´¤¯ q ¥² ¯ ç²­§³ ´¥ Ï´ ´ ¯  ¶ ´¥ ¯ ¥­³¬Ã

© Ï´Ë Ä ¤Â¥¶Ê£ ´ ´¥Â n´¥­³¬Ã§² ¯ ¥­³¬ ¯ Ä©§» ³ , ¯³§ ¯¥¶ ¸£ BCJR ·ÊÅ nÅ © ¥ ¯ ¥­³¬

 ¯¥qÄ , ´¥Â n´¥­³¬Ã§² ¯ ¥­³¬Â ¯¥qÄ Ã§²¯· ©¯Æ§Â ³ à  ¯¥qÄ ¥n¯£ ³ Ë Ã¬ ¬£¥¥ ²

¯ ¥­³¬Â ¯¥qÄ Ã§²¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Ä ¤ ´ § ´¥ §¯ ©m´¥² ·ÊÅ n ´¥ ¯ ¥­³¬

à © Ï´Ë ²£·¬£¥¥ ² · ©m´¥² ·ÊÆ£mÅ n ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë ¯ ´ ·Ë Ä ¤ ³Ê©Æ

¥² ·ÊÅ n ´¥ ¯ ¥­³¬Ã © Ï´Ë ²£·¬£¥¥ ² · ¸Ë £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë (£¹Ê¯

¥² Ï´ ´ ·Ê m´ SNR ¬»  ·¤ ¯)

2.6 Ã ¸ ­³ n´¤ 1. 2.

ì  ¥¹Ê¯ ¬ ´ ² Ï´ ³ (FSM) ç²Ã ¢´  ¥§§¶¬ ¯ © ¥Â n´¥­³¬Â ¯¥qÄ Å ¥» ·Ê

2.1 ( ) ç² 2.1 ( )

´ © ¥Â n´¥­³¬Â ¯¥qÄ ³ Ë ¬´£Ã Å ¥» ·Ê 2.1  n´¥­³¬§Ï´ ³ n¯£»§ m¯Æ ·Ë ¹Ê¯­´§Ï´ ³

n¯£»§Â¯´ q º yk1 ç² yk2 2.1) xk = {1 1 0 1} 2.2) xk = {1 0 1 0 1}

2.3) xk = {1 1 0 1 0 1} 3.

´ ³©¯¤m´ ·Ê 2.2 Å n© ¥Â n´¥­³¬ ¯ Ä©§» ³ Å ¥» ·Ê 2.6  ¹Ê¯Â n´¥­³¬§Ï´ ³ n¯£»§ m¯Æ ·Ë 3.1) {1 0 1 1} 3.2) {1 1 0 1 0 1} 3.3) {1 0 1 1 0 0 1 1}

4.

´ ³©¯¤m´ ·Ê 2.3 ¯ ¥­³¬§Ï´ ³ n¯£»§ m¯Æ ·Ë

รหัสเทอรโบ

4.1) zk = {10 01 11 01} 4.2) zk = {11 10 00 10 01} 4.3) zk = {01 00 10 11 00 10} 5.

2

¶¬» q¬£ ´¥ (2.26)

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6.

´ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 n´ Ï´­ Å­n§Ï´ ³ n¯£»§¯¶ º ak = {1, 1, –1}, m¯ ¬³ ´ H D 1 0.5D , ¬³ ´ ¥ © nk = {–0.2, –0.1, 0.2, 0.1} ç²£· ©´£Ã ¥ ¥©  m´ ³ T2 1/ 2Q ¯ ¥­³¬§Ï´ ³ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ BCJR n´ Ï´­ Å­n m´©¬´¥¯² ¶¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak £· m´Â m´ ³ Ma ak \0.2, 0.1, 0.2, 0^

7.

´ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 n´ Ï´­ Å­n§Ï´ ³ n¯£»§¯¶ º ak = {1, 1, –1}, m¯ ¬³ ´ H D 1 2D D 2 , ¬³ ´ ¥ © nk = {–0.2, –0.3, 0.2, –0.4, 0.3} ¯ ¥­³¬§Ï´ ³ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ BCJR n´ Ï´­ Å­n m´©¬´¥¯² ¶¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak £· m´Â m´ ³ Ma ak \0.2, 0.1, 0.2, 0, 0^

8.

´ © ¥Â n´¥­³¬Â ¯¥qÄ Å ¥» ·Ê 2.18  n´¥­³¬§Ï´ ³ n¯£»§ {x0 x1 x2 x3} = {1 0 1 1} £¹Ê¯

© ¥¯¶  ¯¥q§·¡Â©¯¥q Ê·Å n ²Å­n §§³ q ¹¯ {x2 x0 x3 x1} ç² ­º ´£ ³© Ï´Â ¶ ¯ © ¥

 n´¥­³¬¤m¯¤ ³ Ë ¬¯ ¹¯

8.1) (g1, g2) = (07, 05) 8.2) (g1, g2) = (17, 11) 8.3) (g1, g2) = (23, 37) 8.4) (g1, g2) = (37, 21) Ä ¤ ·Ê g1 ¹¯ ­º ´£ n ¯ §³ ç² g2 ¹¯ ­º ´£ n ¯ n´ ­ n ´ 9.

¯ ¶ ´¤­§³ ´¥ Ï´ ´ ç² ©´£¬Ï´ ³ ¯ © ¥¯¶  ¯¥q§·¡Â©¯¥q

10. ¯ ¶ ´¤ ©´£­£´¤ ¯ m´©¬´¥Â¯ q ¥¶ ¶ 11. ¯ ¶ ´¤ ©´£Ã m´ ¥­³¬Â ¯¥qÄ Ã m¯ ´ ç²¥­³¬Â ¯¥qÄ Ã m¯¯ º ¥£ 12. ¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ © ¥Â ´² (puncturer) ¥n¯£ ³ Ë Ã¬ ³©¯¤m´ ´¥ Ï´ © ¥² ¯ 13. ¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ¯· ©¯Æ§Â ³ à  ¯¥qÄ

64

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

·Ê 3 © ¥ ¥© ­´Ã ¯¡ q ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q Å ³ º ³ Â¥¶Ê££· ´¥ Ï ´¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë £´Å nÅ ´¥ ¯ ¥­³¬ n¯£»§ Ä ¤¯ q ¥² ¯ ­§³ ·Ê¬Ï´ ³ Å ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë

É ¹¯© ¥ ¥© ­´Ã ¯¡ q (soft detector) 粩 ¥ ¯ ¥­³¬Ã ¯¡ q (soft decoder) ¸Ê ² Ï´­ n ´ ·Êç  §·Ê¤ m´©¬´¥Ã ¯¡ q (soft information) ¥²­©m´ ³  ¹Ê¯ m©¤Å­n¬£¥¥ ²

¯ ¥² ·£´ ¸Ë Å Ã m§²¥¯ ¯ ´¥© Ï´Ë ´ ·Ê §m´©£´Å ·Ê 2 ¯³§ ¯¥¶ ¸£ BCJR [18]

Â É ¯³§ ¯¥¶ ¸£¯²Ä ¬Â ¯¥¶¯¯¥¶¬» ¬º (MAP: maximum a posteriori) ç²Â­£´² ·Ê¬º (optimal)

Å ´¥­´ m´ ¥²£´ ¯ ¬ ´ ²­¥¹¯ n¯£»§Â¯´ q º ¯ ¥² © ´¥£´¥q ¯¡ (Markov process) ³ ³ Ë Å m© Ã¥ ·Ê£· ´¥ ¶ n ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë [3] ¸ Æ n Ï´¯³§ ¯¥¶ ¸£ BCJR £´Å n

¬¥n´ © ¥ ¥© ­´Ã ¯¡ q粩 ¥ ¯ ¥­³¬Ã ¯¡ q

¸ ãn©m´ ´¥ Ï´ © ­´Â£ ¥¶ ¬ ´ ² (state metric) Å ¯³§ ¯¥¶ ¸£ BCJR ²£·§³ « ²

Â É Ã Â©·¤  ¶ (recursive) ¸Ê Ï´Å­n m´¤Å ´¥ ¯ ¥­³¬ n¯£»§ ¯¤m´ Æ¥ É ´£¯³§ ¯¥¶ ¸£ BCJR

Æ£m ¶¤£ Ï ´Æ Å n ¥¶ Å ¶ ¥²£©§¬³ ´ ¯ ­§´¤È ´ ¥²¤º q  ¥´²Å n ¥³ ¤´ ¥Å ´¥

Ï´ © ¬» ( m Ï´ © ³© Ï´Â ¶ ´¥ © ç² ´¥ » ) ç²Å n¡³ q ³ à ƣmÂ É Â ¶ ¬n Å ´¥

Å ¥² [23, 24] ³ ³ Ë ³ ©¶ ³¤ ¸ Æ n ³ ´¯³§ ¯¥¶ ¸£ ·Ê­£¹¯ MAP (MAP-like algorithm)

·Ê Ï´ ´ Å Ä Â£ §¯ ´¥¶ ¸£ (logarithm domain) ¸Ê ¬´£´¥ à n ³ ­´Â¥¹Ê¯ ´¥ Ï´ ©  ¶ ³©Â§ ç²£· ©´£ ³ n¯ n ¯¤ ©m´£´ £¹Ê¯Â ·¤ ³ ¯³§ ¯¥¶ ¸£ BCJR

Å ·Ë ²¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ ·Ê­£¹¯ MAP ­§m´ ·Ë ¸Ê Æ nà m Max-

Log-MAP [23, 24, 38, 39], Log-MAP [23, 24], ç² SOVA (soft-output Viterbi algorithm)

[19, 42] ¸Ê £·¬£¥¥ ²Å §n ·¤ ­¥¹¯Â ·¤  m´¯³§ ¯¥¶ ¸£ BCJR ¥n¯£ ³ Ë Ã¬ ¬£¥¥ ²Ã§²  ¥·¤  ·¤ ©´£ ³ n¯ ¯ ¯³§ ¯¥¶ ¸£ m´ È ³ Ë ­£

รหัสเทอร โบ วงจรตรวจหาแบบซอฟต

Ï´ © ( m ¡³ q ³ § · Ë Ï´§³ ) ¥©£ ³ Ë £· ©´£¯m¯ Æ­© m¯ m´ ©´£Ã ¥ ¥© ¯ ¬³ ´ ¥ ©

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65

¥» ·Ê 3.1 ©´£¬³£ ³ q ¯ MAP, Log-MAP, Max-Log-MAP, ç² SOVA

3.1 Ï ´ © ¥ ¥© ­´©·Â ¯¥q ¶ (Viterbi detector) [10, 13] Â É © ¥ ¥© ­´Ã ©¥ ²Â É ¬» ¬º ­¥¹¯

© ¥ ¥© ­´Ã ML (maximum-likelihood) Ä ¤ n¯£»§Â¯´ q º ·ÊÆ n ²Â É m´ ¥²£´ ¯ §Ï´ ³ n¯£»§ ·Ê n¯ ´¥ ¥© ­´ ­¥¹¯¯´ §m´©Æ n©m´© ¥ ¥© ­´Ã ML ² Ï´Å­n n¯ ¶ §´ ¯ §Ï´ ³

n¯£»§£· m´ n ¯¤¬º à mÆ£mÆ n¥³ ¥² ³ ©m´ ¶ n¯£»§Ã m§² ¶ ·Ê¯¤m»Å §Ï´ ³ n¯£»§ ³ Ë Â É ¶ n¯£»§ ·Ê

·¬º ³Ê ¹¯© ¥ ¥© ­´Ã ML Æ£mÆ n Ï´Å­n ¶ n¯£»§Ã m§² ¶ £· n¯ ¶ §´ n ¯¤¬º ¯ ´ ·Ë

© ¥ ¥© ­´©·Â ¯¥q ¶Æ£m¬´£´¥ Ï ´£´Å nÅ ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë Æ n  ¥´²¥² ·Ë ²£· ´¥

ç  §·Ê¤ m´©¬´¥Ã ¯¡ q (­¥¹¯ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§) ¥²­©m´ © ¥ ¥© ­´Ã SISO

(soft input soft output) 粩 ¥ ¯ ¥­³¬Ã SISO

¯³§ ¯¥¶ ¸£ BCJR Â É ¯³§ ¯¥¶ ¸£Ã MAP ·ÊÆ n » Ï ´£´Å nÅ ¥² ´¥ ¯ ¥­³¬Ã

© Ï´Ë Å m© Ã¥ ¯¤m´ Æ¥ É ´£¯³§ ¯¥¶ ¸£ BCJR £· n¯ Ï´ ³ Å ´¥ Ï ´Æ Å n ¥¶ Å ¶ ¥²£©§ §

¬³ ´ ¯ ­§´¤È ´ ¥²¤º q ³ ³ Ë ³ ©¶ ³¤ ¸ Æ n ³ ´¯³§ ¯¥¶ ¸£ Max-Log-MAP ç²

SOVA ¸Ê £·¬£¥¥ ²Å §n ·¤ ³ ¯³§ ¯¥¶ ¸£ BCJR ´ ³ Ë Å Â©§´ m¯£´ ¸ Æ n ³ ´¯³§ ¯¥¶ ¸£ Log-MAP ·Ê£·¬£¥¥ ²Â ·¤  m´ ³ ¯³§ ¯¥¶ ¸£ BCJR à m£· ©´£ ³ n¯ n ¯¤ ©m´£´ ¸ Ï´Å­n

¬´£´¥ Ï ´Æ Å n ¥¶ Å ¶ ¥²£©§ §¬³ ´ Æ n ¥» ·Ê 3.1 ì ©´£¬³£ ³ q ¯ ¯³§ ¯¥¶ ¸£Ã

MAP 粯³§ ¯¥¶ ¸£ ·Ê­£¹¯ MAP

3.2 ¯³§ ¯¥¶ ¸£ MAX-LOG-MAP ¯³§ ¯¥¶ ¸£ Max-Log-MAP [23, 24, 38, 39] ³ ´£´ ´ ¯³§ ¯¥¶ ¸£ BCJR Ä ¤¯´ª³¤¡³ q ³

m´¬» ¬º (maximum function) 粡³ q ³ §¯ ´¥¶ ¸£ (logarithm function) Ä ¤£· º ¥²¬ q

­§³  ¹Ê¯Å­n¬´£´¥ Ï ´£´Å n ¥¶ Å ´ ¶ ³ ¶Æ n ( ³Ê ¹¯Å nÅ ¶ ¥²£©§ §¬³ ´ Æ n) 粤³

£·¬£¥¥ ²Å §n ·¤ ³ ¯³§ ¯¥¶ ¸£ BCJR Ä ¤ ³Ê©Æ ¯³§ ¯¥¶ ¸£ Max-Log-MAP ² ¹¯©m´Â É

¯³§ ¯¥¶ ¸£Â­£´² ·Ê¬º à ¥¯ (suboptimal) ¸Ê Å­n n¯£»§Â¯´ q º à ¯¡ q Ê·£· º ¢´ n¯¤ ©m´ n¯£»§Â¯´ q º à ¯¡ q ¯ ¯³§ ¯¥¶ ¸£ BCJR

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´ à ϴ§¯ m¯ ¬³ ´ 粬£ ´¥ m´ È ¯ ¯³§ ¯¥¶ ¸£ BCJR Å ­³© n¯ ·Ê 2.2

´¥ Ï´Å­n¯³§ ¯¥¶ ¸£ Max-Log-MAP ¯¤m»Å ¥» ·Ê m´¤ m¯ ´¥ Ï ´Æ Å n ´ ¥¶ ²¯´ª³¤Â¯ §³ « q ln x ¯ §¯ ´¥¶ ¸£ ·Ê©m´ xi e i 粬» ¥ ´¥ ¥²£´ m´§¯ ´¥¶ ¸£ [24]

(3.1)

ln e x1 e x 2 ! e xn x max xi

i \1,...,n ^

£¹Ê¯ xi ¹¯Â§ Ï´ © ¥¶ ç² n ¹¯Â§ Ï´ ©  ɣ © ³ ³ Ë m´ LLR ¯ ¶ n¯£»§ ak Å ¬£ ´¥

(2.24) ³ ¥» Å­£mÆ n É

¬­ ¬­ M p ak ln Bk u Hk u , q Ck 1 q ­­­ ln B k u Hk u , q Ck 1 q ­­­ (3.2) ­ ­ u ,q S1 ®­ u ,q S 1 ®­

¶ ´¥ ´ qÃ¥ ´ n´ ©´£¹¯ ¯ ¬£ ´¥ (3.2) ²Æ n ¬­ ¬ ln B u H u ,q Ck 1 q

­ ­ Bk u Hk u ,q Ck 1 q ­­­ ln ln e k k ­­­ ­­ u ,q S ­ ® u ,q S1 ® 1

¬ ln B u

ln Hk u ,q

ln Ck 1 q

­ ­­ e k ln ­­ u ,q S ®­ 1 ¬ u H u ,q C B q ­ e k k k 1 ­­­ ln ­ u ,q S ®­ 1

(3.3)

Hk u ,q ln Hk u ,q

(3.4)

k u ln B k u

B

(3.5)

C q ln C q

k 1 k 1

(3.6)

£¹Ê¯

วงจรตรวจหาแบบซอฟต

3

บทที่

´ ¬£ ´¥ (3.1) Ï´Å­n ¥²£´ m´¬£ ´¥ (3.3) Æ n É

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67

¬­ u Hk u , q Ck 1 q

Bk u Hk u ,q Ck 1 q ­­­ x max B ln ­­ u ,q S1 k u ,q S1 ®

(3.7)

Å Ï´ ¯  ·¤© ³ q ʬ · ¯ ´ n´ ©´£¹¯ ¯ ¬£ ´¥ (3.2) ²Æ n©m´ ¬­ u Hk u ,q C k 1 q

ln Bk u Hk u , q Ck 1 q ­­­ x max B ­­ u ,q S 1 k u ,q S ® 1

(3.8)

à m´¬£ ´¥ (3.7) ç² (3.8) § Å ¬£ ´¥ (3.2) ²Æ n m´ LLR ¯ ¶ n¯£»§ ak ¬Ï´­¥³ ¯³§ ¯¥¶ ¸£ Max-Log-MAP £· m´Â m´ ³

k u Hk u , q Ck 1 q

max M p ak x max B u ,q S1

u ,q S 1

B k u H k u ,q C k 1 q

(3.9)

´¥­´ m´ Hk u ,q Å ¬£ ´¥ (3.4) Ŭm¡³ q ³ §¯ ´¥¶ ¸£ ¥¥£ ´ ¶ ³ Ë ¬¯ n´ ¯ ¬£ ´¥ (2.29) ²Æ n£ ¥¶ ¬´ ´Å­£m ¹¯ 1 ¬­ aˆ u ,q M a ­­ 1 yk rˆ u ,q 2 a k

Hk u ,q ln 2 2 2QT2 ®­­ 2T

(3.10)

´¥­´ m´ B k u Å ¬£ ´¥ (3.5) Ŭm¡³ q ³ §¯ ´¥¶ ¸£ ³ Ë ¬¯ n´ ¯ ¬£ ´¥ (2.14) ²Æ n Q 1 Q 1 ¬ ­¬ ln H u ,q Bk u

­ ­­ k 1 q ln B k 1 q

ln e k B Hk u ,q B k u ­­­ ln ­­ ­ ® ® u 0 u 0

Q 1 ¬ ln H u ,q

ln Bk u

­ ­­ ln e k ­ u 0 ®­

Q 1 ¬ H u ,q B u ­ ln e k k ­­­ ®­ u 0

´ ¬£ ´¥ (3.1) Ï´Å­n ¥²£´ m´¬£ ´¥ (3.11) Æ n É

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(3.11)

(3.12)

k 1 q x max Hk u ,q B k u

B u

¬Ï´­¥³ º ¬ ´ ² q ·Ê Ï´Å­n ´¥Â §·Ê¤ ¬ ´ ² (u, q) Å Ã ¢´  ¥§§¶¬Â É ¥¶

´¥­´ m´ Ck 1 q Å ¬£ ´¥ (3.6) Ŭm¡³ q ³ §¯ ´¥¶ ¸£ ³ Ë ¬¯ n´ ¯ ¬£ ´¥ (2.16) ²Æ n Q 1 ¬­ Q 1 ¬ ln Ck 1 q Hk u ,q

­ ­­ ln ­­ C u ln C u

ln C H q u , q e

k k k 1 k ­­ ­ q 0 ®­ q 0 ®­­

Q 1 ¬ ln C q

ln Hk u ,q

­ ­ ln e k 1 ­­­ q 0 ®­

Q 1 ¬ C q H u ,q ­ e k 1 k ­­­ ln q 0 ®­­

(3.13)

Å Ï´ ¯  ·¤© ³ ´ ¬£ ´¥ (3.1) Ï´Å­n ¥²£´ m´¬£ ´¥ (3.13) Æ nÂ É C u x max C q H u ,q

k k 1 k

(3.14)

q

3.2.1 ¬¥º ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ £ ¸ Max-Log-MAP ¯³§ ¯¥¶ ¸£ Max-Log-MAP £· ³ Ë ¯ ´¥ Ï´ ´ m´ È Â­£¹¯ ³ ¯³§ ¯¥¶ ¸£ BCJR Å ¥» ·Ê 2.12

 ·¤ à m¯³§ ¯¥¶ ¸£ Max-Log-MAP ²Å n¬£ ´¥ (3.9) Å ´¥­´ m´ LLR ¯ ¶ n¯£»§ ak Ä ¤ ·Ê u ç² C q ­´Æ n ´ ¬£ ´¥ (3.10), (3.12) ç² (3.14) ´£ ´¥´£¶Â ¯¥q H u ,q , B k

k

k 1

§Ï´ ³ ¥» ·Ê 3.2 ¬¥º ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ Max-Log-MAP ­£´¤Â­ º ´¥ Ï ´¯³§ ¯¥¶ ¸£ Max-Log-MAP Å ¥» ·Ê 3.2 Æ Å n ´ ¥¶ Å ´ ¶ ³ ¶ Æ£m Ï´Â É n¯ u ç² C u ¬Ï´­¥³ º ¬ ´ ² Ï´ ´¥ ¯¥q£¯§Æ§Â ³ (normalization) m´Â£ ¥¶ ¬ ´ ² B k

k

u ç² º ©§´ k  m  ·¤© ³ ·Ê Ï´Å ¯³§ ¯¥¶ ¸£ BCJR  ¥´²¯³§ ¯¥¶ ¸£ Max-Log-MAP ²Æ£m

วงจรตรวจหาแบบซอฟต

¬Ï´­¥³ º ¬ ´ ² u ·Ê Ï´Å­n ´¥Â §·Ê¤ ¬ ´ ² (u, q) Â É ¥¶ Å Ã ¢´  ¥§§¶¬

3

บทที่

³ ­´Â¥¹Ê¯ n ¯¤Â ¶ Â É Â ¶ ³©Â§ (numerical underflow)

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

69

¯³§ ¯¥¶ ¸£ Max-Log-MAP

0 0 , B 0 1 ,!, B 0 Q 1 ¯± < 0, d,!, d> 1. Ï´­ m´Â¥¶Ê£ n £ ¥¶ ¬ ´ ² ¢B 2. ´¥Â©·¤  ¶ à n´ ­ n ´ (forward recursion) ¬Ï´­¥³ k 0,1, !, L O 1 ¬Ï´­¥³ q 0,1, !,Q 1 Ï´ © ­´ m´ Hk u ,q ´£¬£ ´¥ (3.10) ¬Ï´­¥³ º u ·Ê Ï´Å­n (u, q) Â É ¥¶

k 1 q ´£¬£ ´¥ (3.12) Ï´ © ­´ m´ B (¬¶ Ë ¬º ´¥© Ï´Ë ¯ q) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ k) 3. Ï´­ m´Â¥¶Ê£ n £ ¥¶ ¬ ´ ²10 ¡ CL O 0 , CL O 1 , !, CL O Q 1 ¯° < 0, d,!, d>

¢

±

4. ´¥Â©·¤  ¶ à ¤n¯ §³ (backward recursion) ¬Ï´­¥³ k L O 1, L O 2, !, 0 ¬Ï´­¥³ u 0,1, !,Q 1 Ï´ © ­´ m´ Hk u ,q ´£¬£ ´¥ (3.10) ¬Ï´­¥³ º q ·Ê Ï´Å­n (u, q) Â É ¥¶ Ï´ © ­´ m´ Ck u ´£¬£ ´¥ (3.14) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ u) Ï´ © ­´ m´ M p ak ´£¬£ ´¥ (3.9) ³ ¬¶ Å ­´ m´ ak ´£¬£ ´¥ (2.25) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ k) ¥» ·Ê 3.2 ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ Max-Log-MAP

³©¯¤m´ ·Ê 3.1 ´ ³©¯¤m´ ·Ê 2.4 ì ³ Ë ¯ ´¥ ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ MaxLog-MAP ç² Ï´­ Å­n m´©¬´¥¯² ¶¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ¹¯ Ma ak = {2, –2, 2, 0} ©¶ · Ï´

´ ³©¯¤m´ ·Ê 2.4 n¯£»§ ·Ê ¯ n ´¥Å­nÅ n¯³§ ¯¥¶ ¸£ Max-Log-MAP ¥© ­´ ¹¯ yk {y 0 , y1 , y 2 , y3 } {0.9, 0.2, 0.3, 0.6}

10

£¹Ê¯¬££ ¶©m´£· ´¥ ³ ³ Å­n º ¬n ¬´ ´Å à ¢´  ¥§§¶¬¬¶ Ë ¬º ·Ê¬ ´ ² Z L O 0 £¶ ² ³ Ë n¯ Ï´­ m´Â¥¶Ê£ n ¯ CL O q B L O q ¬Ï´­¥³ º ¬ ´ ² q

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

ç²Ã ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ H D 1 0.5D ì Å ¥» ·Ê 2.13 ¸Ê £·¬¯ ¬ ´ ² ¹¯¬ ´ ² (a) 粬 ´ ² (b) ³ ³ Ë ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¯³§ ¯¥¶ ¸£ Max-Log-MAP £· ³ Ë ¯ ´¥ Ï´ ´ ³ ·Ë

0 a 0 ç² B 0 b d 1. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬ ´ ² B

´¥Â©·¤  ¶ à n´ ­ n ´ 2. ¥²¤² ·Ê 0 (£¹Ê¯ k = 0) ¯³§ ¯¥¶ ¸£ Max-Log-MAP ¥³ n¯£»§ y0 = 0.9 ç² Ma a 0 2 £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ H 0 u , q ´£¬£ ´¥ (3.10) ¬Ï´­¥³ º m´ u ç² q ·Ê Ï´Å­n ´¥Â §·Ê¤ ¬ ´ ² (u, q) Â É ¥¶ ´£Ã ¢´  ¥§§¶¬Å ¥» ·Ê 2.13 ¸Ê ²Æ n 2

H 0 a ,a 0 Q 0.9 1.5

2

H 0 b ,a 0 Q 0.9 0.5

2

H 0 a ,b 0 Q 0.9 0.5

2

H 0 b ,b 0 Q 0.9 1.5

1 2

2

1 2

2

1 2

2

1 2

2

x 19.0956 x 7.1575

x 0.4973 x 0.1309

 ¹Ê ¯ ´ T2 1/ 2Q ´ ³ Ë Ï´ ´¥ ¥³ m´Â£ ¥¶ ¬ ´ ² ´£¬£ ´¥ (3.12) ³ ·Ë 1 a max \B 0 a H 0 a , a , B 0 b H 0 b ,a ^ B

1 b max \B 0 a H 0 a ,b , B 0 b H 0 b , b ^ B max \0 0.4973 , d 0.1309 ^ 0.4973

วงจรตรวจหาแบบซอฟต

max \0 19.0956 , d 7.1575 ^ 19.0956

3. ¥²¤² ·Ê 1 (£¹Ê¯ k = 1) ¯³§ ¯¥¶ ¸£ Max-Log-MAP ¥³ n¯£»§ y1 = –0.2 ç² Ma a1 2 £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ ³ ·Ë 2

H1 a , a 0 Q 0.2 1.5

1 2

2

3

x 4.3093

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บทที่

71

2

H1 b , a 0 Q 0.2 0.5

2

H1 a , b 0 Q 0.2 0.5

2

H1 b , b 0 Q 0.2 1.5

1 2

2

1 2

2

1 2

2

x 0.7173

x 2.5394 x 10.0792

2 a ç² B 2 b ³ ·Ë ´ ³ Ë Ï´ ´¥ ¥³ m´Â£ ¥¶ ¬ ´ ² B 2 a max \B 1 a H1 a ,a , B 1 b H1 b ,a ^ B max \ 19.0956 4.3093 , 0.4973 0.7173 ^ 1.2146 2 b max \B 1 a H1 a ,b , B 1 b H1 b ,b ^ B max \ 19.0956 2.5394 , 0.4973 10.0792 ^ 9.5819

4. ¥²¤² ·Ê 2 ç² 3 (£¹Ê¯ k = {2, 3}) ¯³§ ¯¥¶ ¸£ Max-Log-MAP ¥³ n¯£»§ {y2, y3}= {0.3,

0.6} ç² \Ma a 2 , Ma a 3 ^ \2, 0^ £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ ç² ¥³ m´Â£ ¥¶ k 1 q ¬Ï´­¥³ q {a, b}  m  ·¤© ³ ³ ©¶ · ´¥ ·Ê¯ ¶ ´¤Å ³ Ë ¯ ·Ê 2 ç² 3 ¬ ´ ² B

k 1 q ´£ ·Êì Å ¥» ·Ê 3.3 Ä ¤ m´ ·Ê¯¤m» ¶ ³ ¬n ¬´ ´Ã m§² ¸Ê ²Æ n m´ Hk u , q ç² B

¬n ¹¯ m´ Hk u ,q ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² (u, q) ³ Ë È Ã§² ³©Â§ ·Ê¯¤m» ¥ Ä­ k u ç² Ck u Å ¥» ª«¬m© ³ ·Ë ¯ à m§²¬ ´ ²Ã¬ ¸ m´Â£ ¥¶ ¬ ´ ² B k u

B C u

k

Ë ¬º ´¥ Ï´ ´ Å m© ´¥Â©·¤ ¬Ï´­¥³ à m§² k {0, 1, 2, 3} ç² u {a, b} ³Ê ¹¯Â£¹Ê¯¬¶  ¶ à n´ ­ n ´ (forward recursion) É ²Æ n 4 a 1.7124 B

ç²

4 b 0.4558 B

4 u ¬Ï´­¥³ u {a, b} ³Ê ¹¯ 5. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬ ´ ² C4 u B C a 1.7124 4

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

ç²

C b 0.4558 4

¥» ·Ê 3.3 ´¥ Ï´ © ¢´¤Å ¯³§ ¯¥¶ ¸£ Max-Log-MAP Å ³©¯¤m´ ·Ê 3.1

´¥Â©·¤  ¶ à ¤n¯ §³ 6. ¥²¤² ·Ê 3 (£¹Ê¯ k = 3) ¯³§ ¯¥¶ ¸£ Max-Log-MAP ¥³ n¯£»§ y3 = 0.6 ç² Ma a 3 0 £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ É ²Æ n

2

H 3 b ,a 0 Q 0.6 0.5

2

H 3 a ,b 0 Q 0.6 0.5

2

H 3 b ,b 0 Q 0.6 1.5

1 0

2

1 0

2

1 0

2

1 0

2

x 13.8544 x 3.8013

x 0.0314 x 2.5447

´ ³ Ë Ï´ ´¥ ¥³ m´Â£ ¥¶ ¬ ´ ² C3 a ç² C3 b ³ ·Ë C a max \ H a , a C a , H a ,b C b ^ 3 3 4 3 4

max \ 13.8544 1.7124 , 0.0314 0.4558 ^ 0.4872

วงจรตรวจหาแบบซอฟต

2

H 3 a ,a 0 Q 0.6 1.5

C b max \ H b , a C a , H b ,b C b ^ 3 3 4 3 4

max \ 3.8013 1.7124 , 2.5447 0.4558 ^ 3.0005

3

บทที่

´ ³ Ë Ï´ ´¥ Ï´ © ­´ m´ M p a3 ´£¬£ ´¥ (3.9) ³Ê ¹¯

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73

\

3 a H 3 a ,b C4 b

, M p a 3 x max B

B 3 b H3 b,b C4 b

^

\

3 a H3 a ,a C4 a

, max B

B 3 b H3 b ,a C4 a

^

max \ 9.9642 0.0314 0.4558 , 2.0889 2.5447 0.4558 ^ max \ 9.9642 13.8544 1.7124 , 2.0889 3.8013 1.7124 ^ 0.9116 3.4248 2.5132

 ¹Ê ¯ ´ M p a3 0 ³ ³ Ë ¯³§ ¯¥¶ ¸£ Max-Log-MAP ² ¯ ¥­³¬ n¯£»§Â É aˆ3 1 7. ¥²¤² ·Ê 2 (£¹Ê¯ k = 2) ¯³§ ¯¥¶ ¸£ Max-Log-MAP ¥³ n¯£»§ y2 = 0.3 ç² Ma a 2 2 £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ É ²Æ n 2

H 2 a ,a 0 Q 0.3 1.5

2

H 2 b , a 0 Q 0.3 0.5

2

H 2 a ,b 0 Q 0.3 0.5

2

H 2 b ,b 0 Q 0.3 1.5

1 2

2

1 2

2

1 2

2

1 2

2

x 11.1788 x 3.0106

x 0.8743 x 3.5239

´ ³ Ë Ï´ ´¥ ¥³ m´Â£ ¥¶ ¬ ´ ² C2 a ç² C2 b ³ ·Ë C a max \ H a ,a C a , H a , b C b ^ 2 2 3 2 3

max \ 11.1788 0.4872 , 0.8743 3.0005 ^ 2.1262 C b max \ H b ,a C a , H b , b C b ^ 2 2 3 2 3

max \ 3.0106 0.4872 , 3.5239 3.0005 ^ 3.4978

´ ³ Ë Ï´ ´¥ Ï´ © ­´ m´ M p a 2 ´£¬£ ´¥ (3.9) ³Ê ¹¯

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

\

2 a H 2 a , b C3 b

, M p a 2 x max B

B 2 b H 2 b,b C 3 b

^

\

2 a H 2 a , a C3 a

, max B

B 2 b H 2 b ,a C3 a

^

max \ 1.2146 0.8743 3.0005 , 9.5819 3.5239 3.0005 ^ max \ 1.2146 11.1788 0.4872 , 9.5819 3.0106 0.4872 ^ 0.9116 10.451 9.5394

 ¹Ê ¯ ´ M p a 2 0 ³ ³ Ë ¯³§ ¯¥¶ ¸£ Max-Log-MAP ² ¯ ¥­³¬ n¯£»§Æ nÂ É aˆ2 1 8. ¥²¤² ·Ê 1 ç² 0 (£¹Ê¯ k = {1, 0}) ¯³§ ¯¥¶ ¸£ Max-Log-MAP ¥³ n¯£»§ {y1, y0}= {–0.2,

0.9} ç² \Ma a 0 , Ma a1 ^ \2, 2^ £´Å n Ï´ © ­´Â£ ¥¶ ¬´ ´ ³ Ë ­£ ç² ¥³ m´Â£ ¥¶

Ë ¯ ·Ê 6 ç² 7 É ² ¬ ´ ² Ck u ¬Ï´­¥³ u {a, b}  m  ·¤© ³ ³ ©¶ · ´¥ ·Ê¯ ¶ ´¤Å ³ Ë ¬º ´¥Â©·¤  ¶ à ¤n¯ Æ n m´ H u ,q ç² C u ´£ ·Êì Å ¥» ·Ê 3.3 ³ ³ Ë Â£¹Ê¯¬¶ k

k

§³ ²Æ n M p a 0 24.221

ç²

M p a1 12.168

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9. £¹Ê¯¬¶ Ë ¬º ´¥ Ï´ ´ ¯³§ ¯¥¶ ¸£ Max-Log-MAP ²Å­n m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¯ ¥­³¬ ¶ n¯£»§Æ nÂ É \aˆ0 , aˆ1 , aˆ2 ,aˆ3 ^ \1, 1,1,1^

( ¶ ¬º n´¤Æ£m£·¯¤m» ¥¶ Å ¥² à m

Â É §§³ q Ê·Â ¶ ´ ´¥ Ï´ ¯ Ä©§» ³ ) ¸Ê ¥ ³ ¶ n¯£»§ {ak}

·Ê¬m £´ ´ © ¥¢´ ¬m

ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ Max-Log-MAP

วงจรตรวจหาแบบซอฟต

¶ n¯£»§ ak ¹¯ \M p a 0 , M p a1 , M p a 2 , M p a3 ^ x \24.22, 12.17,9.54, 2.51^ ç²

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´ ³©¯¤m´ ·Ê 2.5 n¯£»§ ·Ê ¯ n ´¥Å­nÅ n¯³§ ¯¥¶ ¸£ Max-Log-MAP ¥© ­´ ¹¯

3

บทที่

yk {y 0 , y1 , y 2 , y3 , y 4 } {1.2, 0.7, 0.2, 0.5, 0.7}

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75

¥» ·Ê 3.4 ´¥ Ï´ © ¢´¤Å ¯³§ ¯¥¶ ¸£ Max-Log-MAP Å ³©¯¤m´ ·Ê 3.2

ç²£·Ã ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ H D 1 D 2 ´£¥» ·Ê 2.15 ¸Ê £· ³ Ë ­£ ¬·Ê¬ ´ ² ¹¯ ¬ ´ ² (a), (b), (c) ç² (d)

´ ³ Ë Ï´ ´¥ ¯ ¥­³¬ n¯£»§Ä ¤Å n¯³§ ¯¥¶ ¸£ Max-Log-MAP  m  ·¤© ³ ©¶ · ´¥ ·Ê

¯ ¶ ´¤Å ³©¯¤m´ ·Ê 3.1 É ²Æ n m´Â£ ¥¶ ¬´ ´Ã§²Â£ ¥¶ ¬ ´ ² ³ ì Å ¥» ·Ê 3.4 £¹Ê¯ m´ ·Ê¯¤m»

¶ ³ ¬n ¬´ ´Ã m§²Â¬n ¹¯ m´ Hk u ,q ç² ³©Â§ ·Ê¯¤m» ¶ ³ Ä­ ¯ à m§²¬ ´ ²Ã¬ ¸

k u ç² Ck u Å ¥» ª«¬m© B k u / Ck u ¬Ï´­¥³ à m§² k {0, 1, m´Â£ ¥¶ ¬ ´ ² B

…, 4} ç² u {a, b, c, d}

´ m´Â£ ¥¶ ¬´ ´Ã§²Â£ ¥¶ ¬ ´ ² ³ ì Å ¥» ·Ê 3.4 Ï´Å­n¬´£´¥ Ï´ © ­´ m´

LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ´£¬£ ´¥ (3.9) ¸Ê ²Æ n©m´

\M p a0 , M p a1 , M p a 2 , M p a3 , M p a 4 ^ x \7.28, 26.65, 7.28, 10.57,5.54^ ç² ¯ ¥­³¬ ¶ n¯£»§Æ n É

\aˆ0 ,aˆ1 ,aˆ2 ,aˆ3 ,aˆ4 ^ \1, 1,1, 1,1^ ¸Ê ¥ ³ ¶ n¯£»§ ak ·Ê¬m £´ ´ © ¥¢´ ¬m (¬¯ ¶ ¬º n´¤Æ£m£·¯¤m» ¥¶ Å ¥² à mÂ É §§³ q

·Ê ¶ ´ ´¥ Ï´ ¯ Ä©§» ³ ¥²­©m´ n¯£»§¯¶ º ç² m¯ ¬³ ´ ) ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ Max-Log-MAP

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

3.2.2 n¯¬³  ¯ ¯³§ ¯¥¶ ¸£ Max-Log-MAP ´ ·Ê §m´©£´ n´ n ¯³§ ¯¥¶ ¸£ Max-Log-MAP ² Ï´ ´¥ ¥²£´ m´Â£ ¥¶ ¬ ´ ² Bk u ç² Ck 1 q ¯ ¯³§ ¯¥¶ ¸£ BCJR Ä ¤Å n¡³ q ³ m´¬» ¬º ´£¬£ ´¥ (3.1) ³ ³ Ë ¯³§ ¯¥¶ ¸£ Max-

Log-MAP ²Â ¶ ³ n¯ ¶ §´ ´ ´¥ ¥²£´ m´ (approximation error) ¯¤m´ ­§· §·Ê¤

Æ£mÆ n ç²Â ¹Ê ¯ ´ £ ¥¶ ¬ ´ ² ³ Ë ¬¯ » Ï´ © à ©·¤  ¶ º m© ©§´ ¸ Ï´Å­n n¯ ¶ §´ ´ ´¥ ¥²£´ m´Ã ¥m ¥² ´¤ (propagate) Æ §¯ ³ Ë §Ï´ ³ n¯£»§ y

Ä ¤ ³Ê©Æ £¹Ê¯¯³§ ¯¥¶ ¸£ Max-Log-MAP Ï´ ´ ·Ê¥² ³ SNR ¬» É ² ³ ­´Â¥¹Ê¯

n¯ ¶ §´ ´ ´¥ ¥²£´ m´ n ¯¤ ¯¤m´ Æ¥ É ´£¯³§ ¯¥¶ ¸£ Max-Log-MAP ² Ï´ ´ Æ nÆ£m ·

£¹Ê¯ Ï´ ´ ·Ê¥² ³ SNR ÏÊ´ ( ¥´² n¯ ¶ §´ ´ ´¥ ¥²£´ m´£· ©´£¥º Ã¥ Å §n ·¤ ³

¬³ ´ ¥ © Å ¥² [24] ç²Â ¶ ³ ³ ­´Â¥¹Ê¯ ´¥Ã ¥m ¥² ´¤ ¯ n¯ ¶ §´ ´ ´¥ ¥²£´ m´) ¸ ãn©m´¯³§ ¯¥¶ ¸£ Max-Log-MAP ²£· ©´£ ³ n¯ n ¯¤ ©m´¯³§ ¯¥¶ ¸£ BCJR

à m É£·¬£¥¥ ² n¯¤ ©m´¯³§ ¯¥¶ ¸£ BCJR £´ ³ ³ Ë Å ´¥ ³ ¬¶ Å ©m´ ²Â§¹¯ ¯³§ ¯¥¶ ¸£Å £´ Å n ´ n»Å n ² n¯ ¥² · ¥² ¯£¥²­©m´ ©´£ ³ n¯ 粬£¥¥ ² ·Ê¤¯£¥³ Æ n ¯¤m´ Æ¥ É ´£

­³© n¯ ·Ê 3.3 ²¯ ¶ ´¤¯³§ ¯¥¶ ¸£ Log-MAP ¸Ê ³ ´£´ ´ ¯³§ ¯¥¶ ¸£ Max-Log-MAP Ä ¤£·

¬£¥¥ ²Â ·¤  m´ ³ ¯³§ ¯¥¶ ¸£ BCJR à m£· ©´£ ©´£ ³ n¯ n ¯¤ ©m´£´

3.3 ¯³§ ¯¥¶ ¸£ LOG-MAP  ¹Ê ¯ ´ ¯³§ ¯¥¶ ¸£ Max-Log-MAP Å n¬£ ´¥ (3.1) Å ´¥ ¥²£´ m´ ´¥´£¶Â ¯¥q m´ È ¯ ¯³§ ¯¥¶ ¸£ BCJR ¸ Ï´Å­n ¶ ³ ³ ­´Â¥¹Ê¯ n¯ ¶ §´ ´ ´¥ ¥²£´ m´ ¸Ê ¬m §Å­n£·

¬£¥¥ ² n¯¤ ©m´¯³§ ¯¥¶ ¸£ BCJR ¯¤m´ Æ¥ É ´£ n¯ ¶ §´ ´ ´¥ ¥²£´ m´Å ¬£ ´¥ (3.1) ¬´£´¥ à nÆ Æ nÄ ¤Å n¡³ q ³ §¯ ´¥¶ ¸£ ´Ä  ·¤ (Jacobian logarithm) [24, 38] ³Ê ¹¯ ( »

ln e x1 e x 2 max x1 , x 2 ln 1 e

x1 x 2

max x1 , x 2 fc x1 x 2

£¹Ê¯ fc x1 x 2 ln 1 e

x1 x 2

วงจรตรวจหาแบบซอฟต

¶¬» qÆ nÅ ¢´ © )

(3.15)

¹¯¡³ q ³ à nÆ n¯ ¶ §´ (correction function)

¯ ´ ·Ë  ¹Ê¯Å­n m´¤ m¯ ´¥¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ Log-MAP ² ¶ ¤´£

3

บทที่

¡³ q ³ m´¬» ¬º à ŭ£m ³ ·Ë

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

77

(3.16)

max x1 , x 2 max x1 , x 2 fc x1 x 2

³ ³ Ë m´ ln e x1 e x 2 ! e xn Å ¬£ ´¥ (3.1) ¬´£´¥ ­´ m´ ·Ê » n¯ Æ n ³ ·Ë ¬££º ¶©m´ ¥´ m´

x ¸Ê £· m´Â m´ ³ x ln e x1 e x 2 ! e xn 1 ln % £¹Ê¯ % e x1 e x 2 ! e xn 1 e x  ¥´² ² ³ Ë ²Æ n©m´

ln % ln e x1 e x 2 ! e xn 1 e xn ln % e xn ln e e xn

max ln % , xn fc ln % xn max x , xn fc x xn

(3.17)

max x , xn

´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ Log-MAP ²Â­£¹¯ ³ ¯³§ ¯¥¶ ¸£ Max-Log-MAP  ·¤ à m

² ¥²£´ m´ ´¥´£¶Â ¯¥q m´ È ¯ ¯³§ ¯¥¶ ¸£ BCJR Ä ¤¯´ª³¤¬£ ´¥ (3.16) ç² (3.17) Ã

¬£ ´¥ (3.1) ³ ³ Ë ´ ¬£ ´¥ (3.9) ¯³§ ¯¥¶ ¸£ Log-MAP ² Ï´ © ­´ m´ LLR ¯ ¶ n¯£»§

ak ³ ·Ë

Mk max Bˆ k u Hk u ,q Cˆ k 1 q max Bˆ k u H k u ,q Cˆ k 1 q (3.18) u ,q S1

u ,q S 1

Ä ¤ ·Ê£ ¥¶ ¬´ ´ Hk u ,q ­´Æ n ´ ¬£ ´¥ (3.10) ç² Bˆ k 1 q max Hk u , q Bˆ k u

u

Cˆ k u max Cˆ k 1 q Hk u ,q

q

(3.19) (3.20)

Å ´ ¶ ³ ¶¯³§ ¯¥¶ ¸£ Log-MAP ²£·¬£¥¥ ²Â ·¤  m´ ³ ¯³§ ¯¥¶ ¸£ BCJR à mÅ n ¥³ ¤´ ¥

Å ´¥ Ï´ © n ¯¤ ©m´ ¥©£ ³ Ë £· ©´£¯m¯ Æ­© m¯ m´ ©´£Ã ¥ ¥© ¯ ¬³ ´ ¥ © n ¯¤ ©m´ ¯³§ ¯¥¶ ¸£ BCJR ¯¤m´ Æ¥ É ´£ ¸ ãn©m´¯³§ ¯¥¶ ¸£ Log-MAP ²£·¬£¥¥ ² · ©m´¯³§ ¯¥¶ ¸£

Max-Log-MAP à m É£· ©´£ ³ n¯ £´ ©m´  ¥´² ² ³ Ë Å ´¥ ³ ¬¶ Å ©m´ ²Â§¹¯ ¯³§ ¯¥¶ ¸£Å £´Å n ´ n»Å n ² n¯ ¥² · ¥² ¯£¥²­©m´ ©´£ ³ n¯ 粬£¥¥ ² ·Ê¤¯£¥³ Æ n

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

0.0000 0.7791

–18.5956

–18.5956 –4.2216

–3.3093

1.7146 –0.9355

–11.6788

–9.9544 –1.4871

–0.0026

–3.5394

1.3743

–1.0314

–6.6575

1.7173

–3.5106

–2.8013

–0.6309 – 0.1508

–11.0818 –4.4586

0.2876 0.2876

–3.5447

–3.0239

–11.0792 –0.0027 0.7817

–12.8544

3.0889 –2.3097

¥²¤² ·Ê 0

¥²¤² ·Ê 3

–0.4557 –0.4557

¥» ·Ê 3.5 ´¥ Ï´ © ¢´¤Å ¯³§ ¯¥¶ ¸£ Log-MAP Å ³©¯¤m´ ·Ê 3.3

³©¯¤m´ ·Ê 3.3 ´ ³©¯¤m´ ·Ê 3.1 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ Log-MAP ç² Ï´­ Å­n m´©¬´¥¯² ¶¥¯ ¶ ¯¥¶ ¯ ¶ n¯£»§ ak ¹¯ Ma ak = {1, –4, 3, –2} ©¶ · Ï´

´ ³©¯¤m´ ·Ê 3.1 ¯³§ ¯¥¶ ¸£ Log-MAP ²¥³ n¯£»§ yk = {0.9, –0.2, 0.3, 0.6} ç²

Ma ak = {1, –4, 3, –2} £´Å nÅ ´¥ ¯ ¥­³¬ n¯£»§  m  ·¤© ³ ©¶ · ´¥ ·Êì Å ³©¯¤m´ ·Ê 3.1

¸Ê ²Æ n m´ ´¥´£¶Â ¯¥q m´ È ¯ ¯³§ ¯¥¶ ¸£ Log-MAP ´£¥» ·Ê 3.5 £¹Ê¯ m´ ·Ê¯¤m» ¶ ³ ¬n ¬´ ´

à m§²Â¬n ¹¯ m´ Hk u ,q ç² ³©Â§ ·Ê¯¤m» ¶ ³ Ä­ ¯ à m§²¬ ´ ²Ã¬ ¸ m´Â£ ¥¶ ¬ ´ ² Bˆ k u ç² Cˆ k u Å ¥» ª«¬m© Bˆ k u

Cˆ u

k

¬Ï´­¥³ à m§² k {0, 1, 2, 3} ç² u {a, b}

à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ´£¬£ ´¥ (3.18) ¸Ê ²Æ n©m´

\M p a0 , M p a1 , M p a 2 , M p a3 ^ x \23.60, 16.32,12.22, 1.49^ ç² ¯ ¥­³¬ ¶ n¯£»§Æ n É

\aˆ0 ,aˆ1 ,aˆ2 ,aˆ3 ^ \1, 1,1, 1^ ¸Ê ¥ ³ ¶ n¯£»§ ak ·Ê¬m £´ ´ © ¥¢´ ¬m ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ Log-MAP

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

วงจรตรวจหาแบบซอฟต

´ m´Â£ ¥¶ ¬´ ´Ã§²Â£ ¥¶ ¬ ´ ² ³ ì Å ¥» ·Ê 3.5 Ï´Å­n¬´£´¥ Ï´ © ­´ m´ LLR

3

บทที่

79

¥» ·Ê 3.6 ´¥ Ï´ © ¢´¤Å ¯³§ ¯¥¶ ¸£ Log-MAP Å ³©¯¤m´ ·Ê 3.4

³©¯¤m´ ·Ê 3.4 ´ ³©¯¤m´ ·Ê 3.2 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ Log-MAP ç² Ï´­ Å­n m´©¬´¥¯² ¶¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ¹¯ Ma ak = {–1, 2, 1, 2, –2} ©¶ · Ï´

´ ³©¯¤m´ ·Ê 3.2 ¯³§ ¯¥¶ ¸£ Log-MAP ¥³ n¯£»§ yk = {1.2, –0.7, –0.2, 0.5, –0.7}

ç² Ma ak = {–1, 2, 1, 2, –2} £´Å nÅ ´¥ ¯ ¥­³¬ n¯£»§ ¸Ê ²Æ n m´ ´¥´£¶Â ¯¥q m´ È ¯ ¯³§ ¯¥¶ ¸£ Log-MAP ´£¥» ·Ê 3.6 £¹Ê¯ m´ ·Ê¯¤m» ¶ ³ ¬n ¬´ ´Ã m§²Â¬n ¹¯ m´ Hk u ,q ç² ³©Â§ ·Ê¯¤m» ¶ ³ Ä­ ¯ à m§²¬ ´ ²Ã¬ ¸ m´Â£ ¥¶ ¬ ´ ² Bˆ k u ç² Cˆ k u Å ¥» ª«¬m© Bˆ u / Cˆ u ¬Ï´­¥³ à m§² k {0, 1, 2, 3, 4} ç² u {a, b, c, d} k

k

´ ¥» ·Ê 3.6 Ï´Å­n¬´£´¥ Ï´ © ­´ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak

´£¬£ ´¥ (3.18) ¸Ê ²Æ n©m´

\M p a0 , M p a1 , M p a 2 , M p a3 , M p a 4 ^ x \0.899, 21.646, 0.898, 8.566, 0.525^ ç² ¯ ¥­³¬ ¶ n¯£»§Æ n É

\aˆ0 ,aˆ1 ,aˆ2 ,aˆ3 ,aˆ4 ^ \1, 1,1,1,1^ ¸Ê ¥ ³ ¶ n¯£»§ ak ·Ê¬m £´ ´ © ¥¢´ ¬m ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ Log-MAP

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

3.4 ¯³§ ¯¥¶ ¸£ SOVA ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶Ã ¯¡ q­¥¹¯Â¥·¤ ¬³ Ë È ©m´¯³§ ¯¥¶ ¸£ SOVA (soft output Viterbi algori-

thm) [19] Â É ¯³§ ¯¥¶ ¸£ ·Ê¬´£´¥ Å­n n¯£»§Â¯´ q º Â É m´ LLR ¯ ¶ n¯£»§¯¶ º Æ n m  ·¤©

³ ¯³§ ¯¥¶ ¸£ MAP (­¥¹¯ BCJR), Max-Log-MAP ç² Log-MAP Ä ¤ ³©Ê Æ ¯³§ ¯¥¶ ¸£ SOVA ²£·¬£¥¥ ²Â ·¤  m´ ³ ¯³§ ¯¥¶ ¸£ Max-Log-MAP à m£ · ©´£ ³ n¯ n ¯¤ ©m´ [39] ¸ Ï´Å­n

¯³§ ¯¥¶ ¸£ SOVA Â É ·Ê ¶¤£Å n ´ Å ­§´¤È ´ ¥²¤º q ¥©£ ¸ °´¥q ¶¬ qÆ ¥¡q ¥mº Å­£mÈ ·ÊÅ n ¥² ´¥ ¯ ¥­³¬ n¯£»§Ã © Ï´Ë n©¤ ­£´¤Â­ º

n»¯m´ ©¥ Ï´ ©´£Â n´Å ­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ( » ·Ê 4 Å ­ ³ ¬¹¯

[10]) m¯ ª¸ «´­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ SOVA  ¹Ê¯Å­n¬´£´¥  n´Å ¯³§ ¯¥¶ ¸£ SOVA

Æ n m´¤¤¶Ê ¸Ë

¯³§ ¯¥¶ ¸£ SOVA ² Ï´ ´ §n´¤ ³ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [13]  ·¤ à m£· n¯Ã m´ ·Ê

¬Ï´ ³ ¯¤m»¬¯ ¥² ´¥ ¹¯

1) ¯³§ ¯¥¶ ¸£ SOVA Å n£ ¥¶ ¬´ ´ ·Ê » ¥³ ¥º (modified branch metric) ·Ê¥©£ § ¥² ¶ ¯¥¶ (a priori probability) ¯ ¶ n¯£»§¯¶ º ¯ ©´£ m ´ ²Â É ¯² ¶¥¯

2) ¯³§ ¯¥¶ ¸£ SOVA Å­n n¯£»§Â¯´ q º à ¯¡ q (soft output) ·ÊÂ É ³© ¯ ¸ ©´£ m ´Â ¹Ê¯ ¹¯ (reliability) ¯ ´¥ ³ ¬¶ Å ¯ ¶ n¯£»§Ã m§² ¶

¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 £ ¥¶ ¬´ ´ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶Å ¥²¤² ·Ê k

(k-th stage) ¯ ´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² u ·Ê©§´ k Æ ¤³ ¬ ´ ² q ·Ê©§´ k + 1 ³Ê ¹¯

1 ¬­ ­­ 1 y rˆ u , q 2 Sk u ,q ln p yk | ak

ln 2QT2 ®­­ 2T2 k

(3.21)

£¹Ê¯ rˆ u , q ¹¯ n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² (u, q) ´£ à ¢´  ¥§§¶¬ ç² V2 ¹¯ ©´£Ã ¥ ¥© ¯ ¬³ ´ ¥ © nk

วงจรตรวจหาแบบซอฟต

Sk u , q £· m´Â m´ ³ [10, 13]

©´£ m ´ ²Â É ¯² ¶¥¶¯¯¥¶ ¯ ¶ n¯£»§¯¶ º ak ¬´£´¥ Ŭm n´Æ Š£ ¥¶ ¬´ ´Æ n ´£

¬£ ´¥ (3.10) ³ ³ Ë Â£ ¥¶ ¬´ ´ ·ÊÅ nÅ ¯³§ ¯¥¶ ¸£ SOVA ²£· m´Â m´ ³

1 ¬­ aˆ u , q M a ­­ 1 y rˆ u ,q 2 a k (3.22) Hk u , q ln p yk ;ak

ln 2QT2 ®­­ 2T2 k 2

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บทที่

81

£¹Ê¯ p yk ;ak p yk | ak p ak , aˆ u , q ¹¯ n¯£»§¯¶ º ¯ m¯ ¬³ ´ ·Ê¬¯ §n¯ ³ ´¥  §·Ê¤ ¬ ´ ² (u, q), ç² Ma ak ¹¯ m´ ©´£ m ´ ²Â É ¯² ¶¥¶¯¯¥¶ ¯ ¶ n¯£»§¯¶ º ak ¯³§ ¯¥¶ ¸£ SOVA ² n ­´Â¬n ´ ·Ê£· m´Â£ ¥¶ ¬» ¬º ´£Ã ¢´  ¥§§¶¬ £¹Ê¯Â£ ¥¶

¬n ´ (path metric) ·Ê¬ ´ ² q ©§´ k + 1 £· m´Â m´ ³ §¥©£ ¯ £ ¥¶ ¬´ ´Å ¬£ ´¥ (3.22) ³Ê ¹¯

'k 1 q

k

H

(3.23)

i

i 0

£¹Ê¯ Hi ¹¯Â£ ¥¶ ¬´ ´ ©§´ i ·Ê¬¯ §n¯ ³ “¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» (survivor path)” ·Ê £´ ¸ ¬ ´ ² q ©§´ k + 1 ³ ³ Ë ¯³§ ¯¥¶ ¸£ SOVA ² Ï´ ´ ­£¹¯ ³ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ Å ´¥Â§¹¯ §Ï´ ³ n¯£»§¯¶ º (­¥¹¯ m´ ¥²£´ ¯ §Ï´ ³ n¯£»§¯¶ º aˆk ) ´£Â¬n ´ ·Ê£· m´

£ ¥¶ ¬n ´ ¬» ¬º ¸Ê Â¥·¤ ©m´ “¬n ´ ML (maximum-likelihood)” ­¥¹¯Â¬n ´ ©¥ ²Â É

¬» ¬º  ·¤ à m¯³§ ¯¥¶ ¸£ SOVA ²Å n£ ¥¶ ¬´ ´Å ¬£ ´¥ (3.22) ¯ ´ ·Ë ¯³§ ¯¥¶ ¸£ SOVA

¤³ Å­n m´ LLR ¯ ¶ n¯£»§Ã m§² ¶ Æ n ¸Ê Â É m´ ·Ê m ¯ ¸ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§©m´ ©¥ £· m´Â É ¯²Æ¥Ã§²£· ©´£ m ´Â ¹Ê¯ ¹¯£´ n ¯¤Â ·¤ Å

3.4.1 ´¥­´ m´ LLR ¯ ¶ n¯£»§ ¯³§ ¯¥¶ ¸£ SOVA ¬´£´¥ ­´ m´ LLR ¯ ¶ n¯£»§Ã m§² ¶ Æ n ³ ·Ë ¶ ´¥ ´Ã ¢´  ¥§§¶¬ Å ¥²¤² ·Ê k Å ¥» ·Ê 3.7 £ ¥¶ ¬n ´ ·Ê¬ ´ ² q ©§´ k + 1 ³Ê ¹¯ 'k 1 q ­´Æ n ´

'k 1 q ln p yk0 ; ak0

(3.24)

£¹Ê¯ yk0 <y 0 , y1 ,!, yk > ¹¯§Ï´ ³ n¯£»§ ·Ê n¯ ´¥ ¯ ¥­³¬ ³ Ë Ã m©§´ ·Ê 0 ¸ ©§´ k ç² ak0

<a 0 ,a1 ,!,ak > ¹¯§Ï´ ³ n¯£»§¯¶ º ³ Ë Ã m©§´ ·Ê 0 ¸ ©§´ k ·Ê¬¯ §n¯ ³ yk0 ¬£ ´¥ (3.24) ³ ¥» Å­£mÆ n É

p yk0 ; ak0 e

'k 1 q

(3.25)

n¯£»§Â¯´ q º ¯ ¯³§ ¯¥¶ ¸£ SOVA ·ÊÂ É ³© m ¸ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ´¥ ³ ¬¶ Å ¶

n¯£»§ (¬Ï´­¥³ ¥­³¬Ã Æ ´¥·) ¬´£´¥ ­´Æ n ³ ·Ë ´ ¥» ·Ê 3.7 ² ©m´£·Â¬n ´ ´¥Â §·Ê¤ ¬ ´ ² 2 ¬n ´ ·Ê£´ ¸ ¬ ´ ² q ©§´ k + 1 ³Ê ¹¯ (u, q) ç² (s, q) ¸Ê £·Â£ ¥¶ ¬n ´

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'k u

Sk 1 q Qk 1 q

H k u , q

'k 1 q

1

2

%k 1 q 'k 1 q 'k 1 q

yk ¥» ·Ê 3.7 à ¢´  ¥§§¶¬¬Ï´­¥³ ¯ ¶ ´¤¯³§ ¯¥¶ ¸£ SOVA 1

2

1

2

'k 1 q ç² 'k 1 q ´£§Ï´ ³ n´¬££º ¶Å­n 'k 1 q 'k 1 q ì ©m´Â¬n ´ (1)  É

¬n ´ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ·Ê£´ ¸ ¬ ´ ² q ©§´ k + 1 ³ ³ Ë ¯³§ ¯¥¶ ¸£ SOVA ²

§¹¯ ¬n ´ (1) Å­nÂ É ¬m© ­ ¸Ê ¯ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» ·Ê£´ ¸ ¬ ´ ² q ©§´ k + 1 ³Ê ¹¯ Sk 1 q

n´ ¶ ¤´£ § m´ ¯ £ ¥¶ ¬n ´ (path metric difference) Å­n£· m´Â m´ ³ 1

2

(3.26)

%k 1 q 'k 1 q 'k 1 q

¸Ê ²Æ n©m´ %k 1 q p 0 ¬£¯ ³ ³ Ë ©´£ m ´ ²Â É ¯ ´¥ ³ ¬¶ Å ·Ê » n¯ (correct decision)

1

Pr ¢ correct decision at Zk 1 q ¯±

e 1

e

'k 1 q

'k 1 q

e

2

'k 1 q

e

%k 1 q

1 e

%k 1 q

(3.27)

» n¯ £· m´Â m´ ³ £¹Ê¯ Pr <x > ¹¯ ©´£ m ´ ²Â É ¯ x ç² m´ LLR ¯ ´¥ ³ ¬¶ Å ·Ê Pr correct decision at Zk 1 q ¯ ¬­ ¢ ± ­ % q

LLR ln ­ k 1 1 Pr ¢ correct decision at Zk 1 q ¯± ®­­

วงจรตรวจหาแบบซอฟต

¬´£´¥ ­´Æ n ´ [19, 40]

(3.28)

¸Ê ­£´¤ ©´£©m´ § m´ ¯ £ ¥¶ ¬n ´ ¯ ¬n ´ ·ÊÆ n£´ ¬´ ³ (merge) Å ¯³§ ¯¥¶ ¸£ ©·Â ¯¥q ¶ ²£· m´Â m´ ³ m´ LLR ¯ ©´£ m ´ ²Â É ¯ ´¥ ³ ¬¶ Å ·Ê » n¯

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©§´

aˆk1 5

+ 1

%1k 1 4 aˆk2 5 aˆk 5

aˆk3 3

%k3 1

%k0 1

Sk 1 q

'k 1 q

aˆk3 5

%k4 1

aˆk 5

%k5 1 aˆk5 5

aˆk1 3

aˆk2 3

¬n ´ ML (¬n ´ ·¤ Ê ³ £· ·©¶ ¯¤m» Å·Ê n ¯ ¥­³¬§Ï´ ³ n¯£»§)

%k2 1

yk k-th stage (¥²¤² ·Ê k) ¬n ´ · Ê » ³ ¶Ë (discarded path)

¥» ·Ê 3.8 à ¢´  ¥§§¶¬ ¥n¯£ ³ § m´ ¯ £ ¥¶ ¬n ´ ç² ¶ n¯£»§¬Ï´­¥³ ¯³§ ¯¥¶ ¸£ SOVA

Å ´ ¶ ³ ¶¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ² ³ ¬¶ Å ¶ n¯£»§ ·Ê©§´ k ³Ê ¹¯ aˆk ­§³ ´ ·Ê©§´ m´ Æ ET ­ m ©¤ £¹Ê¯ ET ¹¯ ©´£§¸ ´¥ ¯ ¥­³¬ (decoding depth) ç² T ¹¯ ´ ©§´ ¯ ¶ ¸Ê Ä ¤ ³©Ê Æ ²Å n E p 5(O 1) [32] £¹Ê¯ O ¹¯­ m ©¤ ©´£ Ï´ ¯ m¯ ¬³ ´ ³ ³ Ë ·Ê©§´

k (­¥¹¯¥²¤² ·Ê k) ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ² ¯ ¥­³¬ ¶ n¯£»§ ·Ê©§´ k – G ³Ê ¹¯ aˆk E ¶ ´¥ ´ à ¢´  ¥§§¶¬Å ¥» ·Ê 3.8 ¬Ï´­¥³ E 5 Ä ¤Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» (ì n©¤Â¬n ¸ ¬· Ï´) ·Ê£´ ¸ ¬ ´ ² q ©§´ k + 1 ¹¯ Sk 1 q ç²£·Â£ ¥¶ ¬n ´  m´ ³ 'k 1 q ¯ ´ ·Ë

¥» ·Ê 3.8 ¤³ ì “¬n ´ ·Ê » ³ ¶ Ë (discarded path)” (ì n©¤Â¬n ²¬·Â ´) ¸Ê £· ³ Ë ­£

E 1 ¬n ´ n´ Ï´­ Å­n %dk ¹¯ § m´ ¯ £ ¥¶ ¬n ´ ¥²­©m´ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m»Ã§²

¬n ´ ·Ê » ³ ¶ Ë Â©§´ ·Ê m´ Æ Ã§n© d ­ m ©¤ ´ ©§´ k £¹Ê¯ d = 0, 1, …, G Ä ¤Â¬n ´

·Ê » ³ ¶ Ë Â©§´ k – d ²Â¥·¤ ©m´ “¬n ´ ·Ê d (d-th path)” ¯ ´ ·Ë n´Å­n aˆk E ¹¯ ¶

n¯£»§¯¶ º ·Ê¬¯ §n¯ ³ ¬n ´ ML ©§´ k – G (­¥¹¯ ¶ n¯£»§ ·Ê¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ²

Ï´ ´¥ ¯ ¥­³¬ ·Ê©§´ k) ç² aˆkd i ¹¯ ¶ n¯£»§¯¶ º ·Ê¬¯ §n¯ ³ ¬n ´ ·Ê d (¬n ´ ·Ê »

³ ¶ Ë ) ©§´ k – i £¹Ê¯ i ¹¯Â§ Ï´ ©  ɣ

n´ ¶ n¯£»§ aˆkd E ¬n ´ ·Ê d (¬n ´ ·Ê » ³ ¶ Ë ) £· m´Â m´ ³ ¶ n¯£»§ aˆk E

ì ©m´¥² ²Æ£m ¶ n¯ ¶ §´ n´¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶Â§¹¯ ¬n ´ ·Ê » ³ ¶ Ë Â É Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» ³ ³ Ë Å ¥ · ·Ë ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ´¥ ³ ¬¶ Å ¶ n¯£»§£· m´Â m´ ³ m´¯ ³ q (infinity)

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¯¤m´ Æ¥ É ´£ n´ aˆkd E v aˆk E ì ©m´£· n¯ ¶ §´ ¯ ¶ n¯£»§Â ¶ ¸Ë ©§´ k E Š¬n ´ ·Ê d (¬n ´ ·Ê » ³ ¶ Ë ) ¸Ê ² ¶ ¤´£Ä ¤ (3.29)

eˆkd E aˆk E aˆkd E

£¹Ê¯ aˆk E \o1^ , aˆkd E \o1^ , ç² ¹¯ ³© Ï´Â ¶ ´¥ © Å ¡· § qÆ ´¥·­¥¹¯ GF(2) Ä ¤ ·Ê GF ¤m¯£´ ´ Galois field ·Ê£·Â¯ §³ « q ´¥ ©  m´ ³ 1 ³Ê ¹¯ [40] 1 1 1

1 1 1

1 1 1

1 1 1

(3.30)

Å Ï´ ¯  ·¤© ³ ³ ¬£ ´¥ (3.28) ²Æ n©m´ m´ LLR ¯ n¯ ¶ §´ ¯ ¶ ²£· m´Â m´ ³ %dk  ¥´² ² ³ Ë Â£¹Ê¯¥©£ ³ Ë ¬¯ ¥ · ² ©m´ m´ LLR ¯ n¯ ¶ §´ ¯ ¶ n¯£»§ ©§´ k E Š¬n ´ ·Ê d (¬n ´ ·Ê » ³ ¶ Ë ) £· m´Â m´ ³

M

eˆkd E

¬­­­ ¦¦£d, ­ ¤

®­­­ ¦¦¦¥%dk

d p eˆk E 1 ln p eˆkd E 1

if aˆk E aˆkd E if aˆk E v aˆkd E

(3.31)

Å ´ ¶ ³ ¶Ã m§²Â¬n ´ ·Ê » ³ ¶ Ë ²Å­n¥m¯ ¥¯¤­¥¹¯­§³ ´ (evidence)  ·Ê¤© ³

©´£ m ´Â ¹Ê¯ ¹¯ ·Ê ¶ n¯£»§ aˆk E ² » ¯ ¥­³¬Æ n¯¤m´ » n¯ ³ ³ Ë n¯ ¶ §´ ¥©£ ·ÊÂ É § £´ ´ ¬n ´ ·Ê » ³ ¶ Ë ·ÊÂ É Æ Æ n ³ Ë ­£ ¬Ï´­¥³ aˆk E ­´Æ n ´ E

eˆk E

eˆ

d k E

eˆk0 E eˆk1 E ! eˆkE E

(3.32)

 ¥´² ² ³ Ë m´ LLR ¯ ¶ n¯£»§ aˆk E  ·¤ Æ nÂ É [40] M aˆk E aˆk E M eˆk E aˆk E M

¬­ eˆkd E ­­­ ®­ d 0 E

(3.33)

วงจรตรวจหาแบบซอฟต

d 0

Ä ¤ ·Ê aˆk E \o1^ Â É ³© Ï´­  ¥¹Ê¯ ­£´¤ ¯ m´ LLR ( ¸Ê Â É m´ ¥²£´ ¯ ¶ n¯£»§ ·Ê ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ² Ï´ ´¥ ¯ ¥­³¬) ç² M eˆk E p 0 Â É ³© Ï´­ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ aˆk E ©m´£· m´£´ n ¯¤Â ·¤ Å §m´© ¹¯ n´ M eˆk E £· m´£´ Éì ©m´ ¶ n¯£»§ aˆk E ·Ê¯³§ ¯¥¶ ¸£ ©·Â ¯¥q ¶ ¯ ¥­³¬¯¯ £´£· ©´£ » n¯ £´  m ³ (ç²Å ´ §³ ³ )

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n´ ¶ ¤´£ · ¶ ¯ ¡³ q ³ ©¥ ²Â É Ã §¯ ´¥¶ ¸£ [40] ³ ·Ë M x1

(3.34)

M x 2 M x1 x 2

£¹Ê¯ x1 ç² x2 ¹¯ ³©Ã ¥¬mº£Ã Æ ´¥· Ê·Â É ¬£´ ¶ ¯ {–1, 1} ç² · ¶ ¯ m´ LLR ¸Ê £· ©´£¬³£ ³ q ¹¯ M x

d M x

M x

d M x

M x

¹¯ ³© Ï´Â ¶ ´¥ ´

0 0

Ä ¤ ·Ê f ­£´¤ ¸ £· ©´£ m ´Â ¹Ê¯ ¹¯¬» £´ (infinite reliability), –f ­£´¤ ¸ Æ£m£· ©´£ m ´Â ¹Ê¯ ¹¯

(totally unreliable), ç² 0 ­£´¤ ¸ ©´£ m ´Â ¹Ê¯ ¹¯£· ©´£ §º£Â ¥¹¯ (ambiguous reliability)

¯´ª³¤¬£ ´¥ (3.34)  ¥´² ² ³ Ë m´ LLR ¯ ¶ n¯£»§ aˆk E Å ¬£ ´¥ (3.33) ³ ¥»

Å­£mÆ nÂ É E E ¬­ M aˆk E aˆk E M eˆkd E ­­­ aˆk E d 0 ®­ d 0

M eˆ

\

aˆk E M eˆk0 E

M eˆk1 E

!

d k E

M eˆkE E

^

(3.35)

´ ¬£ ´¥ (3.31) 粯´ª³¤Â¯ §³ « q ¯ ¶ ¤´£ · ¶ ¯ ¡³ q ³ ©¥ ²Â É Ã §¯ ´¥¶ ¸£ ³ ³ Ë n´¬£ ´¥ (3.35) ­´ §¥©£Â ´² m´ d ·Ê Ï´Å­n aˆkd E v aˆk E É ²Æ n©m´ [40] M aˆk E aˆk E

E

%dk

(3.36)

d 0

Å Ï´ ¯  ·¤© ³ ¯´ª³¤Â¯ §³ « q ¯ ¶ ¤´£ · ¶ ¯ ¡³ q ³ ©¥ ²Â É Ã §¯ ´¥¶ ¸£ [40] ¬£ ´¥ (3.36) ¬´£´¥ ¥²£´ m´Æ n É

£ ¦ ¦ d² M aˆk E x aˆk E ¦ ¤ min %k ¦ » ¦ ¦ 0,1, ! , E d \ ^ ¦ ¦ ¥ ¼

(3.37)

³Ê ¹¯ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§ aˆk E ¸Ë ¯¤m» ³ § m´ ¯ £ ¥¶ ¬n ´ %dk ·Ê£· m´ n ¯¤¬º ´£Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» ³ ³ Ë Â ¥¹Ê¯ ­£´¤ ¯ M aˆk E Å ¬£ ´¥ (3.37) ¹¯ m´ ¥²£´ ¯ ¶ n¯£»§ aˆk E ç² ´ ¯ M aˆk E ¹¯ m´ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§ ·Ê » ¯ ¥­³¬

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3.4.2 n¯¬³  ¯ ¯³§ ¯¥¶ ¸£ SOVA ´ ¬£ ´¥ (3.37) ²Â­É Æ n©m´ m´ LLR ¯ ¶ n¯£»§ ² ¸Ë ³ § m´ ¯ £ ¥¶ ¬n ´ ´£ ·Ê 1

2

i

ì Å ¬£ ´¥ (3.26) ³Ê ¹¯ %k q 'k q 'k q Ä ¤ ·Ê 'k q ¬Ï´­¥³ i = {1, 2} ¹¯ §¥©£ ¯ £ ¥¶ ¬´ ´ ´£¬£ ´¥ (3.23) £¹Ê¯Â£ ¥¶ ¬´ ´ Hk u , q ­´Æ n ´ ¬£ ´¥ (3.22) ¯¤m´ Æ¥ É ´£Â ¹Ê¯§ ©´£ ³ n¯ Å ´¥ Ï´ © ­´ § m´ ¯ £ ¥¶ ¬n ´ %k q

¯³§ ¯¥¶ ¸£ SOVA ¬´£´¥ Å n£ ¥¶ ¬´ ´ ·Ê¯¤m»Å ¥» Hk u , q x

1 2T

2

2

yk rˆ u , q

aˆ u , q Ma ak

2

(3.38)

Æ nÄ ¤Æ£m ¥² m¯¬£¥¥ ² ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ £ ¸ SOVA  ¹Ê ¯ ´ ©§´ ·Ê ´Ï © ­´ m´ § m´

¯ £ ¥¶ ¬n ´ Å ¬£ ´¥ (3.26) ɤ³ Å­n §§³ q m´Â ¶£

3.4.3 ¬¥º ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ £ ¸ SOVA Ï´­ Å­n Qk 1 q ¹¯ ³© Ï ´­ n ´ (predecessor) ·Ê¬ ´ ² q ©§´ k + 1 ¸Ê ²Â É m´¬ ´ ² m¯ ­ n ´ ( ©§´ k) ·Ê Ï´Å­n ¶ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º £´¤³ ¬ ´ ² q ©§´ k + 1 Ä ¤

´¥Â §·Ê¤ ¬ ´ ² ·Ë ² ¹¯Â É ¬m© ­ ¸Ê ¯ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Sk 1 q ³©¯¤m´  m ¶ ´¥ ´

à ¢´  ¥§§¶¬Å ¥» ·Ê 3.7 ¬££º ¶©m´Â¬n ´ (1) Â É Â¬n ´ ·Ê ·¬º ·Ê Ï´Å­n 'k 1 q £· m´¬» ¬º ³ ³ Ë ²Æ n©m´ Qk 1 q u ³Ê ¹¯¬ ´ ² u Â É ¬ ´ ² m¯ ­ n ´ ¸Ê Ï´Å­n ¶  §·Ê¤ ¬ ´ ² ·Ê · ¬º £´¤³ ¬ ´ ² q ©§´ k + 1 ³ ³ Ë ­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ SOVA ¬¥º Â É ³ Ë ¯

³©¯¤m´ ·Ê 3.5 ´ ³©¯¤m´ ·Ê 2.4 Å n¯³§ ¯¥¶ ¸£ SOVA Å ´¥ ¯ ¥­³¬ n¯£»§ yk Ä ¤ Ï´­ Å­n Ma ak = {–1, 2, 1, 2} ç² ©´£§¸ ´¥ ¯ ¥­³¬ E 3 ©¶ · Ï´

´ ³©¯¤m´ ·Ê 2.4 n¯£»§ ·Ê ¯ n ´¥Å­nÅ n¯³§ ¯¥¶ ¸£ SOVA ¥© ­´ ¹¯

วงจรตรวจหาแบบซอฟต

m´ È Æ n ´£¥» ·Ê 3.9

yk {y 0 , y1 , y 2 , y3 } {0.9, 0.2, 0.3, 0.6}

ç²Ã ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ H D 1 0.5D ì Å ¥» ·Ê 2.13 ¸Ê £·¬¯ ¬ ´ ² ¹¯¬ ´ ² (a) 粬 ´ ² (b) ³ ³ Ë ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¯³§ ¯¥¶ ¸£ SOVA £· ³ Ë ¯ ´¥

3

บทที่

Ï´ ´ ³ ·Ë

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¯³§ ¯¥¶ ¸£ SOVA ´¥ ¯ ¥­³¬ n¯£»§Ã °´¥q (­£¹¯ ³ Ë ¯ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [1]) 1. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬n ´ '0 (u ) 0 ¬Ï´­¥³ º m´ u \0,1, !,Q 1^ 2. ¬Ï´­¥³ k 0,1, !, L O 1 E £¹Ê¯ E ¹¯ ©´£§¸ ´¥ ¯ ¥­³¬ Ï´­ Å­n n¯£»§ ·Ê ² Ï´ ´¥ ¯ ¥­³¬ yk 0 ¬Ï´­¥³ k p L O ¬Ï´­¥³ q 0,1, !,Q 1 Ï´ © ­´ m´ Hk u ,q ´£¬£ ´¥ (3.38) ¬Ï´­¥³ º ¬ ´ ² u ·Ê Ï´Å­n (u, q) Â É ¥¶ Ï´ © ­´ m´ 'k 1 q ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ´£¬£ ´¥ (3.23) Ï´ © ç² ³ ¸ m´ § m´ ¯ £ ¥¶ ¬n ´ %k 1 q ´£¬£ ´¥ (3.26) ³ ¸ ³© Ï ´­ n ´ Qk 1 q (Å nÅ ´¥­´Â¬n ´ ·Ê d ­¥¹¯Â¬n ´ ·Ê » ³ ¶ Ë ) ³ ¸ ¬n ´ ·Ê¤³ £· ·© ¶ ¯¤m» Sk 1 q

(¬¶ Ë ¬º ´¥© Ï´Ë ¯ q) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ k) 1 3. ¯ ¥­³¬§Ï´ ³ n¯£»§¯¶ º aˆ L ´£Â¬n ´ ML (¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Ê£ · · m´ 'L O E ¬» ¬º ) 0

´¥ ¯ ¥­³¬ n¯£»§Ã ¯¡ q ( ´¥­´ m´ LLR) 4. Ï´­ m´Â¥¶Ê£ n ¯ ´ ¯ m´ LLR Å­n£· m´Â m´ ³ M aˆk d ¬Ï´­¥³ k 0,1, !, L 1 5. ¬Ï´­¥³ k E, E 1, !, L 1 E ¬Ï´­¥³ d 0,1, !, E  ¥·¤  ·¤ ¶ n¯£»§ aˆk E ·Ê ¯ ¥­³¬Æ n ´£Â¬n ´ ML ³ ¶ n¯£»§ aˆkd E ·Ê ¯ ¥­³¬Æ n ´£Â¬n ´ ¬n ´ ·Ê d (¬n ´ ·Ê » ³ ¶ Ë ) n´ aˆkd E v aˆk E Å­n ¥³ ¥º ´ ¯ m´ LLR ´£ ©´£¬³£ ³ q ³ ·Ë

\

M aˆk E min M aˆk E , %dk 1

^

(¬¶ Ë ¬º ´¥© Ï´Ë ¯ d) ¯ ¥­³¬ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak E ´

M p aˆk E aˆk E M aˆk E

(¬¶ Ë ¬º ´¥© Ï´Ë ¯ k) ¥» ·Ê 3.9 ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ SOVA [19, 40]

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1. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬n ´ '0 u 0 ¬Ï´­¥³ º ¬ ´ ² u = {a, b} 2. ¥²¤² ·Ê 0 ¸ 6 (¬Ï´­¥³ k = 0, 1, …, 6) Å­n Ï´ ´¥ ´¥ ¯ ¥­³¬ n¯£»§Ã °´¥q ­£¹¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ´£ ³ Ë ¯ Å ¥» ·Ê 3.9 Ä ¤¥²­©m´ ³ Ë ¯ ´¥ ´¥ ¯ ¥­³¬ n¯£»§ ÉÅ­n

³ ¸ m´ § m´ ¯ £ ¥¶ ¬n ´ %k 1 q 粬 ´ ² m¯ ­ n ´ Qk 1 q ¬Ï´­¥³ q =

{a, b} ³ ì Å ¥» ·Ê 3.10 ( ) £¹Ê¯ ³©Â§ ·Ê¯¤m» ¥ Ä­ ¯ à m§²¬ ´ ²Ã¬ ¸ m´ § m´ ¯ £ ¥¶ ¬n ´ %k 1 q , ³©¯³ «¥ ·Ê¯¤m»Å © Â§É Ã¬ ¸ m´¬ ´ ² m¯ ­ n ´ Qk 1 q

ç²Â¬n §» ª¥ ·Ê§´ m´ à m§²Ä­ ¹¯Â¬n ´ ML ·Ê£·Â£ ¥¶ ¬n ´ ¬» ¬º ³Ê ¹¯ '7 a > '7 b Ä ¤ ·Ê§» ª¥Â¬n ¸ à ¶ n¯£»§¯¶ º ak = 1 粧» ª¥Â¬n ²Ã ¶ n¯£»§¯¶ º

ak = –1 ³ ³ Ë ¯³§ ¯¥¶ ¸£ SOVA ² ¯ ¥­³¬ n¯£»§Ã °´¥q Æ n É

\aˆ0 ,aˆ1 ,aˆ2aˆ3 ^ \1, 1,1,1^ £¹Ê¯ ¶ ¬º n´¤Æ£m£·¯¤m» ¥¶ Å ¥² à mÂ É §§³ q Ê· ¶ ´ ´¥ Ï´ ¯ Ä©§» ³ ¥²­©m´ n¯£»§ ¯¶ º ç² m¯ ¬³ ´

´¥ ¯ ¥­³¬ n¯£»§Ã ¯¡ q (¬Ï´­¥³ ©´£§¸ ´¥ ¯ ¥­³¬ G = 3) 3.

Ë ¯ ·Ê 1 ²Æ n©m´ ¥²¤² ·Ê 3 (£¹Ê¯ k = 3)  ¹Ê¯­´ m´ M p a 0 ´ n¯£»§ ·Ê ¯ ¥­³¬Æ nÅ ³ aˆk E aˆ0 1 ¥» ·Ê 3.10 ( ) ì ¬n ´ ·Ê d (¬n ´ ·Ê » ³ ¶ Ë ) ¬Ï´­¥³ d = {0, 1,

…, G} ¥n¯£ ³ Ë ¶ n¯£»§ aˆkd E ç² § m´ ¯ £ ¥¶ ¬n ´ %dk 1 ·Ê¬¯ §n¯ ³ ¬n ´

\

^

·Ê d Å ¥ · ·Ë ²Æ n©m´ aˆ00 , aˆ10 , aˆ02 v aˆ0 ³ ³ Ë ´ ¯ m´ LLR ¯ ¶ n¯£»§ a0 £· m´  m´ ³

\

^

ç² m´ LLR ¯ ¶ n¯£»§ a0 £· m´Â m´ ³ M aˆ0 aˆ0 M aˆ0 1 4.2832 4.2832 4.

Ë ¯ ·Ê 1 ²Æ n©m´ ¥²¤² ·Ê 4 (£¹Ê¯ k = 4)  ¹Ê¯­´ m´ M p a1 ´ n¯£»§ ·Ê ¯ ¥­³¬Æ nÅ ³ aˆ1 1 ¥» ·Ê 3.10 ( ) ì ¬n ´ ·Ê d (¬n ´ ·Ê » ³ ¶ Ë ) ¥n¯£ ³ Ë ¶ n¯£»§ aˆ1d ç²

\

^

§ m´ ¯ £ ¥¶ ¬n ´ %d5 ·Ê¬¯ §n¯ ³ ¬n ´ ·Ê d Å ¥ · ·Ë ²Æ n©m´ aˆ11 , aˆ12 v aˆ1 ³ ³ Ë ´ ¯ m´ LLR ¯ ¶ n¯£»§ a1 £· m´Â m´ ³

\

วงจรตรวจหาแบบซอฟต

M aˆ0 min d, %04 , %14 , %24 4.2832

3

^

M aˆ1 min d, %15 , %52 4.2832

บทที่

ç² m´ LLR ¯ ¶ n¯£»§ a1 £· m´Â m´ ³ M aˆ1 aˆ1 M aˆ1 1 4.2832 4.2832

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

89

¬ ´ ²

11.9381

9.6814

4.2566

16.8496

9.5398

3.0265

9.5398

(a)

(b)

(b)

(b)

(b)

(b)

(b)

(b)

¬ ´ ²

(a)

(a)

(a)

(b)

(a)

(a)

(a)

0.6283

2.8850

8.3097

4.2832

3.0265

9.5398

3.0265

(b) ¥²¤² ·Ê 0

¥²¤² ·Ê 6

( ) 9.6814

â 0

â 0 = 1

2

0

%4

â 0 1 â 0

0

â 0 = –1 1

â 0 = –1

2

Mp a 0 4.2832

2

â 0

1

3

3

%4 8.3097

0.6283

â 0

â 0 = –1

0

%4

%4

3

4.2832

â 0 = 1

( ) 3

9.5398

9.6814

â1

0

3

%5

%5

2

â1 = –1 0

â1 = –1

â1

Mp a1 4.2832

1

0

â1

â1 = 1

1

â1

2

â1

2

â1 = 1

1

%5

%5 8.3097

3

â1 = –1

4.2832

( ) 9.5398

â 2 = 1 0

â 2 = 1

Mp a 2 4.2832

1

1

â 2

â 2

%6

2

â 2

1

â 2 = 1

0

2

â 2 = –1

3

%6

3

â 2 = 1

3

â 2

â 2

0

2

%6

%6

8.3097

9.5398

4.2832

( ) 9.5398

â 3 = 1

3

â 3

0

â 3 = –1

Mp a 3 9.5398

0

â 3 1 â 3

9.5398

2

0

%7

%7

1

â 3 = –1 2

â 3 = –1

2

â 3

3

â 3 = 1

1

%7

3

â 3

%7 4.2832

9.5398

( )

¥» ·Ê 3.10 ³ Ë ¯ ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¯³§ ¯¥¶ ¸£ SOVA Å ³©¯¤m´ ·Ê 3.5

90

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

5.

Ë ¯ ·Ê 1 ²Æ n©m´ ¥²¤² ·Ê 5 (£¹Ê¯ k = 5)  ¹Ê¯­´ m´ M p a 2 ´ n¯£»§ ·Ê ¯ ¥­³¬Æ nÅ ³ aˆ2 1 ¥» ·Ê 3.10 ( ) ì ¬n ´ ·Ê d (¬n ´ ·Ê » ³ ¶ Ë ) ¥n¯£ ³ Ë ¶ n¯£»§ aˆd2 ç²

\ ^

§ m´ ¯ £ ¥¶ ¬n ´ %d6 ·Ê¬¯ §n¯ ³ ¬n ´ ·Ê d Å ¥ · ·Ë ²Æ n©m´ aˆ22 v aˆ2 ³ ³ Ë ´ ¯ m´ LLR ¯ ¶ n¯£»§ a2 £· m´Â m´ ³

\

^

M aˆ2 min d, %62 4.2832

ç² m´ LLR ¯ ¶ n¯£»§ a2 £· m´Â m´ ³ M aˆ2 aˆ2 M aˆ2 1 4.2832 4.2832 6.

Ë ¯ ·Ê 1 ²Æ n©m´ ¥²¤² ·Ê 6 (£¹Ê¯ k = 6)  ¹Ê¯­´ m´ M p a3 ´ n¯£»§ ·Ê ¯ ¥­³¬Æ nÅ ³ aˆ3 1 ¥» ·Ê 3.10 ( ) ì ¬n ´ ·Ê d (¬n ´ ·Ê » ³ ¶ Ë ) ¥n¯£ ³ Ë ¶ n¯£»§ aˆ3d ç²

\

§ m´ ¯ £ ¥¶ ¬n ´ %d7 ·Ê¬¯ §n¯ ³ ¬n ´ ·Ê d Å ¥ · ·Ë ²Æ n©m´ aˆ30 , aˆ13 , aˆ32

^

v â3 ³ ³ Ë ´ ¯ m´ LLR ¯ ¶ n¯£»§ a3 £· m´Â m´ ³

\

^

M aˆ3 min d, %07 , %17 , %72 9.5398

ç² m´ LLR ¯ ¶ n¯£»§ a3 £· m´Â m´ ³ M aˆ3 aˆ3 M aˆ3 1 9.5398 9.5398  ¥´² ² ³ Ë ¯³§ ¯¥¶ ¸£ SOVA ²Å­n m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak  m´ ³

\M p a0 , M p a1 , M p a 2 , M p a3 ^ x \4.2832, 4.2832, 4.2832,9.5398^ ç² ¯ ¥­³¬ ¶ n¯£»§Æ n É

¸Ê ¥ ³ ¶ n¯£»§ ak ·Ê¬m £´ ´ © ¥¢´ ¬m ( ¶ ¬º n´¤Æ£m£·¯¤m» ¥¶ Å ¥² à mÂ É §§³ q Ê·

 ¶ ´ ´¥ Ï´ ¯ Ä©§» ³ ¥²­©m´ n¯£»§¯¶ º ç² m¯ ¬³ ´ ) ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ SOVA

วงจรตรวจหาแบบซอฟต

\aˆ0 ,aˆ1 ,aˆ2 ,aˆ3 ^ \1, 1,1,1^

³©¯¤m´ ·Ê 3.6 ´ ³©¯¤m´ ·Ê 2.5 Å n¯³§ ¯¥¶ ¸£ SOVA Å ´¥ ¯ ¥­³¬ n¯£»§ yk Ä ¤ Ï´­ Å­n Ma ak = {–1, 1, 2, –1, 1} ç² ©´£§¸ ´¥ ¯ ¥­³¬ E 3 ©¶ · Ï´

´ ³©¯¤m´ ·Ê 2.5 n¯£»§ ·Ê ¯ n ´¥Å­nÅ n¯³§ ¯¥¶ ¸£ SOVA ¥© ­´ ¹¯

3

บทที่

yk {y 0 , y1 , y 2 , y3 , y 4 } {1.2, 0.7, 0.2, 0.5, 0.7}

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

91

¥» ·Ê 3.11 ³ Ë ¯ ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¯³§ ¯¥¶ ¸£ SOVA Å ³©¯¤m´ ·Ê 3.6

ç²£·Ã ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ H D 1 D 2 ´£¥» ·Ê 2.15 ¸Ê £· ³ Ë ­£ ¬·Ê¬ ´ ² ¹¯ ¬ ´ ² (a), (b), (c) ç² (d)

´ ³ Ë Ï´ ´¥ ¯ ¥­³¬ n¯£»§Ä ¤Å n¯³§ ¯¥¶ ¸£ SOVA  m  ·¤© ³ ©¶ · ´¥ ·Ê¯ ¶ ´¤Å

³©¯¤m´ ·Ê 3.5 É ²Æ n § m´ ¯ £ ¥¶ ¬n ´ %k 1 q 粬 ´ ² m¯ ­ n ´ Qk 1 q ¬Ï´­¥³

k = {0, 1, …, 7} ç² q = {a, b, c, d} ³ ì Å ¥» ·Ê 3.11 Ä ¤ ·Ê¬n §» ª¥ ·Ê§´ m´ à m§² Ä­ ¹¯Â¬n ´ ML ·Ê£·Â£ ¥¶ ¬n ´ ¬» ¬º (£¹Ê¯§» ª¥Â¬n ¸ à ¶ n¯£»§¯¶ º ak = 1

粧» ª¥Â¬n ²Ã ¶ n¯£»§¯¶ º ak = –1) ´ n¯£»§ ·ÊÅ­n£´Å ¥» ·Ê 3.11 Ï´Å­n¬´£´¥ Ï´ © ­´ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ´£¬£ ´¥ (3.37) ¸Ê ²Æ n©m´

\M p a0 , M p a1 , M p a 2 , M p a3 , M p a 4 ^ x \16.59, 17.85, 24.88, 12.57,17.08^ ç² ¯ ¥­³¬ ¶ n¯£»§Æ n É

\aˆ0 ,aˆ1 ,aˆ2 ,aˆ3 ,aˆ4 ^ \1, 1,1, 1,1^ ¸Ê ¥ ³ ¶ n¯£»§ ak ·Ê¬m £´ ´ © ¥¢´ ¬m (¬¯ ¶ ¬º n´¤Æ£m£·¯¤m» ¥¶ Å ¥² à mÂ É §§³ q

·Ê ¶ ´ ´¥ Ï´ ¯ Ä©§» ³ ¥²­©m´ n¯£»§¯¶ º ç² m¯ ¬³ ´ ) ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ SOVA

92

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

3.5 ¯³§ ¯¥¶ ¸£ Bi-Directional SOVA ¯³§ ¯¥¶ ¸£ SOVA ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 3.4 £· ³ Ë ¯ ´¥ Ï´ ´ ·Ê m¯ n´ ³ n¯ ¸Ê ¯´ Ï´Å­n ¤´ m¯ ´¥ Ï´ ©´£Â n´Å Å ­³© n¯ ·Ë ²¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ SOVA ¯· ¥» Ã

­ ¸Ê ·ÊÂ¥·¤ ©m´ “¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ (bi-directional SOVA)” [41, 42] ¸Ê ²Å­n

m´ LLR ¯ ¶ n¯£»§Å §n ·¤ ³ ¯³§ ¯¥¶ ¸£ SOVA ç² m´¤ m¯ ´¥ Ï ´Æ Å n ´ ¥¶

¶ ´¥ ´Ã Ï´ §¯ ¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 ¯³§ ¯¥¶ ¸£ SOVA ²Å­n n¯ £»§

¯´ q º Â É m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ´£¬£ ´¥ (2.23) ³Ê ¹¯ Pr <ak 1 | y > ¬­ ­­ M p ak ln Pr <ak 1 | y >®­

(3.39)

£¹Ê¯ ak {–1, 1} ¹¯ n¯£»§¯¶ º ¯ m¯ ¬³ ´ , y = [y0, y1, …, yL + Q – 1] ¹¯§Ï´ ³ n¯£»§ ·Ê n¯ ´¥ ¯ ¥­³¬ n¯£»§, L ¹¯ ©´£¤´© ¯ §Ï´ ³ n¯£»§¯¶ º , ç² O ¹¯­ m ©¤ ©´£ Ï´ ¯

m¯ ¬³ ´

¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ²¯´ª³¤Ã ¢´  ¥§§¶¬Å ´¥ ¯ ¥­³¬ n¯£»§¯¶ º

¯ m¯ ¬³ ´ Ä ¤ ²Â§¹¯ §Ï´ ³ n¯£»§¯¶ º a = [a0, a1, …, aL – 1] ´£Â¬n ´ ·Ê£·Â£ ¥¶

¬n ´ ¬» ¬º (maximum path metric) ­¥¹¯Â¬n ´ ML £¹Ê¯Â£ ¥¶ ¬n ´ ·Ê£´ ¸ ¬ ´ ² q

©§´ k + 1 ­´Æ n ´ ¬£ ´¥ (3.24) ³Ê ¹¯

'k 1 q ln p yk0 ; ak0

(3.40)

¸Ê É ¹¯ §¥©£ ¯ £ ¥¶ ¬´ ´ ´£Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Ê·£´ ¸ ¬ ´ ² q ©§´ k + 1 Ä ¤ ·Ê

Hk u , q ln p yk ; ak

x

1 2T

2

2

yk rˆ u , q

aˆ u , q Ma ak

2

(3.41)

´ ¯  ¬q (Bayes’ rule) ²Æ n©m´ p a | y

p a; y

p y

p y | a p a

p y

(3.42)

วงจรตรวจหาแบบซอฟต

£ ¥¶ ¬´ ´ ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² (u, q) ·Ê¥²¤² k ­´Æ n ´ ¬£ ´¥ (3.38) ³Ê ¹¯

3

บทที่

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

93

 ¹Ê ¯ ´ p(y) ¹¯©m´Â É m´ ³© ¸Ê Æ£m ·Ê¤© n¯ ³ ´¥ ³ ¬¶ Š§¹¯ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ³ ³ Ë ¯´ª³¤¬£ ´¥ (3.25) ²Æ n©m´ ©´£ m ´ ²Â É ¯ ´¥Â§¹¯ ¬n ´ ML Â É ¬³ ¬m© ³

\

p a | y exp 'Lmax

O

^

(3.43)

£¹Ê¯ 'Lmax

O ¹¯Â£ ¥¶ ¬n ´ ·Ê£· m´¬» ¬º ´£Â¬n ´ ML ©§´ L + Q ³Ê ¹¯ m´ ¥²£´ ¯ §Ï´ ³ n¯£»§¯¶ º aˆ <aˆ0 ,aˆ1 , !, aˆL 1 > ² » ¯ ¥­³¬ ´£Â¬n ´ ML ·Ë n´ Ï´­ Å­n 'ck ¹¯Â£ ¥¶ ¬n ´ ·Ê£· m´¬» ¬º ¯ ¬n ´ ·Ê£· ¶ n¯£»§ akc ¥ n´£ ³ ¶ n¯£»§ aˆk ¯ ¬n ´ ML ·Ê©§´ k ³ ³ Ë n´ ¶ n¯£»§ ¯ ¬n ´ ML ·Ê©§´ k £· m´Â m´ ³ aˆk 1 ²Æ n©m´ “ ¶ n¯£»§ ¥ n´£ (complementary bit)” ¹¯ akc 1 ¸Ê ²Æ n©m´

\

p ak 1| y exp 'Lmax

O

^

ç²

\

p ak 0 | y exp 'ck 1

^

(3.44)

粯³ ¥´¬m© ¯ ©´£ m ´ ²Â É ³ Ë ¬¯ Å ¬£ ´¥ (3.44) ­¥¹¯ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯

¶ n¯£»§ ak £· m´Â m´ ³

£¦ 'Lmax ² ¦£ p ak 1 | y ¦¦² e O ¦¦ 'max 'c ¦ ln ¦¤ ln » ¤ 'c » e L O e k 1 ¦¦ p ak 1 | y ¦¦ ¦¦ e k 1 ¦ ¦¼ ¥ ¼ ¦ ¥¦

(3.45)

1

1

Ï´­ Å­n 'k 1 ¹¯Â£ ¥¶ ¬n ´ ·Ê£· m´¬» ¬º ¬Ï´­¥³ º ¬n ´ ·Ê£· ak 1 ç² 'k 1 ¹¯Â£ ¥¶ ¬n ´ ·Ê£· m´¬» ¬º ¬Ï´­¥³ º ¬n ´ ·Ê£· ak 1 Å­n ¶ ´¥ ´¬¯ ¥ · m¯Æ ·Ë

1) n´ ¶ n¯£»§ ·Ê ¯ ¥­³¬ ´£Â¬n ´ ML ·Ê©§´ k ¹¯ aˆk 1 ì ©m´ ¶ n¯£»§ ¥ n´£ ¹¯ 1

1

c –1 ³ ³ Ë 'k 1 'Lmax

O ç² 'k 1 'k 1 ¸Ê ²Æ n©m´ m´ LLR ¯ ¶ n¯£»§ ak Å ¥ ·

·Ë£· m´Â m´ ³ 'Lmax ¬ £¦ p ak 1 | y ²¦ e O ­ 1

1

max c ¦ ¦ ln ¤ » ln 'c ­­­ 'L O 'k 1 'k 1 'k 1 ¦ ¦ ­ ¦ e k 1 ® ¥ p ak 1 | y ¦¼

(3.46)

2) n´ ¶ n¯£»§ ·Ê ¯ ¥­³¬ ´£Â¬n ´ ML ·Ê©§´ k ¹¯ aˆk 1 ì ©m´ ¶ n¯£»§ ¥ n´£ ¹¯ 1

1

c 1 ³ ³ Ë 'k 1 'Lmax

O ç² 'k 1 'k 1 ¸Ê ²Æ n©m´ m´ LLR ¯ ¶ n¯£»§ ak Å ¥ · ·Ë

£· m´Â m´ ³

94

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

'ck 1 ¬­ ¦£ p ak 1| y ¦²¦ e 1

1

c max ­ ln ¦¤ ln » 'max ­­ 'k 1 'L O 'k 1 'k 1 ¦ ¦ ­ L

O y p a 1|

k ¦ e ® ¥ ¼¦

(3.47)

¬£ ´¥ (3.46) ç² (3.47) ì Å­nÂ­É ©m´Æ£m©m´ m´ ¥²£´ ¯ ¶ n¯£»§ ak ´£Â¬n ´ ML

²£· m´Â m´Å m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¯ ¶ n¯£»§ ak ²£· m´Â m´ ³ £ p ak 1 | y ¦² ¦ ¦» ' 1 ' 1

M p ak ln ¦ ¤ k 1 k 1 ¦ ¦¦ p a 1| y

k ¦ ¥ ¼

(3.48)

³Ê ¹¯ m´ LLR ¯ ¶ n¯£»§ ak £· m´Â m´ ³ § m´ ¥²­©m´ £ ¥¶ ¬n ´ ¬» ¬º ·Ê¬¯ §n¯ ³

º ¬n ´ ·Ê£· ak 1 ç²Â£ ¥¶ ¬n ´ ¬» ¬º ·Ê¬¯ §n¯ ³ º ¬n ´ ·Ê£· ak 1 Ä ¤ ·Ê

´ ¯ LLR ­¥¹¯ M p ak Â É ³© m ¸ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§ ·Ê » ¯ ¥­³¬ ç²  ¥¹Ê¯ ­£´¤ ¯ LLR ¯ Å­n ¥´ ¸ m´ ¥²£´ ¯ ¶ n¯£»§ ak ³Ê ¹¯ £¦ 1, if M p ak b 0 aˆk ¦¤ ¦¦1, if M p ak 0 ¥

(3.49)

3.5.1 ´¥­´ m´ LLR ¯ ¶ n¯£»§ ­§³ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ à m ¯¯ Â É 2 ³ Ë ¯ ¹¯ 1) ¯ ¥­³¬ n¯£»§ ´£ ³ Ë ¯ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶  ¹Ê¯­´ m´ ¥²£´ ¯ §Ï´ ³ n¯£»§¯¶ º

<aˆ0 ,aˆ1 ,!,aˆL 1 > ·Ê¬¯ §n¯ ³ ¬n ´ ML ¸Ê Â É Â¬n ´ ·Ê£·Â£ ¥¶ ¬n ´ ¬» ¬º ·Ê©§´

max max ´ ³ Ë Å­n ³ ¸ m´ 'L O ç²Â£ ¥¶ ¬n ´ 'k u ¬Ï´­¥³ º ©§´ k + Q ³Ê ¹¯ 'L O

2) ¯ ¥­³¬ n¯£»§Ã ¤n¯ §³ (backward decoding) ´£Ã ¢´  ¥§§¶¬Â ¶£ (­£¹¯

´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶Å ³ Ë ¯ ·Ê­ ¸Ê ) ³ ì Å ¥» ·Ê 3.12  ¹Ê¯­´ m´Â£ ¥¶ Ë È ©m´ Hbk u , q ´£¬£ ´¥ (3.41) ç²Â£ ¥¶ ¬´ ´ Hbk Zk u , Zk 1 q ­¥¹¯Â ·¤ ¬³

¬n ´ 'bk u ³ Ë Ã m©§´ k = L + Q ¸ k = 0 Ä ¤ ·Ê£ ¥¶ ¬n ´ ­´Æ n ³ ·Ë [41, 42]

\

^

'bk u max Hbk u , q 'bk 1 q

q

วงจรตรวจหาแบบซอฟต

k ç² º ¬ ´ ² u = {0, 1, …, Q – 1}

(3.50)

£¹Ê¯ Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬´ ´ 'bL O q 0 ¬Ï´­¥³ º ¬ ´ ² q ´ ³ Ë Å­n ³ ¸ m´ Hbk u , q ç² 'bk u ¬Ï´­¥³ º ©§´ k ç² º ¬ ´ ² u ç² q ·Ê Ï´Å­n ´¥Â §·Ê¤

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

3

บทที่

95

©§´ k

k+1

H kb u ,q

\

aˆ u ,q

'bk 1 q

^

'bk u max Hbk u ,q 'bk 1 q

q

H kb u , s

aˆ u , s

Zk 1 s

(¬ ´ ² s)

yk k-th stage (¥²¤² ·Ê k)

¥» ·Ê 3.12 à ¢´  ¥§§¶¬¬Ï´­¥³ ´¥ ¯ ¥­³¬ n¯£»§Ã ¤n¯ §³

¬ ´ ² u , q w Zk u , Zk 1 q Â É ¥¶ ´£Ã ¢´  ¥§§¶¬  ¹Ê¯Å nÅ ´¥­´ m´ LLR ¯ ¶ n¯£»§¯¶ º ­£´¤Â­ º

Ë ¯ ·Ê­ ¸Ê ²£· m´Â m´ ³ £ ¥¶ £ ¥¶ ¬´ ´ Hk u , q ·ÊÆ n ´ ´¥ Ï´ © Å ³

Ë ¯ ·Ê¬¯ ¬£¯ ¯ ´ ·Ë ¥²­©m´ ¬´ ´ Hbk u , q ·ÊÆ n ´ ´¥ Ï´ © à ¤n¯ §³ Å ³ ´¥ ¯ ¥­³¬ n¯£»§Ã ¤n¯ §³ Å Ã m§² m© ©§´ k ɬ´£´¥ Ï´ © ­´ m´ LLR ¯ ¶

n¯£»§¯¶ º ak Æ n ³ · ²Æ nÆ£m n¯ ³ ¸ m´ Hbk u , q ç² 'bk u ¬Ï´­¥³ º ©§´ k ç² º ¬ ´ ² u ç² q  ¹Ê¯§ Ï´ © ­ m ©¤ ©´£ Ï´ ·Ê n¯ Å nÅ ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ( » ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ Å ¥» ·Ê 3.13)

­§³ ´ ·ÊÆ n Ï´ ´¥ ¯ ¥­³¬ n¯£»§Å ³ Ë ¯ ·Ê­ ¸Ê çn© É ²Æ n m´ <aˆ0 , aˆ1 , !, aˆL 1 > , max 'L O ç² 'k u ¬Ï´­¥³ º k ç² u ´ ³ Ë Å­n Ï´ © ­´ m´Â£ ¥¶ ¬n ´ ·Ê£· m´¬» ¬º ¯

¶ n¯£»§ ¥ n´£ akc ¸Ê ­´Æ n ´ [41, 42] 'ck 1

max

u ,q , aˆ u ,q vaˆk

\'k u Hbk u ,q 'bk 1 q ^

(3.51)

¬Ï´­¥³ º ´¥Â §·Ê¤ ¬ ´ ² (u, q) ·Ê£· ¶ n¯£»§ aˆ u , q v aˆk ³ ³ Ë m´ LLR à ¯²Ä ¬Â ¯¥¶ ¯¯¥¶ ¯ ¯ ¶ n¯£»§ ak ­´Æ n ´ ¬£ ´¥ (3.48) ³Ê ¹¯ 1

1

M p ak 'k 1 'k 1

96

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(3.52)

1

Ä ¤ ·Ê n´ ¶ n¯£»§ ·Ê ¯ ¥­³¬Æ n ´£Â¬n ´ ML ·Ê©§´ k ¹¯ aˆk 1 É Ï´­ Å­n 'k 1 'Lmax

O

ç² 'k 1 'ck 1 Å ´ §³ ³ n´ ¶ n¯£»§ ·Ê ¯ ¥­³¬Æ n ´£Â¬n ´ ML ·Ê©§´ k ¹¯ aˆk 1

1

1

c 1 É Ï´­ Å­n 'k 1 'Lmax

O ç² 'k 1 'k 1

3.5.2 ¬¥º ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ £ ¸ SOVA à ¬¯ ¶ª ´ ­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ SOVA ¬¥º Â É ³ Ë ¯ m´ È Æ n ´£¥» ·Ê 3.13 ³©¯¤m´ ·Ê 3.7 ´ ³©¯¤m´ ·Ê 2.4 Å n¯§ ³ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ Å ´¥ ¯ ¥­³¬ n¯£»§ yk Ä ¤ Ï´­ Å­n Ma ak = {–1, 2, 1, 2}

©¶ · Ï´

´ ³©¯¤m´ ·Ê 2.4 n¯£»§ ·Ê ¯ n ´¥Å­nÅ n¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ¥© ­´ ¹¯ yk {y 0 , y1 , y 2 , y3 } {0.9, 0.2, 0.3, 0.6}

ç²Ã ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ H D 1 0.5D ì Å ¥» ·Ê 2.13 ¸Ê £·¬¯ ¬ ´ ² ¹¯¬ ´ ² (a) 粬 ´ ² (b) ³ ³ Ë ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ £· ³ Ë ¯ ´¥ Ï´ ´ ³ ·Ë

1. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬n ´ '0 u 0 ¬Ï´­¥³ º ¬ ´ ² u = {a, b} 2. ¥²¤² ·Ê 0 ¸ 3 (¬Ï´­¥³ k = 0, 1, 2, 3) Å­n Ï´ ´¥ ´¥ ¯ ¥­³¬ n¯£»§Ã °´¥q ­£¹¯

¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [1] ´£ ³ Ë ¯ Å ¥» ·Ê 3.14 £¹Ê¯ m´ ·Ê¯¤m» ¶ ³ ¬n ¬´ ´Ã m§²Â¬n ¹¯ m´ Hk u ,q ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² (u, q) ³ Ë È Ã§² ³©Â§ ·Ê¯¤m» ¥ Ä­ ¯ à m§²

¬m© ³ ·Ë

'k u

'bk u

¬Ï´­¥³ à m§² k {0, 1, 2, 3} ç² u {a, b} ¯ ´ ·Ë¬n §» ª¥ ·Ê§´ m´ à m§²Ä­

วงจรตรวจหาแบบซอฟต

¬ ´ ²Ã¬ ¸ m´Â£ ¥¶ ¬n ´ à n´ ­ n ´ 'k u ç²Ã ¤n¯ §³ 'bk u Å ¥» ª«

3.4558 Ä ¤ ·Ê§» ª¥ ¹¯Â¬n ´ ML (¬n ¬·Â ´) ·Ê£·Â£ ¥¶ ¬n ´ ¬» ¬º ³Ê ¹¯ ' max 4

¬n ¸ à ¶ n¯£»§¯¶ º ak = 1 粧» ª¥Â¬n ²Ã ¶ n¯£»§¯¶ º ak = –1 ³ ³ Ë ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ² ¯ ¥­³¬ n¯£»§Ã °´¥q Æ n É

3

บทที่

\aˆ0 ,aˆ1 ,aˆ2aˆ3 ^ \1, 1,1,1^ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

97

¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ´¥ ¯ ¥­³¬ n¯£»§Ã °´¥q (­£¹¯ ³ ³ Ë ¯ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [1]) 1. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬n ´ '0 (u ) 0 ¬Ï´­¥³ º ¬ ´ ² u \0,1, !,Q 1^ 2. ¬Ï´­¥³ k 0,1, !, L O 1 ¬Ï´­¥³ q 0,1, !,Q 1 Ï´ © ­´ m´ Hk u ,q ´£¬£ ´¥ (3.41) ¬Ï´­¥³ º ¬ ´ ² u ·Ê Ï´Å­n (u, q) Â É ¥¶ Ï´ © ­´ m´ 'k 1 q ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ´£¬£ ´¥ (3.23) ³ ¸ m´ 'k 1 q ç²Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Sk 1 q

(¬¶ Ë ¬º ´¥© Ï´Ë ¯ q) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ k) 3. ¯ ¥­³¬§Ï´ ³ n¯£»§¯¶ º aˆ <aˆ0 ,aˆ1 , !, aˆL 1 > ·Ê¬¯ §n¯ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Ê£ · · m´ 'L O max max ¬» ¬º ³Ê ¹¯ 'L O ç² ³ ¸ m´ 'L O

´¥ Ï´ © à ¤n¯ §³  ¹Ê¯ ´¥­´ m´ LLR 4. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬n ´ 'bL O (q ) 0 ¬Ï´­¥³ º ¬ ´ ² q \0,1, !,Q 1^ 5. ¬Ï´­¥³ k L O 1, !,1, 0 ¬Ï´­¥³ u 0,1, !,Q 1 Ï´ © ­´ m´ Hbk u ,q ´£¬£ ´¥ (3.41) ¬Ï´­¥³ º ¬ ´ ² q ·Ê Ï´Å­n (u, q) Â É ¥¶ Ï´ © ­´ m´ 'bk u ´£¬£ ´¥ (3.50) ³ ¸ m´ 'bk u

(¬¶ Ë ¬º ´¥© Ï´Ë ¯ u) Ï´ © ­´ m´Â£ ¥¶ ¬n ´ ·Ê£· m´¬» ¬º ¯ ¶ n¯£»§ ¥ n´£ akc v aˆk ´£¬£ ´¥ (3.51) Ï´ © ­´ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ ak ´£¬£ ´¥ (3.52) (¬¶ Ë ¬º ´¥© Ï´Ë ¯ k) ¥» ·Ê 3.13 ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ [41, 42]

98

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 3.14 ³ Ë ¯ ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ Å ³©¯¤m´ ·Ê 3.7

¸Ê ¥ ³ ¶ n¯£»§ ak ·Ê¬m £´ ´ © ¥¢´ ¬m ( ¶ ¬º n´¤Æ£m£·¯¤m» ¥¶ Å ¥² à mÂ É §§³ q ·Ê ¶ ´ ´¥ Ï´ ¯ Ä©§» ³ ¥²­©m´ n¯£»§¯¶ º ç² m¯ ¬³ ´ ) ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´

´¥ Ï´ © à ¤n¯ §³ 3. Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬n ´ à ¤n¯ §³ 'b4 u 0 ¬Ï´­¥³ º ¬ ´ ² u = {a, b} 4. ¥²¤² ·Ê 3 (£¹Ê¯ k = 3) Ï´ © ­´ m´Â£ ¥¶ ¬´ ´ Hb3 u , q ç² ¥³ ¥º £ ¥¶ ¬n ´ à ¤n¯ §³ 'b3 u Å­n ¥ º ¬ ´ ² É ²Æ n §§³ q ´£ ·Êì Å ¥» ·Ê 3.14  ¹Ê ¯ ´ ¶ n¯£»§ · m´¬» ¬º ¯ ¶ n¯£»§ ´£Â¬n ´ ML ©§´ k = 3 ¹¯ aˆ3 1 ³ ³ Ë Â£ ¥¶ ¬n ´ ·Ê£ ¥ n´£ a 3c 1 ­´Æ n ´ ¬£ ´¥ (3.51) ³Ê ¹¯

max

u ,q , aˆ u ,q vaˆ3

max

u ,q , aˆ u ,q v1

\ ' a H a ,a ' 3

b 3

b 4

a

, '3 b Hb3 b ,a 'b4 a

^

\ 8.7075 14.8544 0 , 1.9111 4.8013 0 ^

6.7124

³ ³ Ë m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¯ ¶ n¯£»§ a3 ­´Æ n ´ ¬£ ´¥ (3.48) ³Ê ¹¯ 1

1

M p a3 ' 4 ' 4

' 4max 'c4 3.4558 6.7124 3.2566

5. ¥²¤² ·Ê 2 (£¹Ê¯ k = 2) Ï´ © ­´ m´Â£ ¥¶ ¬´ ´ Hb2 u , q ç² ¥³ ¥º £ ¥¶ ¬n ´ Ã

วงจรตรวจหาแบบซอฟต

'c4

3

บทที่

¤n¯ §³ 'b2 u Å­n ¥ º ¬ ´ ² É ²Æ n §§³ q ´£ ·Êì Å ¥» ·Ê 3.14  ¹Ê ¯ ´ ¶ n¯£»§

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

99

· m´¬» ¬º ¯ ¶ n¯£»§ ´£Â¬n ´ ML ©§´ k = 2 ¹¯ aˆ2 1 ³ ³ Ë Â£ ¥¶ ¬n ´ ·Ê£ ¥ n´£ a c2 1 ­´Æ n ´ ¬£ ´¥ (3.51) ³Ê ¹¯ 'c3

max

u ,q , aˆ u ,q vaˆ2

max

u ,q , aˆ u ,q v1

\ '

2

a Hb2 a ,a 'b3 a

, ' 2 b Hb2 b ,a 'b3 a

^

\ 2.2854 10.6788 0.9686 , 6.1969 2.5106 0.9686 ^

7.7389

³ ³ Ë m´ M p a 2 ­´Æ n ´ ¬£ ´¥ (3.48) ³Ê ¹¯ 1

1

M p a 2 '3 '3

' 4max 'c3 3.4558 7.7389 4.2832

Ë ¯ ·Ê 4 ç² 5 É ² 6. ¥²¤² ·Ê 1 ç² 0 (£¹Ê¯ k = 1 ç² 0) Ï´ ´¥ Ï´ ©  m  ·¤© ³ Å ³ Æ n£ ¥¶ ¬n ´ ·Ê£· m´¬» ¬º ¯ ¶ n¯£»§ ¥ n´£ a1c 1 ç² a c0 1  m´ ³ 'c2 7.7389

ç²

'1c 7.7389

³ ³ Ë m´ M p a1 ç² M p a1 £· m´Â m´ ³ 1

1

'c2 ' max 7.7389 3.4558 4.2832 4

1

1

' 4max '1c 3.4558 7.7389 4.2832

M p a1 ' 2 ' 2

M p a 0 '1 '1

 ¥´² ² ³ Ë ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ²Å­n m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§

ak  m´ ³

\M p a0 , M p a1 , M p a 2 , M p a3 ^ x \4.2832, 4.2832, 4.2832,3.2566^ ³©¯¤m´ ·Ê 3.8 ´ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 n´ Ï´­ Å­n§Ï´ ³ n¯£»§¯¶ º ak = {1, 1, –1}, m¯ ¬³ ´ H D 1 D 2 , ¬³ ´ ¥ © nk = {0.2, 0.3, –0.2, 0.5, 0.3} Å n¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ Å ´¥ ¯ ¥­³¬ n¯£»§ yk Ä ¤ Ï´­ Å­n Ma ak = {–1, 1, 2, –1, 1} ç² ©´£Ã ¥ ¥© ¯ nk  m´ ³ T2 1/ 2Q

©¶ · Ï´

100

n¯£»§ ·Ê n¯ ´¥Å­nÅ n¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ¥© ­´ ¹¯

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

4. 7 11

9

54

–3

–0

.28

. 12 57

–1

4.7 11 9

9 69 1.6

–3

–3

94 .03

5 84 8.9

–1

–3

7 17 4.4

–5

94 .03

–1

06 .51

–2

¥» ·Ê 3.15 ³ Ë ¯ ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¯³§ ¯¥¶ ¸£ SOVA Å ³©¯¤m´ ·Ê 3.8

yk ak hk nk {1.2, 1.3, 2.2, 1.5, 1.3}

ç²£·Ã ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ H D 1 D 2 ´£¥» ·Ê 2.15 ¸Ê £· ³ Ë ­£ ¬·Ê¬ ´ ² ¹¯ ¬ ´ ² (a), (b), (c) ç² (d)

´ ³ Ë Ï´ ´¥ ¯ ¥­³¬ n¯£»§Ä ¤Å n¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´  m  ·¤© ³ ©¶ ·

´¥ ·Ê¯ ¶ ´¤Å ³©¯¤m´ ·Ê 3.7 É ²Æ n£ ¥¶ ¬´ ´ Hk u , q , £ ¥¶ ¬n ´ à n´ ­ n ´ 'k u

ç²Ã ¤n¯ §³ 'bk u ´£¥» ·Ê 3.15 ¯ ´ ·Ë ¬n §» ª¥ ·Ê§´ m´ à m§²Ä­ ¹¯Â¬n ´ 6.0004 Ä ¤ ·Ê§» ª¥Â¬n ¸ à ¶ n¯£»§ ML (¬n ¬·Â ´) ·Ê£·Â£ ¥¶ ¬n ´ ¬» ¬º ' max 4

¯¶ º ak = 1 粧» ª¥Â¬n ²Ã ¶ n¯£»§¯¶ º ak = –1 ³ ³ Ë ¯³§ ¯¥¶ ¸£ SOVA Ã

\aˆ0 ,aˆ1 ,aˆ2 ,aˆ3 ,aˆ4 ^ \1,1, 1, 1,1^ ¸Ê ¥ ³ ¶ n¯£»§ ak ·Ê¬m £´ ´ © ¥¢´ ¬m ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë ´ ´¥ ¯ ¥­³¬ n¯£»§ n©¤¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´

วงจรตรวจหาแบบซอฟต

¬¯ ¶ª ´ ² ¯ ¥­³¬ n¯£»§Ã °´¥q Æ n É

Å ´¥­´ m´ LLR ¯ ¶ n¯£»§ ak ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ²Â¥¶Ê£ n ­´

\

^

£ ¥¶ ¬n ´ ·Ê£· m´¬» ¬º 'ck 1 ¯ ¶ n¯£»§ ¥ n´£ a c0 , a1c ,a c2 , a 3c , a c4 \ 1, 1,1,1, 1^ ¸Ê £· m´Â m´ ³

\'1c , 'c2 , 'c3 , 'c4,'c5 ^ \ 22.5934, 17.0535, 22.8500, 13.2836, 10.7704^ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

3

บทที่

101

´¥´ ·Ê 3.1 ©´£ ³ n¯ ¯ © ¥ ¥© ­´Ã ¯¡ qà m´ È ·Ê ¯ n Å n ¹Ê¯ ¯ ¥­³¬ n¯£»§­ ¸Ê ¶ © ¥ ¥© ­´Ã ¯¡ q

Ï´ © ³© Ï´Â ¶ ´¥ ´ ¶ ª´¬ ¥q ( m¯­ ¸Ê ¶ )

BCJR (­¥¹¯ MAP) Max-Log-MAP Log-MAP SOVA [35]

´¥ ©

´¥ »

14Q – 3

22Q + 1

24Q

12Q

32Q – 4

12Q

7Q E

Bi-directional SOVA

2

9E 9 2

1

17Q + 1

6Q + 1 12Q

 ¥´² ² ³ Ë ¯³§ ¯¥¶ ¸£ SOVA à ¬¯ ¶ª ´ ²Å­n m´ M p ak  m´ ³

\M p a0 , M p a1 , M p a 2 , M p a3 , M p a 4 ^ x \16.593,11.053, 16.85, 7.2832, 4.7699^ 3.6 ©´£ ³ n¯ ¯ © ¥ ¥© ­´Ã ¯¡ q Å ·Ê ·Ë ´¥Â ¥·¤  ·¤ ©´£ ³ n¯ ¯ © ¥ ¥© ­´Ã ¯¡ q ³ Ë ­£ ·Ê¯ ¶ ´¤Å ·Ê 2 ç² 3

² ¶ ´¥ ´ ´ Ï´ © ³© Ï´Â ¶ ´¥ © (addition operator) ç² ³© Ï´Â ¶ ´¥ » (multiplication operator) ·Ê n¯ Å n ¹Ê¯ ¯ ¥­³¬ n¯£»§­ ¸Ê ¶ Ä ¤¯´ª³¤Â qÅ ´¥ ¶ ´¥ ´ ³ ·Ë

³© Ï´Â ¶ ´¥Â§¹¯ / ´¥Â ¥·¤  ·¤ / ´¥­´ m´¬» ¬º / ´¥ ³ ¬¶ Å Ã °´¥q 1 ³© £· ©´£ ³ n¯  ·¤  m´ ³ ³© Ï´Â ¶ ´¥ © 1 ³©

³© Ï´Â ¶ ´¥ © ç² ´¥§ £· ©´£ ³ n¯  m´ ³ Å ² ·Ê ³© Ï´Â ¶ ´¥ » ç² ´¥­´¥£· ©´£ ³ n¯  m´ ³

¡³ q ³ ¶ ª´¬ ¥q m´ È Â m ¡³ q ³ §¯ ´¥¶ £ ¸ ¥¥£ ´ ¶, ¡³ q ³ § · Ë Ï´§³ , ¡³ q ³ ­´ m´ ¬³£ »¥ q, 粡³ q ³ à nÆ n¯ ¶ §´ Å ¬£ ´¥ (3.16) ¬´£´¥ ­´ m´Æ n Ä ¤Å n ´¥´ n ­´

(look-up table)  ¥´² ² ³ Ë Å ·Ê ·Ë ²Æ£m ³ Â É ©´£ ³ n¯ ¯ © ¥ ¥© ­´

´¥´ ·Ê 3.1 ì ©´£ ³ n¯ ¯ © ¥ ¥© ­´Ã ¯¡ qà m´ È ·Ê n¯ Å n ¹Ê¯ ¯

¥­³¬ n¯£»§­ ¸Ê ¶ 11 £¹Ê¯ Q = 2Q Ï´ © ¬ ´ ²Å à ¢´  ¥§§¶¬ (trellis state) ç² Q ¹¯ Ï´ © ­ m ©¤ ©´£ Ï´ ¯ ´¥qÂ É ·ÊÅ n¬¥n´ à ¢´  ¥§§¶¬ ¯ ´ ·Ë ´¥´ ·Ê 3.2 ç² 3.3 Æ n¤

11

Å ·Ê ·Ë ² ³ Ï´ © ³© Ï´Â ¶ ´¥ © ç² ´¥ » ·Ê n¯ Å n ³ Ë ­£ Ä ¤ ¤´¤´£ Ï´Å­n Ï´ © ­ m ©¤ ©´£ Ï´ (memory) ·Ê© ¥ ¥© ­´Ã ¯¡ q n¯ Å n£· Ï´ © n ¯¤¬º

102

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

´¥´ ·Ê 3.2 ©´£ ³ n¯ ¯ ¯³§ ¯¥¶ ¸£ BCJR ·Ê n¯ Å n ¹Ê¯ ¯ ¥­³¬ n¯£»§­ ¸Ê ¶ BCJR (­¥¹¯ MAP)

Ï´ © ³© Ï´Â ¶ ´¥ ´ ¶ ª´¬ ¥q ( m¯­ ¸Ê ¶ ) ´¥ ©

´¥ »

8Q

12Q

Bk 1 q Å ¬£ ´¥ (2.14)

Q

2Q

Ck u Å ¬£ ´¥ (2.16)

Q

2Q

¯¥q£¯§Æ§Â ³ B k u Å ¬£ ´¥ (2.30)

Q–1

Q

¯¥q£¯§Æ§Â ³ Ck u Å ¬£ ´¥ (2.30)

Q–1

Q

2(Q – 1)

4Q + 1

1

0

14Q – 3

22Q + 1

Hk u ,q Å ¬£ ´¥ (2.29) ³ Ë ´¥Â©·¤  ¶ à n´ ­ n ´Ã§²Ã ¤n¯ §³ 12

m´ LLR M p ak Å ¬£ ´¥ (2.24) ´¥ ³ ¬¶ Å Ã °´¥q ¯ n¯£»§­ ¸Ê ¶ ¥©£

´¥´ ·Ê 3.3 ©´£ ³ n¯ ¯ ¯³§ ¯¥¶ ¸£ Max-Log-MAP ·Ê n¯ Å n ¹Ê¯ ¯ ¥­³¬ n¯£»§­ ¸Ê ¶ Ï´ © ³© Ï´Â ¶ ´¥ ´ ¶ ª´¬ ¥q ( m¯­ ¸Ê ¶ ) ´¥ ©

´¥ »

´¥­´ m´¬» ¬º

12Q

12Q

0

k 1 q Å ¬£ ´¥ (3.12) B

2Q

0

Q

C u Å ¬£ ´¥ (3.14) k

2Q

0

Q

4Q + 1

0

2(Q – 1)

1

0

0

20Q + 2

12Q

4Q – 2

Hk u ,q Å ¬£ ´¥ (3.10) ³ Ë ´¥Â©·¤  ¶ à n´ ­ n ´Ã§²Ã ¤n¯ §³

m´ LLR M p ak Å ¬£ ´¥ (3.9) ´¥ ³ ¬¶ Å Ã °´¥q ¯ n¯£»§­ ¸Ê ¶ ¥©£

³©¯¤m´ ©¶ · ´¥ ³ Ï´ © ³© Ï´Â ¶ ´¥ ´ ¶ ª´¬ ¥q m´ È ¯ ¯³§ ¯¥¶ ¸£ BCJR ç² Max-

Log-MAP  ¹Ê¯Â É Ã © ´ Å­n n»¯m´ ¥´ ©¶ · ´¥ ³ Ï´ © ³© Ï´Â ¶ ´¥Å ´¥´ ·Ê 3.113 12

¬´Â­ º Ê· Ï´ ´¥ Ï´ © m´Â£ ¥¶ ¬´ ´ Ï´ © 2 ¥³ Ë ( ³ Ë ´¥Â©·¤  ¶ à n´ ­ n ´Ã§²Ã ¤n¯ §³ ) É ¹Ê¯§ ¥¶£´

13

´¥ ³ Ï´ © ³© Ï´Â ¶ ´¥ ´ ¶ ª´¬ ¥qÅ ´¥´ ·Ê 3.1 ¯³§ ¯¥¶ ¸£ Log-MAP ²Å n¬£ ´¥ (3.10), (3.15), (3.18),

­ m ©¤ ©´£ Ï´ ·Ê n¯ Å nÂ É m´Â£ ¥¶ ¬´ ´ ·Ë (3.19) ç² (3.20), ¯³§ ¯¥¶ ¸£ SOVA ²Å n¬£ ´¥ (3.23), (3.38) 粬£ ´¥ ·Ê ·Ê¤© n¯ ³ ´¥ ¯ ¥­³¬ n¯£»§Ã

วงจรตรวจหาแบบซอฟต

MAX-LOG-MAP

3

บทที่

¯¡ q ´£¥» ·Ê 3.9 [35], 粯³§ ¯¥¶ ¸£ Bi-directional SOVA ²Å n¬£ ´¥ (3.23), (3.41), (3.50), (3.51) ç² (3.52)

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103

800

BCJR (or MAP) Max-Log-MAP, Log-MAP, Bi-directional SOVA SOVA

Number of multiplication operators

700 600 500 400 300 200 100 0

1

2

3

4

5

Number of target memories (Q)

¥» ·Ê 3.16  ¥·¤  ·¤ Ï´ © ³© Ï´Â ¶ ´¥ » ¯ © ¥ ¥© ­´Ã ¯¡ qà m´ È ( m¯­ ¸Ê ¶ )

Å ´ ¶ ³ ¶ ³© Ï´Â ¶ ´¥ » ¹¯©m´£· ©´£ ³ n¯ £´ ©m´ ³© Ï´Â ¶ ´¥ © £¹Ê¯ Ï ´Æ

¬¥n´ Â É © ¥¯¶Â§É ¥¯ ¶ ¬q  ¥´² ² ³ Ë Å ·Ê ·Ë ² ¶ ´¥ ´Â ´² Ï´ © ³© Ï´Â ¶ ´¥ » Å ´¥  ¥·¤  ·¤ ©´£ ³ n¯ ¯ © ¥ ¥© ­´Ã ¯¡ qà m´ È ( m¯­ ¸Ê ¶ ) ´£ ·Êì Å ¥» ·Ê

3.16 ¸Ê ² ©m´¯³§ ¯¥¶ ¸£ BCJR £· ©´£ ³ n¯ £´ ¬º Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ ´¥qÂ É ·ÊÅ n£·

­ m ©¤ ©´£ Ï´ Ï´ © £´ ¬Ï´­¥³ ¯³§ ¯¥¶ ¸£ Max-Log-MAP, Log-MAP ç² Bi-directional

SOVA £· ©´£ ³ n¯  m´ ³ 粯³§ ¯¥¶ ¸£ SOVA £· ©´£ ³ n¯ n ¯¤¬º ³ ³ Ë ¸ Â É Â­ º § ©m´ Ï´Æ£¯³§ ¯¥¶ ¸£ SOVA ¸ Æ n » Ï ´£´Å n ¥¶ Å ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë ¯ ´ ¥²¤º q

m´ È (¥©£ ³ Ë Å °´¥q ¶¬ qÆ ¥¡q ) £´ ©m´¯³§ ¯¥¶ ¸£ BCJR ¯¤m´ Æ¥ É ´£ n´ ¶ ´¥ ´ ´¥´ ·Ê 3.1

Å ¢´ ¥©£ ² ©m´ ¯³§ ¯¥¶ ¸£ ·Ê£· ©´£ ³ n¯ £´ ¬º ¹¯ BCJR ¥¯ § £´ ¹¯ Log-MAP, MaxLog-MAP, Bi-directional SOVA, ç² SOVA ´£§Ï´ ³

3.7 ¬¥º n´¤ ¯ q ¥² ¯ ·Ê¬Ï´ ³ ¯ ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë É ¹¯ © ¥ ¥© ­´Ã ¯¡ q粩 ¥

¯ ¥­³¬Ã ¯¡ q ¸Ê ² Ï´­ n ´ ·Êç  §·Ê¤ m´©¬´¥Ã ¯¡ q¥²­©m´ ³  ¹Ê¯ m©¤Å­n¥² £· ¬£¥¥ ² ·¤¶Ê ¸Ë Å Ã m§²¥¯ ¯ ´¥© Ï´Ë ¯³§ ¯¥¶ ¸£ BCJR Â É ¯³§ ¯¥¶ ¸£Ã MAP ·Ê

¬´£´¥ Ï ´£´¬¥n´ Â É © ¥ ¥© ­´Ã ¯¡ q粩 ¥ ¯ ¥­³¬Ã ¯¡ qÆ n Ä ¤¥³ ¥² ³ Æ n

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©m´ ¶ n¯£»§Ã m§² ¶ ·Ê ¯ ¥­³¬Æ n ²Â É ¶ n¯£»§ ·Ê ·¬º (­¥¹¯£· n¯ ¶ §´ n ¯¤¬º ) ¯¤m´ Æ¥ É ´£ ¯³§ ¯¥¶ ¸£ BCJR £· ©´£ ³ n¯ £´ ¸ Æ£m ¶¤£ Ï ´£´Å n ¥¶ Å ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë ¯

´ ¥²¤º q m´ È

³ ³ Ë ·Ë ¸ Æ n¯ ¶ ´¤Ã © ¶ ç²­§³ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ ·Ê­£¹¯ MAP Ã

m´ È Æ nà m Max-Log-MAP, Log-MAP, SOVA, ç² Bi-directional SOVA ¸Ê £·¬£¥¥ ² Å §n ·¤ ³ ¯³§ ¯¥¶ ¸£ BCJR à m£· ©´£ ³ n¯ n ¯¤ ©m´ ( ´£ ´¥´ ·Ê 3.1) Ä ¤Â ´²¯¤m´ ¤¶Ê

¯³§ ¯¥¶ ¸£ SOVA ¸Ê ¹¯©m´£· ©´£ ³ n¯ n ¯¤¬º à m£·¬£¥¥ ²Å §n ·¤ ³ ¯³§ ¯¥¶ ¸£ BCJR

£¹Ê¯ Ï ´Æ Å n ´ Å ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë ¯ ´ ¥²¤º q m´ È ( » ³©¯¤m´ Å ­³© n¯ ·Ê 4.6.2)

 ¥´² ² ³ Ë Å ³ º ³ ¸ Æ n ¶¤£ Ï ´¯³§ ¯¥¶ ¸£ SOVA Æ Å nÅ ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë ¯

´ ¥²¤º q m´ È ¥©£ ³ Ë Å °´¥q ¶¬ qÆ ¥¡q n©¤

3.8 Ã ¸ ­³ n´¤ 1. 2.

¯ ¶ ´¤ ©´£Ã m´ ¯ ¯³§ ¯¥¶ ¸£ BCJR, Max-Log-MAP, Log-MAP, SOVA ç²

Bi-directional SOVA

´ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 n´ Ï´­ Å­n§Ï´ ³ n¯£»§¯¶ º ak = {1, 1, –1}, m¯ ¬³ ´ H D 1 D , ¬³ ´ ¥ © nk = {–0.2, –0.3, 0.2, 0.1} ¸Ê £· ©´£ à ¥ ¥©  m´ ³ T2 1/ 2Q ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ Max-Log-MAP ç² Ï´­ Å­n ´m ©¬´¥¯² ¶¥¶¯¯¥¶ 2.1) Ma ak = {0, 0, 0, 0}

2.3) Ma ak = {–4, –6, 2, 0} 2.4)  ¥·¤  ·¤ 粯 ¶ ´¤ §§³ q ÊÆ· n ´ ´¥ ¯ ¥­³¬ n¯£»§Å n¯ ·Ê 2.1 – 2.3 3.

´ à ¸ ­³ n´¤ n¯ ·Ê 2 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ BCJR

4.

´ à ¸ ­³ n´¤ n¯ ·Ê 2 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ Log-MAP

5.

¸ SOVA £¹Ê¯ Ï´­ Å­n ´ à ¸ ­³ n´¤ n¯ ·Ê 2 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ £ ©´£§¸ ´¥ ¯ ¥­³¬Â m´ ³

วงจรตรวจหาแบบซอฟต

2.2) Ma ak = {4, 6, –2, 0}

3

บทที่

5.1) G = 1

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105

5.2) G = 3 5.3)  ¥·¤  ·¤ 粯 ¶ ´¤ §§³ q ÊÆ· n ´ ´¥ ¯ ¥­³¬ n¯£»§Å n¯ ·Ê 5.1 ç² 5.2 6.

´ à ¸ ­³ n´¤ n¯ ·Ê 2 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ £ ¸ Bi-directional SOVA

7.

 ¥·¤  ·¤ 粯 ¶ ´¤ §§³ q ÊÆ· n ´ ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¥² ¬¹Ê¯¬´¥Å n¯ ·Ê 2 £¹Ê¯

º ¯³§ ¯¥¶ ¸£ (BCJR, Max-Log-MAP, Log-MAP, SOVA ç² Bi-directional SOVA) Å n m´©¬´¥¯² ¶¥¶¯¯¥¶ Ma ak  m´ ³

8.

´ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 2.10 n´ Ï´­ Å­n§Ï´ ³ n¯£»§¯¶ º ak = {1, 1, –1}, m¯ ¬³ ´ H D 1 2D D 2 , ¬³ ´ ¥ © nk = {0.1, –0.2, 0.2, 0.5, –0.2} ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ Max-Log-MAP ç² Ï´­ Å­n m´©¬´¥¯² ¶¥¶¯¯¥¶ 8.1) Ma ak = {0, 0, 0, 0, 0} 8.2) Ma ak = {2, 4, –4, 0, 0} 8.3) Ma ak = {–2, –4, 4, 0, 0} 8.4)  ¥·¤  ·¤ 粯 ¶ ´¤ §§³ q ÊÆ· n ´ ´¥ ¯ ¥­³¬ n¯£»§Å n¯ ·Ê 3.1 – 3.3

9.

´ à ¸ ­³ n´¤ n¯ ·Ê 8 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ BCJR

10. ´ à ¸ ­³ n´¤ n¯ ·Ê 8 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ ¸£ Log-MAP ¸ SOVA £¹Ê¯ Ï´­ Å­n 11. ´ à ¸ ­³ n´¤ n¯ ·Ê 8 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ £ ©´£§¸ ´¥ ¯ ¥­³¬Â m´ ³ 11.1) G = 1 11.2) G = 3 11.3)  ¥·¤  ·¤ 粯 ¶ ´¤ §§³ q ÊÆ· n ´ ´¥ ¯ ¥­³¬ n¯£»§Å n¯ ·Ê 8.1 ç² 8.2 ¸ Bi-directional SOVA 12. ´ à ¸ ­³ n´¤ n¯ ·Ê 8 ¯ ¥­³¬ n¯£»§ yk Ä ¤Å n¯³§ ¯¥¶ £ 13.  ¥·¤  ·¤ 粯 ¶ ´¤ §§³ q ÊÆ· n ´ ´¥ ¯ ¥­³¬ n¯£»§ ¯ ¥² ¬¹Ê¯¬´¥Å n¯ ·Ê 8 £¹Ê¯

º ¯³§ ¯¥¶ ¸£ (BCJR, Max-Log-MAP, Log-MAP, SOVA ç² Bi-directional SOVA) Å n m´©¬´¥¯² ¶¥¶¯¯¥¶ Ma ak  m´ ³

106

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

·Ê 4 ¥­³¬Ã¯§ · · · ¥­³¬ ¥© ¬¯ ¢´©² m»­¥¹¯ ·Êà ©´£­ ´Ã m ÏÊ´ (LDPC: low-density parity-check) ­¥¹¯

Â¥·¤ ¬³ Ë È ©m´ “¥­³¬Ã¯§ · · ·” [17] Æ n¥³ ´¥¤¯£¥³ ©m´Â É ¥­³¬Ã nÆ n¯ ¶ §´ (ECC: error-

correction code) ·Ê ·¬º Å ³ º ³ [2, 5]  ¥´²£·¬£¥¥ ²Â n´Å §n · Ï´ ³ ¯ à ¯ (Shannon limit) [25] £´ ©m´¥­³¬ ECC ¶ ¯¹Ê ¸Ê Å ³ º ³ Æ n£· ´¥ Ï ´¥­³¬Ã¯§ · · ·£´Å nÅ ­§´¤È

´ ¥²¤º q ¥©£ ³ Ë Å °´¥q ¶¬ qÆ ¥¡q n©¤

 ¹Ê ¯ ´ ¥­³¬Ã¯§ · · · ¹¯©m´Â É ¥­³¬ §É¯  ¶ ¬n (linear block code) ¥²Â¢ ­ ¸Ê

³ ³ Ë ·Ë ²Â¥¶Ê£ n n©¤ ´¥ §m´© ¸ ¹Ë ´ ¯ ¥­³¬ §É¯  ¶ ¬n ´ ³ Ë É ²Â n Æ ·Ê­§³ ´¥

Ë ¯ ´¥Â n´¥­³¬Ã§² ¯ ¥­³¬Ã¯§ · · · ¥n¯£ Ï´ ´ ¯ ¥­³¬Ã¯§ · · ·  ¹Ê¯Å­n n»¯m´  n´Å ¸ ³

³ Ë Ã¬ ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ (­¥¹¯ ´¥ ¯ ¥­³¬Ã © Ï´Ë ) ·ÊÅ nÅ ¥² ´¥

¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q Å ³ º ³ ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ © ¥ ¥© ­´ à ¯¡ q粩 ¥ ¯ ¥­³¬Ã¯§ · · ·

Å ­³© n¯ ·Ë ² §m´© ¸ ­§³ ´¥ Ï´ ´ ¯ ¥­³¬ §É¯  ¶ ¬n ¥n¯£ ³ Ë ¯ ¶ ´¤ ´¥Â n´¥­³¬Ã§² ¯ ¥­³¬ §É¯  ¶ ¬n  ¹Ê¯Â É ¹Ë ´ Å ´¥ª¸ «´¥­³¬Ã¯§ · · ·Å ­³© n¯ m¯Æ

4.1.1 ¥­³¬ §É¯  ¶ ¬n ¥­³¬ §É¯  ¶ ¬n à (N, K) ¹¯¥­³¬ m¯ ¬³ ´ ·Êà § ¶ m´©¬´¥ (message bit) Ï´ ©

K ¶ Å­nÂ É Ï´¥­³¬ (codeword) ´ N ¶ n´Å­n m = [m1, m2, …, mK ] ¹¯Â©  ¯¥q ¯

¶ m´©¬´¥ ·Ê »  n´¥­³¬Â ¹Ê¯Å­nÆ nÂ É Ï´¥­³¬ c = [c1, c2, …, cN ] ´£¥» ·Ê 4.1 Ä ¤ ¶ ¬m©  ¶

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

วงจรตรวจหาแบบซอฟต รหัสแอลดีพีซี

4.1 Ï ´

43

บทที่ บทที่

107

<c1 , c2 , c3 , !, cN >

<m1 , m 2 , m3 , !, mK >

< p1 , p2 , !, pN K >

¥» ·Ê 4.1 Ä ¥ ¬¥n´ ¯ ¥­³¬ §É¯  ¶ ¬n à (N, K)

·Ê ¶Ê£ ¸Ë £´ Ï´ © N – K ¶ ²Â¥·¤ ©m´ “ ¶ ´¥¶ · (parity bit)” ­¥¹¯Â ·¤ Å ¥» ¯ ©  ¯¥q

p = [p1, p2, …, pN – K ] ¸Ê Â É ¬m© ·Ê m©¤Å­n© ¥¢´ ¥³ ¬´£´¥ ¥© ­´ n¯ ¶ §´ Æ n ç² n´

¶ ´¥¶ ·£· Ï´ © £´  ·¤ ¯ ɯ´ Ï´Å­n¬´£´¥ à nÆ n¯ ¶ §´ (error correction) ¯ n¯£»§ Å­n » n¯ Æ n n©¤

¥­³¬ §É¯  ¶ ¬n ² Ï´ ´¥Â n´Ã§² ¯ ¥­³¬ n¯£»§ ·§² §É¯ Ä ¤ ´ ¯ §É¯ n¯£»§

² ¸Ë ¯¤m» ³ §³ « ² ¯ à m§² ´ ¥²¤º q ¸Ê ¯³ ¥´¬m© ¯ Ï´ © ¶ m´©¬´¥ m¯ Ï´ © ¶ ¯

Ï´¥­³¬ ²Â¥·¤ ©m´ “¯³ ¥´¥­³¬ (code rate)” R ¸Ê ¶ ¤´£Ä ¤ R

K N

(4.1)

£¹Ê¯ 0 < R d 1 ¬£¯ ¬Ï´­¥³ °´¥q ¶¬ qÆ ¥¡q ² n¯ ´¥¥­³¬ ·Ê£·¯³ ¥´¥­³¬Â n´Å §n m´ 1  ¹Ê¯§ ´¥¬» ¬·¤ ¹Ë ·ÊÅ ¬¹Ê¯ ³ ¸ ·Ê n¯ Å nÂ É ¶ ´¥¶ · [43]

4.1.2 £ ¥¶ q ³© Ï´Â ¶ ¶ ´¥ ´ ¶ m´©¬´¥ m = [m1, m2, …, mK] ´ 1uK ( ³Ê ¹¯ 1 à © ¯ ç² K à © ³ Ë )

¥­³¬ §É¯  ¶ ¬n à (N, K) ¬¥n´ Æ nÄ ¤ ´¥ Ï ´ ¶ m´©¬´¥ m £´ » ³ £ ¥¶ q ³© Ï´Â ¶ G ( ·Ê£·¬£´ ¶ Â É Â§ 0 ­¥¹¯Â§ 1)  m´ ³ Ë ´ KuN ¸Ê ¯¤mÅ» ¥» [2]

G K qN ¡ I K qK ¢

1 ¡ ¡ ¡0 ¯ | PK q N K ° ¡ ± ¡# ¡ ¡0 ¢¡

0 " 0

p1,1

p1,2

1 " 0

p2,1

p2,2

# % #

#

#

0 " 1 pK ,1

pK ,2

p1, N K ¯ ° ° " p2, N K ° ° ° % # ° " pK , N K °° ± "

(4.2)

£¹Ê¯ I ¹¯Â£ ¥¶ q¯ §³ « q ´ KuK ç² P ¹¯Â£ ¥¶ q ´¥¶ · ´ Ku(N – K) ·Ê¬¯ §n¯

³ ¶ ´¥¶ ·Å Ï´¥­³¬ ¸Ê ²Æ n §§³ qÂ É Ï´¥­³¬ c = [c1, c2, …, cN] ´ 1uN ³Ê ¹¯

108

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

c mG <m1 m 2 ! mK p1 p2 ! pN K >

(4.3)

¬£ ´¥ (4.3) ì Å­nÂ­É ©m´£· ¶ m´©¬´¥ m ¥´ ¯¤m»¢´¤Å Ï´¥­³¬ c ¸Ê ¥­³¬Ã ·Ë ²Â¥·¤ ©m´ “¥­³¬Ã £·¥² (systematic code)” [2]

³©¯¤m´ ·Ê 4.1  n´¥­³¬ n¯£»§ m = [101] ç² m = [110] £¹Ê¯ Ï´­ Å­n£ ¥¶ q ³© Ï´Â ¶ G £· m´Â m´ ³

1 0 0 1 1 0¯ ¡ ° G ¡¡ 0 1 0 0 1 1°° ¡ 0 0 1 1 0 1° ¢ ±

©¶ · Ï´

(4.4)

£ ¥¶ q ³© Ï´Â ¶ G ·Ë ²Å n n´¥­³¬ ¶ n¯£»§ ¥³ Ë §² 3 ¶ ³Ê ¹¯ m = [m1 m2 m3]

 ¥´² ² ³ Ë Ï´¥­³¬ ·ÊÆ n ´ ´¥Â n´¥­³¬ n©¤Â£ ¥¶ q G ¹¯

1 0 0 1 1 0¯ ¡ ° c mG <m1 m 2 m3 > ¡¡0 1 0 0 1 1°° ¡ 0 0 1 1 0 1° ¢ ± <m1 m 2 m3 m1 m3 m1 m 2 m 2 m3 >

£¹Ê¯ ¹¯ ³© Ï´Â ¶ ´¥ © à £¯ ºÄ§¬¯ (modulo-2 addition) ­¥¹¯ ´¥ Ï´ XOR (exclusive OR) ³ ³ Ë n´ m = [101] ²Æ n c = [101011] ç² n´ m = [110] ²Æ n c = [110101] Â É n

¥­³¬ §É¯  ¶ ¬n à (N, K) ¤³ ¬´£´¥ » Ï´­ n©¤Â£ ¥¶ q ¥© ¬¯ ¢´©² m»­¥¹¯ ·Ê (parity-

check matrix) ­¥¹¯Â¥·¤ ¬³ Ë È ©m´ “£ ¥¶ q ´¥¶ ·Â É ” H ´ (N – K)uN Æ n ¸Ê n¯ ¬¯ §n¯

รหัสแอลดีพีซี

4.1.3 £ ¥¶ q ´¥¶ ·Â É

³ ©´£¬³£ ³ q ³ ·Ë

HGT = 0

(4.5)

4

บทที่

³ ³ Ë ¬Ï´­¥³ Ï´¥­³¬Å È ²Æ n©´m HcT = HGTmT = 0

(4.6)

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109

¬£¯ ¯ ´ ·Ë ¤³ ©m´¬£´ ¶ Å Ã m§²Ã © ¯ ¯ £ ¥¶ q H É ¹¯¬£ ´¥ ´¥¶ ·Â É (paritycheck equation) ¸Ê Â É ³© Ï´­ ©´£¬³£ ³ q ¯ ¶ n¯£»§ ci (i = 1, 2, …, N) Å Ï´¥­³¬

Ä ¤ ³Ê©Æ n´Â£ ¥¶ q ³© Ï´Â ¶ G ¯¤m»Å ¥» à £·¥² (systematic form) ´£¬£ ´¥ (4.2) ³ ³ Ë Â£ ¥¶ q ´¥¶ ·Â É ²£· m´Â m´ ³

H N K qN ¡ P T | I N K q N K ¯° ¢ ±

(4.7)

£¹Ê¯ (.)T ¹¯Â ¥¹Ê¯ ­£´¤Â£ ¥¶ q¬§³  §·Ê¤ (transpose matrix)  m £ ¥¶ q ³© Ï´Â ¶ G Å ¬£ ´¥ (4.4) ³ Å­n¯¤m»Å ¥» ¯ £ ¥¶ q H Æ n ¹¯

1 0 1 1 0 0¯ ¡ ° H ¡¡1 1 0 0 1 0°° ¡ 0 1 1 0 0 1° ¢ ±

(4.8)

4.1.4 ¥²¤² ´ n ¯¤¬º ¯ ¥­³¬ ´¥©³ ¬£¥¥ ² ¯ ¥­³¬ §É¯  ¶ ¬n ²Å n ÏË´­ ³ 𣣶 (Hamming weight) ¯ Ï´¥­³¬ ¸Ê ¶ ¤´£Ä ¤

wH c = Ï´ © ¶ ·Ê£· m´Â m´ ³ 1 ¢´¤Å Ï´¥­³¬ c

(4.9)

 m n´ c = 100100 ²Æ n wH <100100> 2 Â É n ç²¥²¤² ´ 𣣶 (Hamming distance) ¥²­©m´ c1 ç² c2 ² ¶ ¤´£Ä ¤ dH c1, c2 wH c1 c 2

N 1

c

1,i

v c2,i

i 0

(4.10)

³©¯¤m´  m n´ c1 = 110011 ç² c2 = 000111 ²Æ n¥²¤² ´ 𣣶 dH c1 , c 2 3 n´Å­n¥­³¬ c £· ³ Ë ­£ 2k Ï´¥­³¬ ¥²¤² ´ 𣣶 ·Ê n¯¤¬º ¥²­©m´ Ï´¥­³¬ ²Â¥·¤ ³

³©Ê Æ ©m´¥²¤² ´ n ¯¤¬º (minimum distance) ¯ ¥­³¬ ­¥¹¯ dmin ¸Ê ¶ ¤´£Ä ¤

\

^

d min min dH ci , c j

ivj

(4.11)

£¹Ê¯ {i, j} = 0, 1, …, 2k – 1 ³ ³ Ë Â£¹Ê¯ ¥´ ¥²¤² ´ n ¯¤¬º dmin É ² Ï´Å­n ¥´ ©m´¥­³¬ §É¯  ¶ ¬n ·Ë£· ©´£¬´£´¥ Å ´¥Ã nÆ (correct) n¯ ¶ §´ Â É Ï´ © t ¶ £¹Ê¯

110

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

t

d min 1

(4.12)

2

ç²£· ©´£¬´£´¥ ¥© ­´ (detect) n¯ ¶ §´ Æ n Ï´ © e ¶ £¹Ê¯

e = dmin – 1

(4.13)

¯ ´ ·Ë¥²¤² ´ n ¯¤¬º ¯ ¥­³¬ dmin ¤³ ¬´£´¥ ­´Æ nÄ ¤ ¥ ´ £ ¥¶ q ³© Ï´Â ¶

G ç²Â£ ¥¶ q ´¥¶ ·Â É H ³ ·Ë ¥²¤² ´ n ¯¤¬º ¯ ¥­³¬£· ´m  m´ ³ ÏË ´­ ³ 𣣶 n ¯¤¬º ¯ ¬£´ ¶ Å Ã © ¯ ¯ £ ¥¶ q G

Ï´ © à © ³ Ë n ¯¤¬º ¯ £ ¥¶ q H ·Ê © ³ à £¯ ºÄ§¬¯ çn©Æ n §§³ qÂ É ª» ¤q

4.1.5 ´¥ ¯ ¥­³¬ §É¯  ¶ ¬n Å ´ ¶ ³ ¶©¶ · ·ÊÅ nÅ ´¥ ¯ ¥­³¬ §É¯  ¶ ¬n ¹¯ “ ´¥ ¯ ¥­³¬Ã ¶ Ä ¥£ (syndrome decoding)” [2] £¹Ê¯Â©  ¯¥q ¶ Ä ¥£ s ¶ ¤´£Ä ¤

s = HrT

(4.14)

£¹Ê¯ r = c e = [r0, r1, …, rN – 1] ¹¯Â©  ¯¥q ¯ n¯£»§ ·Ê n¯ ´¥ ¯ ¥­³¬, c ¹¯Â©  ¯¥q

¯ Ï´¥­³¬, e = [e0, e1, …, eN – 1] ¹¯Â©  ¯¥q ¯ n¯ ¶ §´ Ä ¤ ·Ê ei {0, 1} ç² ei = 1

­£´¤ ¸ Ï´¥­³¬ ¶ ·Ê i £· n¯ ¶ §´ (ei = 0 ­£´¤ ¸ Ï´¥­³¬ ¶ ·Ê i Æ£m£· n¯ ¶ §´ ) ´ ³ Ë Ã m´ r = c e § Å ¬£ ´¥ (4.14) É ²Æ n

= HeT

(4.15)

³Ê ¹¯ m´ ¶ Ä ¥£ ² ¸ Ë ¯¤m» ³ ©  ¯¥q ¯ n¯ ¶ §´ e  ¥´² ² ³ Ë §Ï´ ³ n¯£»§ ·ÊÆ£m£· ¯ n ¶ §´

รหัสแอลดีพีซี

s = H(c e)T = HcT HeT

( ³Ê ¹¯ r = c) ²£· m´ ¶ Ä ¥£Â m´ ³ ª» ¤q¬£¯

Ä ¤ ³Ê©Æ ´¥ ¯ ¥­³¬ §É¯  ¶ ¬n ²¯´ª³¤ ´¥´ n ­´ (look-up table) [2] ¸Ê  É

´¥´ ·Êì ©´£¬³£ ³ q¥²­©m´ m´ ¶ Ä ¥£Ã§²Â©  ¯¥q e ´£¬£ ´¥ (4.15) ³ ³ Ë Â£¹Ê¯© ¥

¢´ ¥³ n¯ ´¥ ¯ ¥­³¬§Ï´ ³ n¯£»§ r É ² Ï ´§Ï´ ³ n¯£»§ r £´ Ï´ © ­´ m´ ¶ Ä ¥£ ´£¬£ ´¥

4

บทที่

(4.14) ´ ³ Ë É­´Â©  ¯¥q e ·Ê¬¯ §n¯ ³ m´ ¶ Ä ¥£ ·ÊÆ n ´ ´¥´ n ­´ ¸Ê £¹Ê¯Æ n©  ¯¥q e ·Ê n¯ ´¥Ã§n© É Ï´ ´¥ ¯ ¥­³¬§Ï´ ³ n¯£»§ r ´

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111

(4.16)

cˆ r e

³Ê ¹¯©¶ · ´¥ ¯ ¥­³¬ n¯£»§ ·Ë¬´£´¥ m©¤Ã nÆ n¯ ¶ §´ ·Ê ¶ ¸Ë ¢´¤Å §Ï´ ³ n¯£»§ r Æ nÄ ¤

¯³ Ä £³ ¶ ¯¤m´ Æ¥ É ´£ ´¥ ¯ ¥­³¬Ã ¶ Ä ¥£ ²Å n ´ Æ n · ³ ¥² ·ÊÅ n Ï´¥­³¬ ·Ê£· ©´£¤´© n ¯¤Ã§² n¯ ¶ §´ ·Ê ¶ ¸Ë Å Ã m§² Ï´¥­³¬£· Ï´ © n ¯¤

 ¹Ê ¯ ´ ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q ² Ï´ ´¥Â n´¥­³¬Ã§² ¯ ¥­³¬

n¯£»§ ¥³ Ë §²­ ¸Ê   ¯¥q (­¥¹¯ 4096 ¶ ) ³ ³ Ë n´ ¶ m´©¬´¥£· ©´£¤´© k = 4096 ¶ ²Æ n

©m´ Ï´¥­³¬ ·ÊÂ É Æ Æ n ³ Ë ­£ £· Ï´ © 24096 à ¸Ê £¹Ê¯ Ï ´Æ ¬¥n´ ´¥´ n ­´¬Ï´­¥³ m´ ¶ Ä ¥£ ·ÊÂ É Æ Æ n ³ Ë ­£ É ²Æ n ´¥´ n ­´ ·Ê£· ´ Å­ m£´ ( Ï ´£´Å n ¥¶ Å ´ ¶ ³ ¶Æ£mÆ n) ² ³ Ë

´¥ ¯ ¥­³¬Ã ¶ Ä ¥£ ¸ Æ£m¬´£´¥ Ï ´£´Å n ¥¶ Å °´¥q ¶¬ qÆ ¥¡q Æ n

4.2 ¹Ë ´ ¯ ¥­³¬Ã¯§ · · · ¥­³¬Ã¯§ · · · (LDPC) Â É ¥­³¬ §É¯  ¶ ¬n ¥²Â¢ ­ ¸Ê ·Ê » Ï´­ n©¤Â£ ¥¶ q ´¥¶ ·Â É ·Ê

£· Ï´ © § 1 n ¯¤£´ £¹Ê¯Â ·¤ ³ ´ ¯ £ ¥¶ q ´¥¶ ·Â É Â ¹Ê¯Å­n£·¥²¤² ´ n ¯¤¬º (dmin)

¯ ¥­³¬¬» ¥­³¬Ã¯§ · · · » ¶ n Ä ¤ Gallager [17] Å · .ª. 1960 Massachusetts Institute of Technology (MIT) ¥²Â ª¬­¥³ ¯Â£¥¶ ´ ¯¤m´ Æ¥ É ´£Å m© Ã¥ ·Ë ¥­³¬Ã¯§ · · ·Æ£mÆ n¥³

©´£¬ Å Â m´ ·Ê ©¥  ¹Ê ¯ ´ £· n¯ Ï´ ³ ´ n´ ´¥ Ï´ © ´ ³ Ë Å · .ª. 1981 Tanner [44] Æ n ϴ¬ ¯ ´¥Å n ¥´¡Ã  ¯¥q (Tanner graph) ì ©´£¬³£ ³ q Ê·Â ¶ ¸Ë ´ ´¥Â n´¥­³¬

n¯£»§ 粬´£´¥ Ï ´£´Å n m©¤Å ´¥ ¯ ¥­³¬ n¯£»§Å­n m´¤ ¸Ë Æ n n©¤ ç²Å · .ª. 1990 Mackey

ç² Neal [45] ©m´¥­³¬Ã¯§ · · ·£·¬£¥¥ ² ´¥ Ï´ ´ ·Ê n´Å §n · Ï´ ³ ¯ à ¯ £´ ©m´ ¥­³¬Â ¯¥qÄ [3] ¸ Ï´Å­n¥­³¬Ã¯§ · · ·Â¥¶Ê£ §³ £´Â É ·Ê¬ Å ¯¤m´ à ¥m­§´¤¯· ¥³ Ë ­ ¸Ê ¸Ê Å ¥³ Ë · Ë É£³Ê Å Æ n©m´¥­³¬Ã¯§ · · · ²Æ£m » §¹£¯· ¯¤m´ à m ¯  ¥´²Å ³ º ³ Æ n£· ´¥ Ï ´¥­³¬ ï§ · · ·£´Å nÅ ­§´¤È ´ ¥²¤º q ¥©£ ³ Ë Å °´¥q ¶¬ qÆ ¥¡q n©¤

¥­³¬Ã¯§ · · · ¹¯¥­³¬ ´¥¶ ·Â É (parity-check code) ·Ê » Ï´­ n©¤Â£ ¥¶ q ´¥¶ ·Â É

H à £´ § ª» ¤q14 (sparse matrix) [17] ´ MuN Ä ¤ Ï´¥­³¬ c ²£· ©´£¤´© N ¶ ç² Ï´¥­³¬ ³ Ë ­£ n¯ ¬¯ §n¯ ³ ¬£ ´¥ ´¥¶ ·Â É ´£¬£ ´¥ (4.6)

Ä ¤ ³©Ê Æ ¥­³¬Ã¯§ · · ·Ã m ¯¯ Â É ¬¯ ¥²Â¢ ­§³ ¹¯ 14

Ï´ © M

¬£ ´¥

¥­³¬Ã¯§ · · ·­¥¹¯¥­³¬ ´¥¶ ·Â É ·Ê£· ©´£­ ´Ã m ÏÊ´ Å ·Ê ·Ë Ï´©m´ “ ©´£­ ´Ã m ÏÊ´ (low-density)” ¯ Å­n ¥´ ©m´ ©´£­ ´Ã m ¯ § ­ ¸Ê Š£ ¥¶ q ´¥¶ ·Â É H £· m´Â n´Å §n m´ª» ¤q£¹Ê¯ N l d Å ² ·Ê£ ¥¶ q¬mº£ (random matrix) Å È ·Ê£·¬£´ ¶ Â É Â§ ª» ¤qç²Â§ ­ ¸Ê ²£· ©´£­ ´Ã m ¯ § ­ ¸Ê  §·Ê¤Â m´ ³ 1/2 ¬£¯

112

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¥­³¬Ã¯§ · · · ¥ ¶ (regular LDPC code) ²£· ´¥ ¥² ´¤ ³© ¯ § ­ ¸Ê Š£ ¥¶ q H Â É Ã ·Ê ­£¹¯ ³ ¥­³¬Ã¯§ · · · ¯ Gallager [17] ³Ê ¹¯Ã m§²Ã © ¯ ¯ £ ¥¶ q H

²£· Ï´ © § ­ ¸Ê  m´ ³ º à © ¯ ç²Ã m§²Ã © ³ Ë ¯ £ ¥¶ q H ²£· Ï´ © § ­ ¸Ê  m´ ³ º à © ³ Ë

¥­³¬Ã¯§ · · ·Æ£m¬£Ïʴ¬£¯ (irregular LDPC code) [46] ²£· ´¥ ¥² ´¤ ³© ¯ § ­ ¸Ê Â É Ã Æ£m ·Ê ¸Ê Ä ¤ ³©Ê Æ ²£·¬£¥¥ ² · ©m´¥­³¬Ã¯§ · · · ¥ ¶

 ¹Ê¯Å­n m´¤¬Ï´­¥³ ´¥¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ¥­³¬Ã¯§ · · · Å ·Ê ·Ë ² ¶ ´¥ ´Â ´² ¥ · Ê·

à © ¯ ³ Ë ­£ Š£ ¥¶ q H Â É ¯¶¬¥² m¯ ³ à  ¶ ¬n (linearly independent) ¸Ê ² Ï´Å­n

¶ m´©¬´¥ ·ÊÅ nÅ ´¥Â n´¥­³¬£· ©´£¤´©Â m´ ³ K = N – M ¶ [4, 17]

4.2.1 ¥­³¬Ã¯§ · · · ¥ ¶ ¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k) ­£´¤ ¸ ¥­³¬Ã¯§ · · · Ê· » Ï´­ n©¤Â£ ¥¶ q ´¥¶ ·Â É H ´

MuN ·Ê£·Â§ ­ ¸Ê Ï´ © j ³©Å à m§²Ã © ³ Ë Ã§²£·Â§ ­ ¸Ê Ï´ © k ³©Å à m§²Ã © ¯ £¹Ê¯ j < k ç² {j, k} << N ¸Ê ­£´¤ ©´£©m´¬£ ´¥ ´¥¶ ·Â É º ¬£ ´¥ ²¬³£ ³ q ³ n¯£»§ Ï´ ©

k ¶ ç² n¯£»§Ã m§² ¶ ²¬³£ ³ q ³ ¬£ ´¥ ´¥¶ ·Â É Ï´ © j ¬£ ´¥Â¬£¯ ³ ³ Ë Â£ ¥¶ q H ²£·Â§ ­ ¸Ê ³ Ë ­£ Â É Ï´ © Mk = Nj ³©15 ç² n´¬££º ¶©m´Ã © ¯ ³ Ë ­£ Š£ ¥¶ q

H Â É ¯¶¬¥² m¯ ³ à  ¶ ¬n É ²Æ n©m´¯³ ¥´¥­³¬¬Ï´­¥³ ¥­³¬Ã¯§ · · · ¥ ¶£· m´Â m´ ³ R 1

M j 1 N k

(4.17)

Ä ¤ ·Ê j < k  ¹Ê ¯ ´ R d 1 ¬£¯

²¯´ª³¤ ©´£¬³£ ³ q Ê©· m´ Mk = Nj ³ ³ Ë ¸ n¯ §¹¯ ´¥´£¶Â ¯¥q N, j ç² k ·Ê Ï´Å­n M

Nj k

(4.18)

รหัสแอลดีพีซี

Å ´¥Â§¹¯ ´¥´£¶Â ¯¥q m´ È (M, N, j ç² k) ·ÊÅ n ³ ¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k)

Â É Â§ Ï´ ©  ɣ m´ ³ Ë Â m ¥­³¬Ã¯§ · · · ¥ ¶Ã (3, 4) ² n¯ Å n ³ ¥² ·Ê£· N = 1000

­¥¹¯ 1004 à mÆ£m¬´£´¥ Å n ³ ¥² ·Ê£· N = 1002 Æ n Â É n ­¥¹¯¥­³¬Ã¯§ · · · ¥ ¶Ã (2, 4) ·Ê£·Â£ ¥¶ q ´¥¶ ·Â É H ¹¯

15

4

บทที่

¯³ ¥´¬m© ¯ § 1 Š£ ¥¶ q H ´ MuN ¯ ¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k) £· m´Â m´ ³ k / N ³ ³ Ë Ï´©m´ “ ©´£­ ´Ã m ÏÊ´ (low-density)” ¯ ¥­³¬Ã¯§ · · ·­£´¤ ¸ m´ k / N o 0 £¹Ê¯ N o f

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113

H 5q10

1 ¡ ¡1 ¡ ¡¡0 ¡0 ¡ ¡ ¢¡0

1 1 1 0 0 0 0 0 0¯ ° 0 0 0 1 1 1 0 0 0°° 1 0 0 1 0 0 1 1 0°° 0 1 0 0 1 0 1 0 1°° ° 0 0 1 0 0 1 0 1 1±°

(4.19)

²Æ n©m´ M = 5 ç² N = 10 ¸Ê ¬¯ §n¯ ³ ¬£ ´¥ (4.18) ³ ³ Ë ¥­³¬Ã¯§ · · · ·Ë ²Å n n´¥­³¬ ¶ m´©¬´¥ ´ 10 – 5 = 5 ¶ ç²Æ n Ï´¥­³¬ ´ 10 ¶

£ ¥¶ q ´¥¶ ·Â É H Å ¬£ ´¥ (4.19) ¯ Å­n ¥´ ¸ ©´£¬³£ ³ q¥²­©m´ ¬£ ´¥

´¥¶ ·Â É Ã§² ¶ n¯£»§ Ä ¤Ã m§²Ã © ¯ ¯ £ ¥¶ q H ²Â¥·¤ ©m´ “Ä­ Â É (check node)” ç²Ã m§²Ã © ³ Ë ²Â¥·¤ ©m´ “Ä­ ¶ (bit node)”  ¥´² ² ³ Ë ²Æ n¬£ ´¥ ´¥¶ ·Â É ¯ à m§² Ä­ Â É ³ ·Ë

Ä­ Â É ³© ·Ê 1

c1 c2 c3 c4 0

(4.20)

Ä­ Â É ³© ·Ê 2

c1 c5 c6 c7 0

(4.21)

Ä­ Â É ³© ·Ê 3

c2 c5 c8 c9 0

(4.22)

Ä­ Â É ³© ·Ê 4

c3 c6 c8 c10 0

(4.23)

Ä­ Â É ³© ·Ê 5

c4 c7 c9 c10 0

(4.24)

¥­³¬ ´¥¶ ·Â É ¬´£´¥ » Ï´­ n©¤ ¥´¡Ã  ¯¥q (Tanner graph) [44, 50] Æ n ʸ Â É ´¥Ã

£ ¥¶ q ´¥¶ ·Â É H ´ MuN Ä ¤ ·Ê ¥´¡Ã  ¯¥q ²£· N Ä­ ¶ (­ ¸Ê Ä­ m¯­ ¸Ê ¶ )

ç²£· M Ä­ Â É (­ ¸Ê Ä­ m¯­ ¸Ê ¬£ ´¥ ´¥¶ ·Â É ) Å ·Ê ·Ë ²Å n¬³ §³ « q© §£ R à ĭ ¶ ç²Å n¬³ §³ « q¬Ê·Â­§·Ê¤£

à ĭ Â É Â£¹Ê¯Ä­ Â É ²Â ¹Ê¯£ m¯ ³ Ä­ ¶ ·Ê

 ·Ê¤© n¯ ³ ¬£ ´¥ ´¥¶ ·Â É ¯ Ä­ Â É ³ Ë ­¥¹¯ §m´©¯· ³ ¤­ ¸Ê ¹¯Â¬n  ¹Ê¯£ (edge) ¥²­©m´

Ä­ Â É §Ï´ ³ ·Ê m ³ Ä­ ¶ §Ï´ ³ ·Ê n ²Â ¶ ¸Ë É m¯Â£¹Ê¯ hm ,n 1 ¯ ´ ·Ë ¥´¡Ã  ¯¥q ¯´ Â¥·¤ ©m´ “ ¥´¡¬¯ ¬m© (bipartite graph)”  ¥´²¢´¤Å ¥´¡£·Ä­  ·¤ ¬¯ à  m´ ³ Ë

( ³Ê ¹¯Ä­ ¶ ç²Ä­ Â É ) ç²Æ£m£·Â¬n  ¹Ê¯£¥²­©m´ Ä­ ¶  ·¤© ³ ¥» ·Ê 4.2 ì ¥´¡ à  ¯¥q¬Ï´­¥³ ¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k) = (2, 4) ·Ê£·Â£ ¥¶ q ´¥¶ ·Â É H ´£¬£ ´¥

(4.19) ¸Ê ² ©m´Ã m§²Ä­ ¶ £·Â¬n  ¹Ê¯£ Ï´ © 2 ¬n (¬¯ §n¯ ³ j = 2) ç²Ã m§²Ä­ Â É £·Â¬n  ¹Ê¯£ Ï´ © 4

¬n (¬¯ §n¯ ³ k

=

4)

¯ ´ ·Ë ¤³ ©m´ ¥´¡Ã  ¯¥q

¬¯ §n¯ ³ ¬£ ´¥ ´¥¶ ·Â É ³ Ë ­£ ´£¬£ ´¥ (4.20) – (4.24)  m ³

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

c1 c2

c3

c4

c5

c6

c7

c9 c10

c8

¥» ·Ê 4.2 ¥´¡Ã  ¯¥q¬Ï´­¥³ ¥­³¬Ã¯§ · · · ¥ ¶Ã (2, 4) ·Ê£·Â£ ¥¶ q H ´£¬£ ´¥ (4.19)

4.2.2 ¥­³¬Ã¯§ · · ·Æ£m¬£Ï´Ê ¬£¯ ¥­³¬Ã¯§ · · ·Æ£m¬£Ïʴ¬£¯Æ n » ³ ´ ¸Ë £´Å · .ª. 2001 Ä ¤ Richardson [46] Ä ¤ ·Ê£ ¥¶ q

´¥¶ ·Â É H ´ MuN ²£· ´¥ ¥² ´¤ ³© ¯ § ­ ¸Ê Â É Ã Æ£m ·Ê ³Ê ¹¯ Ï´ © § ­ ¸Ê Å Ã m§²Ã © ¯ ç²Ã m§²Ã © ³ Ë Æ£m Ï´Â É n¯ £· m´Â m´ ³

Å ´ ¶ ³ ¶¥­³¬Ã¯§ · · ·Æ£m¬£Ïʴ¬£¯ ² » Ï´­ n©¤ ­º ´£ ´¥Ã à ¥² ³ ³ Ë

(degree distribution polynomial) ¸Ê ¯ Å­n ¥´ ¸ Ï´ © ¯ ¬n  ¹Ê¯£ ¯ à m§²Ä­ ­º ´£ ´¥Ã à ¥² ³ ³ Ë ¯ Ä­ ¶ £· m´Â m´ ³ S x i Si x i £¹Ê¯ Si ¹¯ Ï´ © ¯ Ä­ ¶

Ë ¯ Ä­ Â É ²£· m´Â m´ ³ ·Ê£·¥² ³ ³ Ë Â m´ ³ i Å Ï´ ¯  ·¤© ³ ­º ´£ ´¥Ã à ¥² ³ ³

Y x

Yx i i

i

£¹Ê¯ Yi ¹¯ Ï´ © ¯ Ä­ Â É ·Ê£·¥² ³ ³ Ë Â m´ ³ i

¯ ´ ·Ë¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · Ê· É ¡³ q ³ ¯ ´¥Ã à ¥² ³ ³ Ë ¯ Ä­

Â É Ã§² ¯ Ä­ ¶ ¬´£´¥ » Ï´ ´¤Æ nÄ ¤Å n ¦« ·©¶©³ ´ ´¥ ¯ ©´£­ ´Ã m (density

evolution) [48] ¸Ê ² ¶ ´£ ©´£­ ´Ã m ¯ ©´£ m ´ ²Â É ¯ m´©¬´¥ ·Ê¬m m´ ¥²­©m´ Ä­ ­ ´Ã m £· m´Â n´Å §n m´¯ ³ q £¹Ê¯ Ï´ © ¥¯ ¯ ´¥ ¯ ¥­³¬¢´¤Å © ¥ ¯ ¥­³¬Ã¯§ · · ·

 ¶Ê£ ¸Ë ¸Ê ­£´¤ ©´£©m´© ¥ ¯ ¥­³¬£· ©´££³Ê Å ¬» ·Ê ² ¯ ¥­³¬ n¯£»§Æ n¯¤m´ » n¯ Å ´ ¥ ³ n´£ n´¥² Ï´ ´ ·Ê¥² ³ SNR ÏÊ´È m´Â §·Ê¤ ¯ ©´£­ ´Ã m ²§m»Â n´¬m» m´ ³©Å È

รหัสแอลดีพีซี

Â É Ã§²Ä­ ¶ Ä ¤ ³Ê©Æ n´¥² Ï´ ´ ·Ê¥² ³ SNR ¬»  ·¤ ¯ ² ©m´ m´Â §·Ê¤ ¯ ©´£

¸Ê ­£´¤ ©´£©m´© ¥ ¯ ¥­³¬Ã¯§ · · ·£· n¯ ¥m¯ Å ´¥ ¯ ¥­³¬ n¯£»§ ³ ³ Ë m´ SNR ·ÊÂ É Â¬n à m ¯  ¯ ¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · (¥²­©m´ · ³ Æ£m ·) ²Â¥·¤ ©m´ “ · Â¥¶Ê£Â §·Ê¤

(threshold)” ¬Ï´­¥³ ¬£¥¥ ² ¯ ¥­³¬ ³ ³ Ë ¥­³¬Ã¯§ · · ·Æ£m¬£Ïʴ¬£¯ » ¯¯ à £´Â ¹Ê¯Å­n

m´ · Â¥¶Ê£Â §·Ê¤ ·Ë  n´Å §n · Ï´ ³ ©´£ º ¯ à ¯ (Shannon capacity) [25] Å­n£´ ·Ê¬º

4

บทที่

(£´ ©m´¥­³¬Ã¯§ · · · ¥ ¶) [49]

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115

¥» ·Ê 4.3 ¥´¡Ã  ¯¥q¬Ï´­¥³ ¥­³¬Ã°££¶ à (7, 4) Å ³©¯¤m´ ·Ê 4.2

³©¯¤m´ ·Ê 4.2 ¶ ´¥ ´¥­³¬Ã°££¶ à (7, 4) ·Ê£·Â£ ¥¶ q ³© Ï´Â ¶  m´ ³ 1 ¡ ¡0 G ¡¡ ¡0 ¡0 ¡¢

0 0 0 1 0 1¯ ° 1 0 0 1 1 1 °° 0 1 0 1 1 0°° 0 0 1 0 1 1 °°±

(4.25)

­´Â£ ¥¶ q ´¥¶ ·Â É H 粩´ ¥´¡Ã  ¯¥q ¯ £ ¥¶ q H ·ÊÆ n ©¶ · Ï´

 ¹Ê ¯ ´ £ ¥¶ q G £·Ä ¥ ¬¥n´ ´£¬£ ´¥ (4.2) ³ ³ Ë ¸ ¬´£´¥ ­´Â£ ¥¶ q H Æ n

´ ¬£ ´¥ (4.7) ³ ·Ë

1 1 1 0 1 0 0¯ ¡ ° H ¡¡ 0 1 1 1 0 1 0°° ¡1 1 0 1 0 0 1 ° ¢ ±

(4.26)

ç²£· ¥´¡Ã  ¯¥q ´£¥» ·Ê 4.3 ´ £ ¥¶ q H Å ¬£ ´¥ (4.26) ² ©m´¥­³¬Ã°££¶ à (7, 4) ¬´£´¥ Ï ´£´Å nÂ É ¥­³¬Ã¯§ · · ·Æ£m¬£Ïʴ¬£¯Æ n

4.2.3 ¯ Æ°Â ¯¥qÄ §¶ à  q n´Å­n c = [c1, c2, …, cn] ¹¯Â©  ¯¥q ¯ ¶ n¯£»§ Ï´ © n ¶ £¹Ê¯ ci {0, 1} ç² ¶ ¤´£

¡³ q ³ ´¥¶ · (parity function) ' c \0,1^ ³ ·Ë

' c c1 c2 ! cn

116

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(4.27)

Ä ¤ ·Ê ¹¯ ³© Ï´Â ¶ ´¥ © à £¯ ºÄ§¬¯ , ' c 0 ­¥¹¯ ´¥¶ · m» (even parity) £¹Ê¯Â©  ¯¥q c £· §¥©£ ¯ § ­ ¸Ê Â É Ï´ © m» ç² ' c 1 ­¥¹¯ ´¥¶ · ·Ê (odd parity) £¹Ê¯Â©  ¯¥q c £· §¥©£ ¯ § ­ ¸Ê Â É Ï´ © ·Ê ¯ ´ ·Ë ² ¶ ¤´£ m´ LLR à ¯² ¶¥¶¯¯¥¶ (a priori LLR)

¯ ¡³ q ³ ´¥¶ · ' c Å­n£· m´Â m´ ³

Pr ' c 1¯ ¬­ ¡ °± ­ ­ M' c log ¢ Pr ' c 0¯ ­­­ ¡ ° ¢ ±®

(4.28)

¦£¦1, if M' c p 0 ' c ¤ ¦¦0, if M' c 0 ¦¥

(4.29)

¸Ê ²Æ n©m´

³ ³ Ë n´¬££º ¶©m´ ¶ n¯£»§ ³ Ë ­£ Â É ¯¶¬¥² m¯ ³ ²Æ n©m´ m´ M' c Â É Æ ´£ ¯ Æ°Â ¯¥qÄ §¶ à  q (tanh rule) ³ ·Ë [51, 52] M' c ¬­ ­­ tanh 2 ®­­

n

Mi ¬­ ­ 2 ®­

tanh i 1

(4.30)

( »¢´ © ¬Ï´­¥³ Ï´¯ ¶ ´¤) £¹Ê¯ Mi log Pr <ci 1> / Pr <ci 0> ´ ³ Ë Ã n¬£ ´¥ (4.30) É ²Æ n £n M ¬¦² ¦ M' c 2 tanh 1 ¦¤ tanh i ­­­¦» ¦ 2 ®¦¼¦ ¦ i 1 ¥

(4.31)

n n M' c sign Mi q f f Mi i 1 i 1

¬

­­­­ ®

รหัสแอลดีพีซี

­¥¹¯ ³ Å­n¯¤m»Å ¯· ¥» à ­ ¸Ê Æ n ¹¯ (4.32)

4

( »¢´ © ¬Ï´­¥³ Ï´¯ ¶ ´¤) Ä ¤ ·Ê

บทที่

e x 1¬­ x ¬¬ ­ log tanh ­­­­­­ f x log x ­ 2 ®®­ e 1 ®­

(4.33)

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117

3

f x

2

1

1

3

2

x

¥» ·Ê 4.4 ¡³ q ³ f(x) Å ¬£ ´¥ (4.33)

Å ´ ¶ ³ ¶¬£ ´¥ (4.32) ¶ ¤£ Ï ´£´Å n¬¥n´ Â É °´¥q é¥q£´ ©m´¬£ ´¥ (4.30) ­¥¹¯

(4.31)  ¥´²Å n ·¤ §¥©£ (summation) à ·Ê ²Å n § » (product) ¯ n¯£»§ Ï´ © n q

¯¤m´ Æ¥ É ´£¬£ ´¥ (4.30) ¶ ¤£Å nÅ ´¥©¶Â ¥´²­q¬£¥¥ ² ¯ © ¥ ¯ ¥­³¬Ã¯§ · · · ¯ ´ ·Ë

¡³ q ³ f x Å ¬£ ´¥ (4.33) £· º ¬£ ³ ¶ Ê· m´¬ Å ¹¯ f x Â É ¡³ q ³ © ç²£· m´§ §

¯¤m´ ¬£Ïʴ¬£¯¬Ï´­¥³ x > 0 Ä ¤ ·Ê f 0 d ç² f d 0 ³ ì Å ¥» ·Ê 4.4 ¯ ´ ·Ë f x ¤³ £· ³© ³ (inverse) n©¤ ³Ê ¹¯ f f x

x ¬Ï´­¥³ º m´ x > 0

Ï´­ Å­n cˆ <cˆ1 , !, cˆn > ¹¯ m´ ¥²£´ ¯ c ·ÊÂ É Æ Æ n£´ ¬º Ä ¤ ·Ê cˆi 1 £¹Ê¯ Mi p 0 ç² cˆi 0 £¹Ê¯ Mi 0 ³ ³ Ë Â ¥¹Ê¯ ­£´¤ ¯ M' c ¸Ê Â É ³©¥² º m´ ·ÊÂ É Æ Æ n£´ ¬º

¯ ¡³ q ³ ´¥¶ · ' c ² » Ï´­ n©¤ ' cˆ ´£ ©´£¬³£ ³ q ³ ·Ë

sign M 1 1

sign M' c

n

' cˆ

(4.34)

' cˆ 1

i

i 1

¸Ê ¯ Å­n ¥´ ©m´ ' c ²Â É ´¥¶ · m» É m¯Â£¹Ê¯ Ï´ © ¯ Mi p 0 Â É Â§ m»16 ç² ' c ²Â É ´¥¶ · Ê· É m¯Â£¹Ê¯ Ï´ © ¯ Mi p 0 Â É Â§ ·Ê ¯ ´ ·Ë ´ ¯ M' c ²Â É ³©©³ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ m´ ´¥¶ · ' c ·Ê Ï´ © Æ n ¸Ê ­´Æ n ´ 16

£¹Ê¯ Ï´ © ¯ Mi p 0 Â É Â§ m» É ² Ï´Å­n ' cˆ 0 ç² ´ ¬£ ´¥ (4.34) É ²Æ n©m´ sign M' c 1 ¸Ê £· § Ï´Å­n ' c 0 ´£¬£ ´¥ (4.29)

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M' c f

f M

i

(4.35)

i

n´¬££º ¶©m´ ¶ n¯£»§ ³© ·Ê k ¯ c (­¥¹¯ ck ) £· ©´£ m ´ ²Â É ·Ê ²Â É 1 ç² 0  m´ ³ ²Æ n©m´ Mk 0 ³ ³ Ë q Ê· k Å §¥©£

f M É ²£· m´Â É m´¯ ³ q ¸Ê ¬m §Å­n §¥©£ ³ Ë ­£ i

i

Å ¬£ ´¥ (4.35) £· m´Â É m´¯ ³ q n©¤

 ¹Ê ¯ ´ f d 0 ³ ³ Ë m´ M' c Å ¬£ ´¥ (4.32) ²£· m´Â m´ ³ ª» ¤q¬£¯ n´£· ¶

n¯£»§Å £· m´ Mi 0 ³ Ë ·Ë Â É Â ¥´²©m´ n´£· ¶ n¯£»§Â ·¤ ­ ¸Ê ¶ ·Ê£· ©´£ m ´ ²Â É ·Ê ²Â É 1 ç² 0  m´ ³ É ² Ï´Å­n m´ ´¥¶ · ¯ ©  ¯¥q n¯£»§ c £· ©´£ m ´ ²Â É ·Ê ²Â É 1 ç² 0  m´ ³ n©¤ (Ä ¤Æ£m n¯ Ï´ ¸ ¸ ¶ ¯¹Ê È) ³ ³ Ë n´£· ¶ n¯£»§Å £· ©´£ m ´Â ¹Ê¯ ¹¯ n ¯¤¬º £¹Ê¯Â ·¤ ³ ¶

n¯£»§¯¹Ê È §¥©£Å ¬£ ´¥ (4.35) ² ¸Ë ¯¤m» ³ m´ f Mmin

£¹Ê¯

Mmin min i \ Mi

^ ¸Ê Ï´Å­n

¬£ ´¥ (4.35) § ¥» Æ nÂ É M' c f

f M

x f f M

M i

min

i

min

(4.36)

à m´¬£ ´¥ (4.36) § Å ¬£ ´¥ (4.32) ²Æ n ' cˆ

1

M' c 1

(4.37)

Mmin

Ä ¤¬¥º çn©Å ´¥­´ m´ M' c ¬´£´¥ Å nÆ n ³ Ë ¬£ ´¥ (4.31) ­¥¹¯ (4.32) ¯¤m´ Æ¥ É ´£ n´ n¯ ´¥ § ©´£ ³ n¯ ¯ ¯³§ ¯¥¶ ¸£ ´¥ ¯ ¥­³¬ n¯£»§ ɬ´£´¥ Å n¬£ ´¥ (4.37) Ã Æ n

¶ ´¥ ´¥­³¬Ã £·¥² [2] ¸Ê ²Â n´¥­³¬ n¯£»§ m = [m1, m2, …, mK] Ï´ © K ¶ çn©Æ n Ï´¥­³¬ c = [c1, c2, …, cN] Ï´ © N ¶ Ä ¤£·Ä ¥ ¬¥n´ ´£¬£ ´¥ (4.3) ³Ê ¹¯ c <m | p > <m1 m 2 ! mK p1 p2 ! pN K >

รหัสแอลดีพีซี

4.3 ´¥Â n´¥­³¬Ã¯§ · · ·

(4.38)

Ä ¤ ·Ê p = [p1, p2, …, pN – K] ¹¯ ¶ ´¥¶ · Ï´ © N – K ¶ ³ ³ Ë Â£¹Ê¯Å n¥­³¬Ã £·¥² ¬¶Ê ·Ê

n¯ Ï´Å ´¥Â n´¥­³¬ n¯£»§ É ¹¯ ´¥­´ m´ ¶ ´¥¶ · p ç²Â£¹Ê¯Æ n m´ p çn© É Ï´£´ m¯Â n´ ³ n¯£»§

4

บทที่

m ´£¬£ ´¥ (4.38) É ²Æ n Ï´¥­³¬ c ´£ ·Ê n¯ ´¥

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119

Ä ¤ ³Ê©Æ ¥­³¬Ã¯§ · · · ² » Ï´­ n©¤Â£ ¥¶ q ´¥¶ ·Â É H ´ MuN ³ ³ Ë Å

­³© n¯ ·Ë ²Ã¬ ´¥­´ ¶ ´¥¶ · p ´ £ ¥¶ q H ³ ·Ë ­§³ ´ ·ÊÆ n£ ¥¶ q H ·Ê n¯ ´¥Ã§n© É ²¯´ª³¤ ©´£¬³£ ³ q ´£¬£ ´¥ (4.6) Å ´¥­´ m´ p ³Ê ¹¯

(4.39)

HcT 0M q1

£¹Ê¯ 0Mu1 ¹¯Â©  ¯¥q m´ª» ¤q ´ Mu1 n´ ³ £ ¥¶ q H Å­n¯¤m»Å ¥» (4.40)

H < H1 | H 2 >

£¹Ê¯ H1 £· ´ MuK ç² H2 £· ´ Mu(N – K) ³ ³ Ë Ã m´¬£ ´¥ (4.38) ç² (4.40) § Å ¬£ ´¥ (4.39) ²Æ n

m T ¯ ° 0 T ° ¢p ±

< H1 H 2 > ¡¡

H1m T H 2 p T 0

pT H 2 H1m T (£¯ ºÄ§¬¯ ) 1

(4.41)

³ º¥¬ ³ ¸ ¬´£´¥ ­´ m´ ³ Æ n ( ¹Ê ¯ ´ M = N – K)  ¹Ê ¯ ´ H2 Â É Â£ ¥¶ q ³©¯¤m´ ·Ê 4.3 ´ ³©¯¤m´ ·Ê 4.1  n´¥­³¬ n¯£»§ m = [101] ç² m = [110] Ä ¤Å n£ ¥¶ q ´¥¶ ·Â É H ¸Ê ¬¯ §n¯ ³ £ ¥¶ q ³© Ï´Â ¶ G Å ¬£ ´¥ (4.4) ©¶ · Ï´

¯´ª³¤¬£ ´¥ (4.7) Ï´Å­n¬´£´¥ ­´Â£ ¥¶ q H Æ n ´ £ ¥¶ q G ³ ·Ë 1 0 1 ¡ H < H1 H 2 > ¡¡1 1 0 ¡0 1 1 ¢¡

1 0 0¯° 0 1 0°° 0 0 1°±°

³ ³ Ë ¶ ´¥¶ ¬ · Ï´­¥³ m = [101] ­´Æ n ´ ¬£ ´¥ (4.41) ³Ê ¹¯ 1 0 0¯ ¡ ° T p ¡¡0 1 0°° ¡ 0 0 1° ¢ ±

120

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

1

1 0 1 ¯ 1 ¯ 0¯ ¡ °¡ ° ¡ ° ¡ 1 1 0° ¡ 0° ¡ 1 ° ¡ °¡ ° ¡ ° ¡ 0 1 1° ¡ 1° ¡ 1° ¢ ±¢ ± ¢ ±

 ¥´² ² ³ Ë c = [m p] = [101011] ¸Ê É ¥ ³ §§³ q ÊÆ· nÅ n©¯¤m´ ·Ê 4.1 Å Ï´ ¯  ·¤© ³ ¶ ´¥¶ ·¬Ï´­¥³ m = [110] ­´Æ nÄ ¤ 1 0 0¯ ¡ ° T p ¡¡0 1 0°° ¡ 0 0 1° ¢ ±

1

1 0 1¯ 1¯ 1¯ ¡ °¡ ° ¡ ° ¡ 1 1 0° ¡ 1 ° ¡ 0° ¡ °¡ ° ¡ ° ¡ 0 1 1 ° ¡ 0° ¡ 1 ° ¢ ±¢ ± ¢ ±

 ¥´² ² ³ Ë c = [m p] = [110101] ¸Ê É ¥ ³ §§³ q ÊÆ· nÅ n©¯¤m´ ·Ê 4.1  m ³ ³©¯¤m´ ·Ê 4.3 ì Å­nÂ­É ©m´ ´¥Â n´¥­³¬Ã¯§ · · ·¬Ï´­¥³ ¥­³¬Ã £·¥² ¬´£´¥ Ï´Æ n

Ä ¤ ´¥­´ m´ ¶ ´¥¶ · p ´£¬£ ´¥ (4.41) ´ ³ Ë Éà m´§ Å ¬£ ´¥ (4.38) É ²Æ n Ï´¥­³¬ c ´£ ·Ê n¯ ´¥ ¬Ï´­¥³ ¬£ ´¥ (4.39) ²Å nÅ ´¥ ¥© ¬¯ ©´£ » n¯ ¯ Ï´¥­³¬ ·ÊÆ n

4.4 ´¥ ¯ ¥­³¬Ã¯§ · · · ´¥Â n´¥­³¬Ã¯§ · · ·£· § Ï´Å­n n¯£»§Ã m§² ¶ £· ©´£¬³£ ³ q ³ ´£Ä ¥ ¬¥n´ ¯ £ ¥¶ q ´¥¶ · Â É H ³ ³ Ë ´¥ ¯ ¥­³¬Ã¯§ · · · É ²¯´ª³¤ ©´£¬³£ ³ q­§m´ ·Ë £´ m©¤Å ´¥ ¯ ¥­³¬ n¯£»§

Ä ¤ ³Ê©Æ ¥­³¬Ã¯§ · · · ² » ¯ ¥­³¬ n©¤¯³§ ¯¥¶ ¸£ ´¥ m´ m´©¬´¥17 (MPA: message passing

algorithm) ­¥¹¯Å ·Ê ·Ë ²Â¥·¤ ¬³ Ë È ©m´ “¯³§ ¯¥¶ ¸£ MP” [4, 17] Ä ¤Â¥¶Ê£ n ´ ´¥¬¥n´ ¬£ ´¥ ´¥¶ ·Â É ´ £ ¥¶ q H çn© É ·¤ Â É ¥´¡Ã  ¯¥q ´ ³ Ë É Ï´ ´¥ ¯ ¥­³¬ ¶ n¯£»§ ´£ ³ Ë ¯ ¯ ¯³§ ¯¥¶ ¸£ MP

¶ ´¥ ´ m¯ ¬³ ´ Å ¥» ·Ê 4.5 £¹Ê¯§Ï´ ³ n¯£»§¯¶ º mn {0, 1} Ï´ © K ¶ »  n´¥­³¬ n©¤¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k) Ï´Å­nÆ nÂ É Ï´¥­³¬ cn {0, 1} Ï´ © N ¶ ´ ³ Ë É¬m

 n´Æ Å © ¥Â n´ m» (mapper)  ¹Ê¯Ã § Â É §Ï´ ³ n¯£»§ sn {r1} ³ ³ Ë ¬³ ´ ·Ê© ¥¢´ ¥³

รหัสแอลดีพีซี

4.4.1 ¹Ë ´ Å ´¥ ¯ ¥­³¬Ã¯§ · · ·

Æ n¥³ ¹¯

rn sn wn

17

(4.42)

4

บทที่

¯³§ ¯¥¶ ¸£ MP ´ ¥³ Ë ÉÂ¥·¤ ©m´ sum-product algorithm (SPA) ­¥¹¯ belief propagation algorithm (BPA) ÉÆ n ¸Ê Â É ¥» à ´¥ ¯ ¥­³¬Ã © Ï´Ë Ã ¯¡ q (soft iterative decoding)

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121

wn mn

cn

sn

rn

mˆ n

¥» ·Ê 4.5 m¯ ¬³ ´ AGWN ·Ê£· ´¥Â n´Ã§² ¯ ¥­³¬Ã¯§ · · ·

£¹Ê¯ sn = 2cn – 1 ¹¯ n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ , wn ¹¯¬³ ´ ¥ ©  ´¬q¬· ´©Ã © (AWGN) ·Ê£· m´Â §·Ê¤Â m´ ³ ª» ¤qç² ©´£Ã ¥ ¥©  m´ ³ V2 ­¥¹¯Â ·¤ Â É ¬³ §³ « qÆ n ¹¯ wn N 0, T 2 ´ ³ Ë © ¥ ¯ ¥­³¬Ã¯§ · · · ² n¯ ¯ ¥­³¬ n¯£»§ rn  ¹Ê¯Å­nÆ n §§³ q É

m´ ¥²£´ ¯ n¯£»§¯¶ º mn (­¥¹¯ mˆ n ) ·Ê Ï´Å­n£· n¯ ¶ §´ n ¯¤¬º Å ·Ê ·Ë ² ¶ ´¥ ´Â ´² ¥ · Ê·¥­³¬Ã¯§ · · · Ê·Å nÂ É ¥­³¬Ã £·¥² (systematic code)

¸Ê Ï´Å­n Ï´¥­³¬ ·ÊÆ n£·Ä ¥ ¬¥n´ ´£¬£ ´¥ (4.3) ³Ê ¹¯ m´ mi = ci ¬Ï´­¥³ 1 d i d K n´Å­n m = [m1, m2, …, mK] ¹¯§Ï´ ³ n¯£»§¯¶ º , c = [c1, c2, …, cN] ¹¯ Ï´¥­³¬, ç² r = [r1, r2,

…, rN] ¹¯Â©  ¯¥q ¯ n¯£»§ ·Ê© ¥¢´ ¥³ Æ n¥³ ³ ³ Ë © ¥¢´ ¥³ à ¯²Ä ¬Â ¯¥¶¯¯¥¶¬» ¬º

(MAP: maximum a posteriori) ² ³ ¬¶ Š§¹¯ m´ c ·Ê Ï´Å­n ©´£ m ´ ²Â É ¯²Ä ¬Â ¯¥¶¯¯¥¶

(APP: a posteriori probability) ­¥¹¯ Pr <cn c | r > £· m´¬» ¬º ¬Ï´­¥³ à m§²Â©§´ n ³Ê ¹¯© ¥

¢´ ¥³ à MAP ² Ï´ © ­´ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ Mn ´ Pr <cn 1 | r > ¬­ Pr <cn 1| rn ; ri vn > ¬­ ­­ log ­­ Mn log Pr <cn 0 | r >®­­ Pr <cn 0 | rn ; ri vn >®­­

(4.43)

ç² Ï´ ´¥ ³ ¬¶ Å cˆn 1 £¹Ê¯ Mn p 0 ç² cˆn 0 £¹Ê¯ Mn 0 Ä ¤ ·Ê ´¥´£¶Â ¯¥q ri vn ¹¯ ©  ¯¥q ¯ §Ï´ ³ n¯£»§ ·Ê© ¥¢´ ¥³ Æ n¥³ ³ Ë ­£ ¤ ©n n¯£»§ ³© ·Ê i = n

¯´ª³¤ ¯  ¬q ³©Âª«Å ¬£ ´¥ (4.43) ¬´£´¥ ³ ¥» Å­£mÆ nÂ É Pr <cn 1 | rn ; ri vn >

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

p rn ; cn 1; ri vn

p rn ; ri vn

p rn | cn 1; ri vn p cn 1; ri vn

p rn | ri vn p ri vn

p rn | cn 1 Pr <cn 1| ri vn > p rn | ri vn

(4.44)

Ä ¤ ·Ê p rn | cn c ¹¯¡³ q ³ ©´£­ ´Ã m ©´£ m ´ ²Â É Ã £·Â ¹Ê¯ Æ (conditional probability density function) ¯ n¯£»§ rn £¹Ê¯ Ï´­ ¶ n¯£»§ cn = c {0, 1} £´Å­n 粬£ ´¥ (4.44) £´ ´ ©´£ ¥¶ ·Ê©m´ n´ Ï´­ cn £´Å­n m´ rn ²Â É ¯¶¬¥² ´ ri vn Å Ï´ ¯  ·¤© ³ ³©¬m© Å ¬£ ´¥ (4.43) ɬ´£´¥ ³ ¥» Å­£m­£¹¯ ¬£ ´¥ (4.44) Æ nÂ É Pr <cn 0 | rn ; ri vn >

p rn | cn 0 Pr <cn 0 | ri vn > p rn | ri vn

(4.45)

à m´¬£ ´¥ (4.44) ç² (4.45) § Å ¬£ ´¥ (4.43) ²Æ n p rn | cn 1 Pr <cn 1| ri vn > ¬­ ­­ Mn log p rn | cn 0 Pr <cn 0 | ri vn >®­­ p rn | cn 1 ¬­ Pr c 1| ri vn > ¬­ ­­ log < n ­­ log ­ Pr <cn 0 | ri vn >®­­ p rn | cn 0 ®­

Pr <cn 1| ri vn > ¬­ 2 log r

­­ n T2 Pr <cn 0 | ri vn >®­­

(4.46)

(4.47)

£¹Ê¯ p rn | cn

r 2c 1 2 ¬­ n n ­­ exp ­­ 2 2 T 2 2QT ®­ 1

(4.48)

¹¯ ©´£ m ´ ²Â É ¯ ³©Ã ¥¬mº£ ·Ê£· ´¥Ã à à  ´¬q ·¤ ¬£ ´¥ (4.47) ¯ Å­n ¥´ ©m´

¢´ ¥³ Æ n¥³ ³© ·Ê n ( ³Ê ¹¯ rn) ç² q¬¯ ´ n´ ©´£¹¯ ¹¯ “ m´©¬´¥Â¯ q ¥¶ ¶ (extrinsic

information)” ¯ ¶ n¯£»§ ³© ·Ê n ( ³Ê ¹¯ cn) ¸Ê Æ n£´ ´ n¯£»§ ³ Ë ­£ ·Ê© ¥¢´ ¥³ Æ n¥³

(¤ ©n n¯£»§ ³© ·Ê n) ¯ ´ ·Ë ²Â­É Æ n©m´ m´©¬´¥¯¶ ¥¶ ¶ Â É ¬³ ¬m© ³ n¯£»§ ·Ê© ¥¢´ ¥³

รหัสแอลดีพีซี

qÃ¥ ´ n´ ©´£¹¯ ¹¯ “ m´©¬´¥¯¶ ¥¶ ¶ (intrinsic information)” ¸Ê £´ ´ n¯£»§ ·Ê© ¥

Æ n¥³ ³© ·Ê n ­¥¹¯ rn Ä ¤ m´ ³© 2 / T 2 ²Â¥·¤ ©m´ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ m¯ ¬³ ´ (channel reliability) [51]

4

บทที่ ³©¯¤m´ ·Ê 4.4 ¶ ´¥ ´ m¯ ¬³ ´ ¬££´ ¥Ã Æ ´¥· (BSC: binary symmetric channel) Å ¥» ·Ê 4.6 ì ©m´ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ m¯ ¬³ ´ Â É Æ ´£¬£ ´¥ (4.47)

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123

cn

rn

1–

0

0

1–

1

1

¥» ·Ê 4.6 m¯ ¬³ ´ ¬££´ ¥Ã Æ ´¥· (BSC)

¤ ©n ©´£ m ´Â ¹Ê¯ ¹¯ ¯ m¯ ¬³ ´ ²£· m´Â m´ ³ log 1 B / B à ·Ê ²Â É 2 / T 2 £¹Ê¯ D ¹¯ ©´£ m ´ ²Â É ³ n´£ (crossover probability) ©¶ · Ï´

´ m¯ ¬³ ´ Å ¥» ·Ê 4.6 ²Æ n©m´ p rn 0 | cn 0 1 B , p rn 0 | cn 1

B , p rn 1| cn 0 B , ç² p rn 1| cn 1 1 B ³ ³ Ë ²Æ n©m´ p rn | cn 1

i p r

i \0,1^

n

i | cn 1

0 p rn 0 | cn 1 1 p rn 1 | cn 1 1 B

ç² p rn | cn 0

i p r

i \0,1^

n

i | cn 0

0 p rn 0 | cn 0 1 p rn 1| cn 0 B

 ¥´² ² ³ Ë m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ Mn ¯ m¯ ¬³ ´ BSC £· m´ ´£¬£ ´¥ (4.46) Ä ¤ ·Ê m´©¬´¥¯¶ ¥¶ ¶ Mnint £· m´Â m´ ³ p rn | cn 1 ¬­ 1 B ¬­ Mnint log ­ ­­ log p rn | cn 0 ®­­ B ®­

¬£ ´¥ (4.43) ¬´£´¥ ³ Å­n¯¤m»Å ¥» ·ÊÅ n ´ m´¤ ¸Ë Æ n ³ ·Ë Å­n ¶ ´¥ ´ ¥´¡Ã  ¯¥q

¯ ¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k) ¬Ï´­¥³ Ä­ ¶ ³© ·Ê n ´£¥» ·Ê 4.7 ¸Ê ² ©m´Ä­ ¶ ³© ·Ê

n ²Â ¹Ê¯£ m¯ ³ Ä­ Â É Ï´ © j Ä­ (­£´¤Â§ 1 ¸ j) ç²Ã m§²Ä­ Â É É ²Â ¹Ê¯£ m¯ ³

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

c 1

c1,2 c1,3

cn

c j

c 2

c1,k

c2,2 c2,3

c2,k

c j ,2 c j ,3

c j ,k

Ä­ ¶ Ä­ Â É

1

2

¥» ·Ê 4.7 ¥´¡Ã  ¯¥q ¯ ¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k) £¹Ê¯ ¶ ´¥ ´ Ä­ ¶ ³© ·Ê n

Ä­ ¶ ¯¹Ê È Â É Ï´ © k – 1 Ä­ ¯ ´ ·Ë Ï´­ Å­n c i ¡¢ci ,2 , ci ,3 , !, ci ,k ¯°± ¹¯Â ¯ Ä­ ¶ ³ Ë ­£ Ï´ © k – 1 Ä­ (¤ ©n Ä­ ¶ ³© ·Ê n) ·Ê ¹Ê¯£ m¯ ³ Ä­ Â É ³© ·Ê i £¹Ê¯

i = {1, 2, …, j} ³ ³ Ë ¥» ·Ê 4.7 ¯ Å­n ¥´ ©m´ m´ cn ² ¸Ë ³ m´ ´¥¶ · ¯ c 1 , c 2 , !, c j

­¥¹¯ ' c i

³ ·Ë £¦1, if ' c 1

' c 2

! ' c j

1 ¦ cn ¦¤ ¦¦0, if ' c 1

' c 2

! ' c j

0 ¦¥

(4.49)

³ Ë ·Ë  ¹Ê¯Å­n¬£ ´¥ ´¥¶ ·Â É º ¬£ ´¥ (j ¬£ ´¥) £· m´Â m´ ³ ª» ¤q ´£ ©´£¬³£ ³ q HcT = 0

Å ¬£ ´¥ (4.6) ¯ ´ ·Ë ¹Ê¯Å­n m´¤ m¯ ´¥¯ ¶ ´¤¯³§ ¯¥¶ ¸£ ´¥ ¯ ¥­³¬Ã¯§ · · Å· ­³© n¯ m¯Æ

4.4.2 ©³ ³ ¥ ¯ ¥­³¬Ã¯§ · · · ©³ ³ ¥ (cycle) ­£´¤ ¸ ¬n ´  ¶ ¢´¤Å ¥´¡ ·Ê£· º Â¥¶Ê£ n ç² º ¬¶ Ë ¬º Â É Ä­ ¶  ·¤© ³

รหัสแอลดีพีซี

² Ï ´ ¥´¡Ã  ¯¥qÅ ¥» ·Ê 4.7 £´ ³ ¥» Å­£mÆ nÂ É ¥´¡¥» ·Ê 4.8

Ä ¤ ©´£¤´© ¯ ©³ ³ ¥ (cycle length) £· m´Â m´ ³ Ï´ © ¬n  ¹Ê¯£ ³ Ë ­£ ·Ê Ï´Å­n ¶ Â É ©³ ³ ¥

 ¹Ê ¯ ´ ¥´¡Ã  ¯¥qÂ É ¥´¡¬¯ ¬m© (bipartite graph) ¸ Ï´Å­n ©´£¤´© n ¯¤¬º ¯ ©³ ³ ¥18 £· m´Â m´ ³ 4 ´£ ·Êì n©¤Â¬n ²Å ¥» ·Ê 4.8 ¯¤m´ Æ¥ É ´£ n´Æ£m£·Â¬n ²Å ¥´¡ É ² Ï´Å­n 18

4

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©³ ³ ¥ ·Ê£· ©´£¤´©Â m´ ³ 4 £· § ¥² £´ m¯¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · ³ ³ Ë ¥­³¬Ã¯§ · · · Ê · ·Æ£m ©¥£·©³ ³ ¥ ·Ê£· ©´£¤´©Â m´ ³ 4

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125

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127

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129

cx

cn

cy

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130

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131

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132

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u m ln

£ l 1

l 1

¦ ¦ Mi um li ¦ ¦ 2 tanh ¤ tanh ¦ 2 i N m \ \n^ ¦ ¦ ¦ ¥ 1

¬­­­­¦¦¦²¦ » ­­­¦ ­®¦ ¦ ¦ ¼

(4.59)

(¬¶ Ë ¬º ´¥© Ï´Ë ¯ m) ´¥ ¥³ ¥º Ä­ ¶ (bit-node update) ¬Ï´­¥³ n \1, 2, !, N ^

Mn l

2 l r um ln 2 n T m Mn

(4.60)

(¬¶ Ë ¬º ´¥© Ï´Ë ¯ n)

รหัสแอลดีพีซี

(¬¶ Ë ¬º ´¥© Ï´Ë ¯ l) 4. ¯ ¥­³¬§Ï´ ³ n¯£»§¯¶ º ´ ©´£¬³£ ³ q m¯Æ ·Ë (Å nÆ n ´²¥­³¬Ã £·¥²  m´ ³ Ë )

£¦1, if M l max p 0 ¦ i mˆ i ¦¤ ¦¦0, if M l max 0 i ¦¥

(4.61)

¬Ï´­¥³ i \1, 2, !, N M ^ £¹Ê¯ N – M = K ¹¯ Ï´ © ¯ ¶ n¯£»§¯¶ º ( »¥» ·Ê 4.1)

4

บทที่

¥» ·Ê 4.11 ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ MP ¬Ï´­¥³ ´¥ ¯ ¥­³¬Ã¯§ · · · [4, 17]

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133

Lc r1

Lc r2

Lc r3

Ȝ

0

2 2 T

r1 ¯ ¡ ° ¡r2 ° Lc ¡ ° ¡r ° ¢ 3±

r1 ¯ ¡ ° ¡r2 ° ¡ ° ¡r ° ¢ 3±

¥» ·Ê 4.12 ¥´¡Ã  ¯¥q ÊÅ· nÅ ´¥ ¯ ¥­³¬ n¯£»§Å ³©¯¤m´ ·Ê 4.6

³ ³ Ë ¬³ ´ ·Ê© ¥¢´ ¥³ Æ n¥³ ¹¯ r1 ¯ 1¯ w1 ¯ ¡ ° ¡° ¡ ° ¡r2 ° s ¡1° ¡w 2 ° ¡ ° ¡° ¡ ° ¡r ° ¡1° ¡w ° ¢ ± ¢ 3± ¢ 3±

Ä ¤ ·Ê s {r1} ç² wn N 0, T 2 ¹¯¬³ ´ ¥ © AWGN ­´ m´ LLR à ¯²Ä ¬  ¯¥¶¯¯¥¶ Ȝ <M1 , M2 , M3 > £¹Ê¯ Mn log Pr <cn 1| r > / Pr <cn 0 | r > ¬Ï´­¥³ n = {1, 2, 3} T

£¹Ê¯¬¶ Ë ¬º ´¥© Ï´Ë ¥¯ ·Ê 2 ³Ê ¹¯­´ m´ Mn

2

©¶ · Ï´

´ ¬£ ´¥ (4.7) £ ¥¶ q G ·Ê Ï´­ £´ ²£·Â£ ¥¶ q ´¥¶ ·Â É H ¹¯ 1 1 0¯ ° H ¡ P T | I ¯° ¡ ¢ ± ¡1 0 1 ° ¢ ±

¯´ª³¤Â ¶ ´¥ Ï´ ³ à  ´¬q ·¤ (Gaussian elimination) [53] Ï´Å­n¬´£´¥ ³ ¥» £ ¥¶ q

H Å­£mÆ n É

1 1 0¯ ° H ¡ ¡0 1 1 ° ¢ ±

¸Ê ì Å­nÂ É ¥´¡Ã  ¯¥qÆ n ´£¥» ·Ê 4.12 Ä ¤ ·Ê m´ Mn ­´Æ n ´ ¬£ ´¥ (4.47) ³Ê ¹¯ Pr <cn 1 | ri vn > ¬­ ­­ Mn Lc rn log Pr <cn 0 | ri vn >®­­

£¹Ê¯ Lc 2 / T 2 ¹¯ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ m¯ ¬³ ´

134

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(4.62)

Lc r1

Lc r1

Lc r2

Lc r2

Lc r1

Lc r3

Lc r2

Lc r2

Lc r3

Lc r2

Lc r1

Lc r3

Lc r3

Lc r2

¥» ·Ê 4.13 ´¥¬m m´ m´©¬´¥ ( ) ´ Ä­ ¶ Æ ¤³ Ä­ Â É Ã§² ( ) ´ Ä­ Â É Æ ¤³ Ä­ ¶ £¹Ê¯

¬¶ Ë ¬º ´¥© Ï´Ë ¥¯ ·Ê 1

m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ Ȝ <M1 , M2 , M3 > ¬´£´¥ ­´Æ n ´ ¯³§ ¯¥¶ ¸£ MP ´£ T

¥» ·Ê 4.11 ³ m¯Æ ·Ë Ï´­ m´Â¥¶Ê£ n ¯ M 0 ¯ ¡ 1 ° ¡ 0° 0 Ȝ ¡M2 ° Lc ¡ ° ¡M 0 ° ¡¢ 3 °±

r1 ¯ ¡ ° ¡ ° ¡r2 ° ¡r ° ¢ 3±

¥¯ ·Ê 1 (1st iteration) Ä­ ¶ à m§²Ä­ ²¬m m´©¬´¥ Mn Æ ¤³ Ä­ Â É ´£ ·Êì Å ¥» ·Ê 4.13 ( ) ´ ³ Ë Ä­ 0

Â É Ã m§²Ä­ ² Ï ´ m´©¬´¥ ·ÊÆ n¥³ £´ Ï´ © ´£¬£ ´¥ (4.59) çn© ɬm §§³ q §³ Æ ¤³ Ä­ ¶ ´£ ·Êì Å ¥» ·Ê 4.13 ( ) ­§³ ´ ³ Ë Ä­ ¶ ² Ï ´ m´©¬´¥ ·ÊÆ n¥³ ³ Ë ­£ £´ Ï´ © ´£

¬£ ´¥ (4.60) ¸Ê ²Æ n©m´ m´ Mn ¯ ¶ n¯£»§ ³© ·Ê n £¹Ê¯ n = {1, 2, 3} £· m´Â m´ ³ 1

r r ¯ ¡ 1 2 ° ¡r1 r2 r3 ° ¡ ° ¡ r r ° ¢ 2 3 ±

รหัสแอลดีพีซี

1 ¯ ¡M1 ° ¡ 1° 1 Ȝ ¡M2 ° Lc ¡ ° ¡M 1 ° ¡¢ 3 °±

¥¯ ·Ê 2 (2nd iteration)

Å Ï´ ¯  ·¤© ³ Ä­ ¶ à m§²Ä­ ²¬m m´©¬´¥Æ ¤³ Ä­ Â É ´£ ·Êì Å ¥» ·Ê 4.14 ( ) ´ ³ Ë Ä­ Â É Ã m§²Ä­ ² Ï ´ m´©¬´¥ ·ÊÆ n¥³ £´ Ï´ © ´£¬£ ´¥ (4.59) çn© ɬm §§³ q

4

บทที่

§³ Æ ¤³ Ä­ ¶ ´£ ·Êì Å ¥» ·Ê 4.14 ( ) ­§³ ´ ³ Ë Ä­ ¶ ² Ï ´ m´©¬´¥ ·ÊÆ n¥³ ³ Ë ­£ £´ Ï´ © ´£¬£ ´¥ (4.60) ¸Ê ²Æ n©m´ m´ Mn ¯ ¶ n¯£»§ ³© ·Ê n £· m´Â m´ ³ 2

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135

r2

Lc

r2

Lc r3

Lc r2

Lc r1

Lc r3

Lc r3

r 3

Lc r1

r2

Lc r1

Lc r3

r

Lc 1

Lc r1

Lc r2 Lc r2

r3

Lc r1

¥» ·Ê 4.14 ´¥¬m m´ m´©¬´¥ ( ) ´ Ä­ ¶ Æ ¤³ Ä­ Â É Ã§² ( ) ´ Ä­ Â É Æ ¤³ Ä­ ¶ £¹Ê¯ ¬¶ Ë ¬º ´¥© Ï´Ë ¥¯ ·Ê 2

2 ¯ ¡M1 ° ¡ 2° 2 Ȝ ¡M2 ° Lc ¡ ° ¡M 2 ° ¡¢ 3 °±

r r r ¯ ¡ 1 2 3° ¡r1 r2 r3 ° ¡ ° ¡r r r ° ¢ 1 2 3±

(4.63)

Ë ¬º ´¥© Ï´Ë ¥¯ ·Ê 2 ³Ê ¯ ¸Ê É ¹¯ m´ LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ {c1, c2, c3} £¹Ê¯¬¶ ¯ ´ ·Ë n´Å­n¯³§ ¯¥¶ ¸£ MP Ï´ ´ m¯Æ ¯· É ² ©m´ m´ Ȝ Ȝ ¬Ï´­¥³ l > 2 ³Ê ¹¯ l

2

¯³§ ¯¥¶ ¸£ MP  n´¬m»¬ ´ ² ³© (steady state) çn© ³©¯¤m´ ·Ê 4.6 ¬´£´¥ ­´ Ï´ ¯ Æ n¯ · ©¶ ·­ ¸Ê ³ ·Ë ´ ¬£ ´¥ (4.43) ²Æ n©m´ m´ LLR

à ¯²Ä ¬Â ¯¥¶¯¯¥¶ ¯ ¶ n¯£»§ cn ¬Ï´­¥³ n = {1, 2, 3} £· m´Â m´ ³ (¯´ª³¤ ¯  ¬q) p r | cn 1 Pr <cn 1> / p r ¬­ ­­ Mn log p r | cn 0 Pr <cn 0> / p r ®­­

(4.64)

£¹Ê¯ r <r1 , r2 , r3 > n´¬££º ¶©m´ Pr <cn 1> Pr <cn 0> 0.5 ³ ³ Ë ¬£ ´¥ (4.64) ²§ ¥» T

Æ nÂ É p r | cn 1 ¬­ Mn log ­­ p r | cn 0 ®­­ 2 ¬ C exp 1 r <1 1 1>T ¬­­ ­­ 2 2T ®­ ­­­ log ­ 2 ­ 1 T ¬­ ­ C exp 2 r <1 1 1> ­­ ­­ 2T ® ®­

136

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

1 \2 r1 r2 r3 2 r1 r2 r3 ^ 2T 2

2 r1 r2 r3

T2

¸Ê £· m´Â m´ ³ §§³ q ÊÆ· nÅ ¬£ ´¥ (4.63) £¹Ê¯ C 1/ 2QT 2 ³ ³ Ë ¸ ¬¥º Æ n©m´ n´¥­³¬Ã¯§ · · ·

Æ£m£·©³ ³ ¥ ¯³§ ¯¥¶ ¸£ MP ²§m»Â n´¬m» m´ ·Ê » n¯ £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë Â¥¹Ê¯¤È

³©¯¤m´ ·Ê 4.7 ¶ ´¥ ´ m¯ ¬³ ´ AGWN Å ¥» ·Ê 4.5 £¹Ê¯ ¶ n¯£»§¯¶ º m = [1 0 1] ç² ¥­³¬Ã¯§ · · · Ê·Å n£·Â£ ¥¶ q ³© Ï´Â ¶ G ´£¬£ ´¥ (4.4) Ä ¤ ·Ê¬³ ´ ¥ © Å ¥² £· m´

 m´ ³ w = [–0.5, 0.8, –0.5, 0.5, 0.5, –0.5] ç²£· ©´£Ã ¥ ¥©  m´ ³ V2 = 0.5 ­´ m´

LLR à ¯²Ä ¬Â ¯¥¶¯¯¥¶ Ȝ <M1 , M2 , M3 , M4 , M5 , M6 > £¹Ê¯¬¶ Ë ¬º ´¥© Ï´Ë ¥¯ ·Ê 3 T

©¶ · Ï´

´ ³©¯¤m´ ·Ê 4.1 £¹Ê¯ m = [101] É ²Æ n c = [101011] ³ ³ Ë ¬³ ´ ·Ê© ¥ ¯ ¥­³¬

ï§ · · ·Æ n¥³ ¹¯

r = (2c – 1) + w = [r1, r2, r3, r4, r5, r6] = [0.5, –0.2, 0.5, –0.5, 1.5, 0.5]  ¹Ê ¯ ´ £ ¥¶ q ³© Ï´Â ¶ G ´£¬£ ´¥ (4.4) ¯¤m»Å ¥» à £·¥² (systematic form) ¸ Ï´ Å­n¬´£´¥ ­´Â£ ¥¶ q ´¥¶ ·Â É H Æ n ´£¬£ ´¥ (4.7) ³Ê ¹¯

© ¥ ¯ ¥­³¬ ²Å n£ ¥¶ q H ·Ë Å ´¥ ¯ ¥­³¬§Ï´ ³ n¯£»§ r ¸Ê £· ´¥Ã§  §·Ê¤ m´©¬´¥Ã

¯¡ q ´£ ¥´¡Ã  ¯¥qÅ ¥» ·Ê 4.15 Ä ¤Å à m§²¥¯ ¯ ´¥© Ï´Ë Ä­ Â É Ã§²Ä­ ¶ ²

£· ´¥ Ï´ © m´ um ln ç² Mn ´£¬£ ´¥ (4.59) ç² (4.60) ´£§Ï´ ³ £¹Ê¯ l ¹¯¥¯ ¯ l

l

รหัสแอลดีพีซี

1 0 1 1 0 0¯ ¡ ° H ¡¡1 1 0 0 1 0°° ¡ 0 1 1 0 0 1° ¢ ±

´¥© Ï´Ë ¸Ê Æ n §§³ q ³ ·Ë ¥¯ ·Ê 1 (1st iteration) Ä­ Â É ²¬m m´©¬´¥Ã ¯¡ q um ln ´ Ä­ Â É m Æ ¤³ Ä­ ¶ n ³ ·Ë 1

4

บทที่

u 1 , u 1 , u 1 ¯ <1.3250, 1.3250, 1.3250 > ¡¢ 1l1 1l3 1l 4 °±

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137

Lc r1

Lc r3

Lc r2

Lc r4

Lc r5

Lc r6 Mn

l

n \1, 2,3, 4,5, 6^

um ln l

m \1, 2,3^ ¥» ·Ê 4.15 ¥´¡Ã  ¯¥q ¯ £ ¥¶­ q ´¥¶ ·Â É Å ³©¯¤m´ ·Ê 4.7

u 1 , u 1 , u 1 ¯ <0.7956, 1.9822, 0.5958> ¢¡ 2l1 2l 2 2l5 ±° u 1 , u 1 , u 1 ¯ < 1.3250, 0.5958, 0.5958 ¢¡ 3l 2 3l3 3l 6 ±°

>

ç²Ä­ ¶ n ² Ï´ © m´ LLR Mn Æ n m´ ³ 1

M 1 , M 1 , M 1 , M 1 , M 1 , M 1 ¯ < 4.1206, 4.1072, 3.9208, 3.325, 6.5958, 2.5958> ¡¢ 1 2 3 4 5 6 °±

¥¯ ·Ê 2 (2nd iteration)

Ä­ Â É ²¬m m´©¬´¥Ã ¯¡ q um l n ´ Ä­ Â É m Æ ¤³ Ä­ ¶ n ³ · Ë 2

u 2 , u 2 , u 2 ¯ <1.5710, 1.6358, 2.0021 > ¡¢ 1l1 1l3 1l 4 °± u 2 , u 2 , u 2 ¯ < 2.1048, 3.2585, 1.8660> ¡¢ 2l1 2l 2 2l5 °± u 2 , u 2 , u 2 ¯ < 1.7692, 1.6317, 2.3263> ¡¢ 3l 2 3l3 3l 6 °±

ç²Ä­ ¶ n ² Ï´ © m´ LLR Mn Æ n m´ ³ 2

M 2 , M 2 , M 2 , M 2 , M 2 , M 2 ¯ <5.6758, 5.8276, 5.2675, 4.0021, 7.866, 4.3263> 2 3 4 5 6 ° ¡¢ 1 ±

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥¯ ·Ê 3 (3rd iteration)

Ä­ Â É ²¬m m´©¬´¥Ã ¯¡ q um l n ´ Ä­ Â É m Æ ¤³ Ä­ ¶ n ³ · Ë 3

u 3 , u 3 , u 3 ¯ <1.8249, 1.8872, 3.1478 > ¡¢ 1l1 1l3 1l 4 °± u 3 , u 3 , u 3 ¯ < 2.5375, 3.4867, 2.2586> ¡¢ 2l1 2l 2 2l5 °± u 3 , u 3 , u 3 ¯ < 1.8256, 1.8822, 3.1323> ¡¢ 3l 2 3l3 3l 6 °±

ç²Ä­ ¶ n ² Ï´ © m´ LLR Mn Æ n m´ ³ 3

M 3 , M 3 , M 3 , M 3 , M 3 , M 3 ¯ < 6.3624, 6.1122, 5.7694, 5.1478, 8.2586, 5.1323> 2 3 4 5 6 ° ¢¡ 1 ±

³ ³ Ë Â£¹Ê¯¬¶ Ë ¬º ´¥© ¥¯ ·Ê¬¯ © ¥ ¯ ¥­³¬Ã¯§ · · · É ² ¯ ¥­³¬ ¶ n¯£»§ ´£

¬£ ´¥ (4.61) ¸Ê ²Æ n §§³ q É

ˆ <mˆ 1 mˆ 2 mˆ 3 > <1 0 1> m

¸Ê ¥ ³ ¶ n¯£»§¯¶ º m = [1 0 1] ì ©m´Æ£m£· n¯ ¶ §´  ¶ ¸Ë Å ¥² ¯ ´ ·Ë ¤³ ¬³ Â Â­É ©m´ n´¥² Ï´ ´ Å ¬¢´©² ¶ (¬³ ´ ¥ © Æ£m¥º Ã¥ ) m´ LLR Mn Å Ã m§² l

¥¯ ¯ ´¥© Ï´Ë ²£· m´Â ¶Ê£ ¸Ë Â¥¹Ê¯¤È ¸Ê ­£´¤ ©´£©m´ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ ¶ n¯£»§ ·Ê ¯ ¥­³¬Æ n ²£· ©´£ » n¯ £´ ¤¶Ê ¸Ë

Å ´ ¶ ³ ¶¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · ² ¸Ë ³ £ ¥¶ q ´¥¶ ·Â É H ¸Ê ©¥£·§³ « ²Ã ¬mº£ Å­n£´ ·Ê¬º ç²Æ£m£·©³ ³ ¥ ´ ©¶ ³¤ m´ È [4, 5, 8, 17, 54, 55] ´ n´ ¥­³¬Ã¯§ · · · ²Â n Æ

รหัสแอลดีพีซี

4.5 ´¥¬¥n´ £ ¥¶ q ´¥¶ ·Â É

·Ê ´¥¬¥n´ £ ¥¶ q H ³ ³ Ë Å ­³© n¯ ·Ë ²¯ ¶ ´¤ ´¥¬¥n´ £ ¥¶ q H à m´¤È  ¹Ê¯Â É ¹Ë ´ Å­n ³ n»¬ Å Å ´¥ ³ ´ ´ ´ n´ ¥­³¬Ã¯§ · · ·Å ¯ ´

4

4.5.1 ¥­³¬Ã¯§ · · · ¥ ¶

บทที่

£ ¥¶ q ´¥¶ ·Â É H ¬Ï´­¥³ ¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k) ´ M uN ¬´£´¥ ¬¥n´ Æ n ´

£ ¥¶ q ´¥¶ ·Â É H0 ´ LuN £¹Ê¯ L N / k M / j ¸Ê £· m´Â m´ ³

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

139

1 1 ! 1 0 0 0 ¯ " ¡ ° k ¡ ° ¡ 0 1 1 ! 1 0 " 0 °° ¡ k ¡ ° ¡ H0 ¡ # % % % # °° ¡ 0 1 " ! 1

0 1 0 °° ¡ k ¡ ° ¡ ° 1 1 " ! 1 ° 0 0 ¡ 0 k ¢¡ ±° LqN

(4.65)

£¹Ê¯ 0 = [0 0 … 0] ¹¯Â©  ¯¥qª» ¤q ´ 1uk ¬£ ´¥ (4.65) ¯ Å­n ¥´ ©m´ n¯£»§Å à © ¯ ·Ê

m ²£·¬£´ ¶ Â É Â§ 1 ϴí m ¯ à © ³ Ë ·Ê m 1 k 1 ¸ mk ç²Ã © ³ Ë ¯¹Ê È ²£·

¬£´ ¶ Â É Â§ 0 Å ´ ¶ ³ ¶Â£ ¥¶ q H0 ¬´£´¥ Å n ³ ¥­³¬Ã¯§ · · · ¥ ¶Ã (1, k) Ä ¤ ¬£ ´¥ ´¥¶ ·Â É Ã m§²¬£ ´¥ ²¬³£ ³ q ³ n¯£»§ Ï´ © k ¶ ç² n¯£»§Ã m§² ¶ ²¬³£ ³ q ³

¬£ ´¥ ´¥¶ ·Â É Â ·¤ ­ ¸Ê ¬£ ´¥Â m´ ³ Ë ¯¤m´ Æ¥ É ´£¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · Ê·Å n£ ¥¶ q

H0 ²Æ£m ·  ¹Ê ¯ ´ £ ¥¶ q H0 ²Æ£m¯¶¬¥² m¯ ³ à  ¶ ¬n (linearly dependent)  m Ï´¥­³¬

0000…0 ç² 1100…0 ¹¯©m´Â É Ï´¥­³¬ ·Ê » n¯ ­£¹¯ ³ ³ ³ Ë ¥­³¬ ·Ë ²£·¥²¤² ´ n ¯¤¬º  m´ ³ dmin = 2

Ä ¤ ³Ê©Æ £ ¥¶ q H ¬Ï´­¥³ ¥­³¬Ã¯§ · · · ¥ ¶Ã (j, k) ´ MuN ¬¥n´ Æ n ´

´¥ Ï ´Â¯´Â£ ¥¶ q H0 ·Ê£· ´¥Â¥·¤ ¬³  §·Ê¤ (permutation) n¯£»§Å à © ³ Ë £´©´ m¯ ³ ³ ·Ë Q1 H 0 ¯ ¡ ° ¡ Q H ° 2 0 ° ¡ H ¡ ° ¡ # ° ¡ ° ¡¢ Q j H 0 °± M qN

(4.66)

· · ´¥Â¥·¤ ¬³  §·Ê¤ n¯£»§Å à © ³ Ë ¯ £ ¥¶ q H0 ¬Ï´­¥³ i = {1, £¹Ê¯ Qi H 0 ¹¯Â£ ¥¶ q Ê£ ³ ¶Â£ ¥¶ q H0 ¬´£´¥ Â É Â£ ¥¶ q¥» à ¯¹Ê ÉÆ n  m 2, …, j} ¯¤m´ Æ¥ É ´£Å ´ ¶ H 0 < I I I " I >LqN

(4.67)

£¹Ê¯ I ¹¯Â£ ¥¶ q¯ §³ « q ´ LuL ç² L N / k

´¥Â¥·¤ ¬³  §·Ê¤ ·Ê · ©¥ Ï´Å­n£ ¥¶ q H £·¥²¤² ´ n ¯¤¬º ¯ ¥­³¬ dmin > 2 Ä ¤ ³Ê©Æ

´¥¯¯ à ´¥Â¥·¤ ¬³  §·Ê¤ Ï´ © j à (à m§²Ã £· ©´£¤´© N ³©) Â É ¬¶Ê ·Ê n´ ´¤

¯¤m´ Æ¥ É ´£ Gallager [17] Æ nì Å­nÂ­É ©m´ ´¥Â¥·¤ ¬³  §·Ê¤ à ¬mº£Ã n (pure random) ² Ï´Å­nÆ n£ ¥¶ q H ·Ê ·¬º ¸Ê ¬m §Å­n¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · ·£· m´¬» ¬º

140

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

³©¯¤m´ ·Ê 4.8 ¶ ´¥ ´¥­³¬Ã¯§ · · · ¥ ¶Ã (3, 4) ´ 15u20 m¯Æ ·Ë [17] 1 ¡0 ¡ ¡0 ¡0 ¡ ¡0 ¡ ¡1 ¡0 ¡ H ¡0 ¡0 ¡ ¡0 ¡1 ¡ ¡0 ¡0 ¡ ¡0 ¡0 ¢¡

1 0 0 0 0 0 1 0 0 0 0 1 0 0 0

1 0 0 0 0 0 0 1 0 0 0 0 1 0 0

1 0 0 0 0 0 0 0 1 0 0 0 0 1 0

0 1 0 0 0 1 0 0 0 0 0 0 0 0 1

0 1 0 0 0 0 1 0 0 0 1 0 0 0 0

0 1 0 0 0 0 0 1 0 0 0 1 0 0 0

0 1 0 0 0 0 0 0 0 1 0 0 1 0 0

0 0 1 0 0 1 0 0 0 0 0 0 0 1 0

0 0 1 0 0 0 1 0 0 0 0 0 0 0 1

0 0 1 0 0 0 0 0 1 0 0 1 0 0 0

0 0 1 0 0 0 0 0 0 1 1 0 0 0 0

0 0 0 1 0 1 0 0 0 0 0 0 1 0 0

0 0 0 1 0 0 0 1 0 0 0 0 0 1 0

0 0 0 1 0 0 0 0 1 0 0 0 0 0 1

0 0 0 1 0 0 0 0 0 1 0 1 0 0 0

0 0 0 0 1 0 1 0 0 0 0 0 0 1 0

0 0 0 0 1 0 0 1 0 0 1 0 0 0 0

0 0 0 0 1 0 0 0 1 0 0 0 1 0 0

0¯ 0°° 0° 0°° 1° ° 0° 0°° 0° 0°° 1° 0°° 0° 0°° 0° 1 °±°

(4.68)

Ä ¤Â¬n ¥ Å Ã © ¯ ¬¯ ¬n ²Â É ³©Ã m £ ¥¶ q H0 ç²Â£ ¥¶ q¯· ¬¯ £ ¥¶ q ¶ ´ ´¥Â¥·¤ ¬³  §·Ê¤ ¯ £ ¥¶ q H0 ´£¬£ ´¥ (4.66) £¹Ê¯ Q1 \1 2 3 4 5 ! 20^ , Q2

\1 5 9 13 2 6 10 17 3 7 14 18 4 11 15 19 8 12 16 20^ ç² Q3 \1 5 9 13 17 2 6 10 14 18 7 3 11 15 19 8 16 4 12 20^ £ ¥¶ q H Å ¬£ ´¥ (4.68) ì Å­nÂ­É ©m´Ã m§²Ã © ³ Ë £·Â§ 1 Ï´ © j = 3 ³© ç²Ã m§²Ã © ¯ £·Â§ 1 Ï´ © k = 4 ³© ¯ ´ ·Ë ¤³ ©m´ n¯£»§Å

à © ¯ ·Ê 10 ¹¯ §¥©£ (à £¯ ºÄ§¬¯ ) ¯ n¯£»§Å à © ¯ ·Ê 1 ¸ 9 ç² n¯£»§Å à ©

¯ ·Ê 15 ¹¯ §¥©£ ¯ n¯£»§Å à © ¯ ·Ê 1 ¸ 5 ç² n¯£»§Å à © ¯ ·Ê 11 ¸ 14 ¸Ê

­£´¤ ©´£©m´ n¯£»§Å à © ¯ ·Ê 10 ç² 15 Æ£m¯¶¬¥² m¯ ³ à  ¶ ¬n ³ n¯£»§Å à © ¯

¯¹Ê È ³ ³ Ë Â£ ¥¶ q H ²£·Â ·¤ n¯£»§Å à © ¯  ·¤ 13 à © ¯  m´ ³ Ë ·ÊÂ É ¯¶¬¥² m¯ ³ ²Å n n´¥­³¬ n¯£»§ ¥³ Ë §² K = 20 – 13 = 7 ¶ ç²£·¯³ ¥´¥­³¬Â m´ ³ R K / N 0.35 Ä ¤ ´¥ Å ´ ¶ ³ ¶Â£ ¥¶ q H Å ¬£ ´¥ (4.68) ¬´£´¥ § ¥» Æ nÂ É Â£ ¥¶ q H

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เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

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nº£ m´ ³ ´¥§ º £¹Ê¯Â ·¤ ³ ¬£¥¥ ² ¯ ¥² ·Ê ¶Ê£ ¸Ë ¯¤m´ Æ¥ É ´£­§³ ´ ·ÊÆ n£· ´¥ ³ ´ £ ¥¶ q H  ¶ Ä ¥ ¬¥n´ ³ Ë Ã m · .ª. 2000 Â É n £´ ÉÂ¥¶Ê£¬m §Å­n°´¥q ¶¬ qÆ ¥¡q ¥mº Å­£mÈ

Å ³ º ³ ¬´£´¥ Ï ´¥­³¬Ã¯§ · · ·£´Å n ¥¶ Å ¶ m¯ ¬³ ´ ¯m´ Æ n Ä ¤ ² Ï ´¥­³¬Ã¯§ · · ·£´ Å n¬Ï´­¥³ ´¥ ¯ ¥­³¬Ã © Ï´Ë (iterative decoding) ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ © ¥ ¥© ­´ SOVA 粩 ¥ ¯ ¥­³¬Ã¯§ · · ·

4.6 § ´¥ §¯ Å ­³© n¯ ·Ë ² ¬¯ ¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · ÊÅ· nÅ m¯ ¬³ ´ AWGN ç² m¯ ¬³ ´

4.6.1 m¯ ¬³ ´ AWGN ¶ ´¥ ´ m¯ ¬³ ´ AWGN Å ¥» ·Ê 4.5 £¹Ê¯¥­³¬Ã¯§ · · · ÊÅ· n ¹¯¥­³¬Ã¯§ · · ·Ã à ©§Ï´ ³

รหัสแอลดีพีซี

°´¥q ¶¬ qÆ ¥¡q ÊÅ· n ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë Â ¹Ê¯Ã¬ ©´£¬´£´¥ ¯ ¥­³¬Ã¯§ · · ·

·Ê » ¥³ ¥º (MAC) ·Ê£·Â£ ¥¶ q ´¥¶ ·Â É H ´ 9u15 ´£¬£ ´¥ (4.74) ³Ê ¹¯¥­³¬Ã¯§

· · · ·Ë ²Â n´¥­³¬ n¯£»§¯¶ º ¥³ Ë §² 6 ¶ ç²Å­n Ï´¥­³¬ ´ 15 ¶ ( ¶ ´¥¶ ·£· Ï´ © 9 ¶ )

¯ ´ ·Ë m´¯³ ¥´¬m© Ï´§³ ¯ ¬³ ´ m¯ Ï´§³ ¯ ¬³ ´ ¥ © (SNR) ¶ ¤´£Ä ¤ E ¬ SNR 10 log10 b ­­­ N 0 ®­

4

บทที่ (4.85)

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147

¥» ·Ê 4.16 ¬£¥¥ ² ¯ ¥² Å ¥» ·Ê 4.5 £¹Ê¯© ¥ ¯ ¥­³¬Ã¯§ · · · Ï´ ´ ·Ê ´¥© Ï´Ë Å ¥¯ m´ È

Ä ¤ ·Ê Eb = 1 ¹¯ §³ ´ ¯ ¶ n¯£»§¯¶ º ­ ¸Ê ¶ , N0/2 ¹¯ ©´£­ ´Ã m ¬Â ¥³£ Ï´§³ à ¬¯ n´ (two-sided power spectral density) ¯ ¬³ ´ ¥ © wn N 0, T 2 ,

T 2 N 0 / 2T , ç² T ¹¯ ´ ©§´ ¯ n¯£»§¯¶ º ¶ mn ¯ ´ ·Ë m´¯³ ¥´ n¯ ¶ §´

¯ ¶ (BER: bit-error rate) ¯ à m§² SNR ­´Æ n ´ ´¥¬m n¯£»§¯¶ º ­§´¤È §É¯

( §É¯ §² 6 ¶ )  n´Æ Å ¥² ¥² ³Ê © ¥ ¯ ¥­³¬ n¯£»§ ¥© n¯ ¶ §´ ·Ê ¶ ¸Ë Æ n ¥©£Æ£m n¯¤ ©m´ 1000 ¶

¥» ·Ê 4.16 ì ¬£¥¥ ² ¯ ¥² £¹Ê¯© ¥ ¯ ¥­³¬Ã¯§ · · · Ï´ ´ ´¥© Ï´Ë Å

¥¯ m´ È Â£¹Ê¯Â¬n ¥´¡ ·Ê Ê ¹¯©m´ “Threshold detector” ­£´¤ ¸ © ¥ ¯ ¥­³¬ n¯£»§ ·ÊÅ nÅ ¥» ·Ê 4.5 ²Â §·Ê¤ ´ © ¥ ¯ ¥­³¬Ã¯§ · · ·Â É © ¥ ¥© ­´ · Â¥¶Ê£Â §·Ê¤ ·Ê£· ´¥ ³ ¬¶ Å ¹¯ ¦£1, if rn p 0 mˆ n ¦ ¤ ¦¦¥0, if rn 0

(4.86)

¬Ï´­¥³ n = {1, 2, …, 6} ´ ¥» ² ©m´© ¥ ¯ ¥­³¬Ã¯§ · · ·£·¬£¥¥ ² · ©m´© ¥ ¥© ­´

· Â¥¶Ê£Â §·Ê¤ £´ Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë (iteration) ¢´¤Å © ¥ ¯ ¥­³¬

ï§ · · ·Â ¶Ê£ ¸Ë ¯¤m´ Æ¥ É ´£Â£¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë ¸ ¥² ³ ­ ¸Ê É ² ©m´

¬£¥¥ ² ¯ © ¥ ¯ ¥­³¬Ã¯§ · · ·Â¥¶Ê£ ·Ê ² ·Ê (Å ·Ê ·Ë ²Â­É ©m´¬£¥¥ ² ¯ © ¥ ¯ ¥­³¬ ï§ · · ·Å ¥¯ ·Ê 3 ç² 5 £· m´Å §n ·¤ ³ ) n¯¬¥º ·Ë¬´£´¥ ¤¹ ¤³ Æ nÄ ¤ ´¥©´ ¥´¡Ã¬

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¥» ·Ê 4.17 ¬£¥¥ ² ¯ © ¥ ¯ ¥­³¬Ã¯§ · · · ´¥© Ï´Ë Å ¥¯ m´ È

m´ BER Å Ã m§²¥¯ ¯ ´¥© Ï´Ë m´ SNR m´ È ´£ ·Êì Å ¥» ·Ê 4.17 ¸Ê ©m´­§³ ´

´¥© Ï´Ë Å ¥¯ ·Ê 4 ¬£¥¥ ² ¯ © ¥ ¯ ¥­³¬Ã¯§ · · · ²Â¥¶Ê££· ·Ê ¸Ê ¥´ ´¥ q ·ËÂ¥·¤ ©m´ ¥²  ¶ ¹Ë n¯ ¶ §´ 20 (error floor)

Å ¬m© m¯Æ ·Ë ²Â ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · Ê·Å n£ ¥¶ q ´¥¶ ·Â É H Ã

£·©³ ³ ¥Ã§²Ã Æ£m£·©³ ³ ¥ Ä ¤Å ·Ê ·Ë ² Ï´ ´¥Ã nÆ Â£ ¥¶ q H Å ¬£ ´¥ (4.74) Å­n£·©³ ³ ¥

1 ¡ ¡0 ¡ ¡0 ¡ ¡0 ¡ ¡0 H ¡ ¡0 ¡ ¡ ¡0 ¡ ¡0 ¡ ¢¡ 0

0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1ˆ 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1ˆ 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0

0 0¯° 1ˆ 0°° 0 1°° 0 0°° 1 0°° 0 1°° ° 1ˆ 1° ° 0 0° ° 0 0±°

(4.87)

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Ï´ © 2 ©³ ³ ¥ ³ ·Ë

4

บทที่ 20

©¶ ·­ ¸Ê Å ´¥Ã n ³ ­´ ¹Ë n¯ ¶ §´ ¹¯ ´¥­´Â£ ¥¶ q ´¥¶ · H ·Ê£·¬£¥¥ ²£´ ¸Ë £´Å n ´ Å ¥²

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149

¥» ·Ê 4.18  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · Ê·Å n£ ¥¶ q H à £·©³ ³ ¥Ã§²Ã Æ£m£·©³ ³ ¥

£¹Ê¯ 1 ç² 1̂ ì ϴí m ·Ê£ ¥¶ q H  ¶ ©³ ³ ¥ ¥» ·Ê 4.18  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥­³¬

ï§ · · · ÊÅ· n£ ¥¶ q H à £·©³ ³ ¥Ã§²Ã Æ£m£·©³ ³ ¥ Ä ¤ ·Ê¬n ¸ ¹¯Â£ ¥¶ q H à ƣm£· ©³ ³ ¥ ç²Â¬n ² ¹¯Â£ ¥¶ q H à £·©³ ³ ¥ ¸Ê Â­É Æ n ³  ©m´¥­³¬Ã¯§ · · · ÊÅ· n£ ¥¶ q H

à ƣm£·©³ ³ ¥Å­n¬£¥¥ ² · ©m´¥­³¬Ã¯§ · · · Ê·Å n£ ¥¶ q H à £·©³ ³ ¥Å º ¥¯ ¯ ´¥

© Ï´Ë ³ ³ Ë ¥­³¬Ã¯§ · · · Ê · ·Æ£m ©¥Å n£ ¥¶ q H ·Ê£·©³ ³ ¥ [4, 5]

4.6.2 m¯ ¬³ ´ à © Ï´Ë Å ¬m© ·Ë ²Ã¬ ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 2.4 ¸Ê Â É Â ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë Ä ¤¯´ª³¤ ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ © ¥ ¥© ­´Ã ¯¡ q粩 ¥

¯ ¥­³¬Ã¯§ · · · ´£ ·Êì Å ¥» ·Ê 4.19 Ä ¤ ·Ê¥­³¬Ã¯§ · · · ·ÊÅ n ¹¯¥­³¬Ã¯§ · · ·Ã à ©

§Ï´ ³ ·Ê » ¥³ ¥º (MAC) ·Ê£·Â£ ¥¶ q ´¥¶ ·Â É H ´£¬£ ´¥ (4.71) Ä ¤Å n ´¥´£¶Â ¯¥q j = 4,

k = 40 ç² p = 103 ³Ê ¹¯¥­³¬Ã¯§ · · · ·Ë ²Â n´¥­³¬ n¯£»§¯¶ º ¥³ Ë §² (40 – 3)u103 = 3708 ¶ ç²Å­n Ï´¥­³¬ ´ 40u103 = 4120 ¶ (£· ¶ ´¥¶ · Ï´ © 4120 – 3708 = 412 ¶ ) ¸Ê ²Æ n©m´¥­³¬Ã¯§ · · · ·Ë£·¯³ ¥´¥­³¬ R = K/N = 0.9

´ ¥» ·Ê 4.19 m´©¬´¥ mn {0, 1} ·Ê£· ´ ©§´ ¯ ¶  m´ ³ T ´ 3708 ¶

» ¬m  n´© ¥Â n´¥­³¬Ã¯§ · · ·Ã§²© ¥Â n´ m» Ï´Å­nÆ nÂ É §Ï´ ³ n¯£»§ sn {r1} ´ 4120 ¶ ´ ³ Ë §Ï´ ³ n¯£»§ sn ² » ¬m m´ m¯ ¬³ ´ ·Ê£·¡³ q ³ m´¤Ä¯ H D i 0 hi D i 2

1 2D D 2 Ä ¤ ·Ê D ¹¯ ³© Ï´Â ¶ ´¥­ m © ©§´­ ¸Ê ­ m ©¤ Ï´Å­nÆ nÂ É ¬³ ´ ¯m´ §³

150

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wn mn

sn

H D

zn

mˆ n

rn

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(4.88)

rn sn hn wn

£¹Ê¯ hn ¹¯ m´¬³£ ¥²¬¶ ¶ Î ³© ·Ê n ¯ m¯ ¬³ ´ , ¹¯ ³© Ï´Â ¶ ´¥ ¯ Ä©§» ³ , ç² wn ¹¯

¬³ ´ ¥ ©  ´¬q¬· ´©Ã © ·Ê£· m´Â §·Ê¤Â m´ ³ ª» ¤qç² m´ ©´£Ã ¥ ¥©  m´ ³ N0/(2T)

´ ³ Ë §Ï´ ³ n¯£»§ rn É ² » Ï´ ´¥ ¯ ¥­³¬Ã © Ï´Ë ¸Ê £· ´¥Ã§  §·Ê¤ m´©¬´¥Ã ¯¡ q

¥²­©m´ “SISO equalizer” ( ³Ê ¹¯© ¥ ¥© ­´Ã ¯¡ qà m´ È ´£ ·Ê¯ ¶ ´¤Å ·Ê 3)

粩 ¥ ¯ ¥­³¬Ã¯§ · · · Ê·£· ´¥© Ï´Ë ¢´¤Å ¯³§ ¯¥¶ ¸£ MP Ï´ © 3 ¥¯ ¯ ´ ·Ë m´ SNR

·ÊÅ n¬Ï´­¥³ ¥² ·Ê »  n´¥­³¬ (coded system) ² ¶ ¤´£Ä ¤

h Ec i i 10 log10 N0 N 0R

2

¬­ ­­ ­­ ®­

(4.89)

£¹Ê¯ Ec = 1 ¹¯ §³ ´ ¯ ¶ n¯£»§ ·Ê »  n´¥­³¬­ ¸Ê ¶ ç² m´ BER ¯ à m§² SNR Æ n£´

´ ´¥¬m n¯£»§¯¶ º ­§´¤È §É¯ ( §É¯ §² 3708 ¶ )  n´Æ Å ¥² ¥² ³ Ê © ¥ ¯ ¥­³¬ ï§ · · · ¥© n¯ ¶ §´ ·Ê ¶ ¸Ë Æ n¥©£Æ£m n¯¤ ©m´ 1000 ¶ ­§³ ´ ¥² Ï´ ´ à © Ï´Ë m´ Æ Å ¥¯ ·Ê 5

·Ê Ï´ ´ ¥m©£ ³ © ¥ ¯ ¥­³¬Ã¯§ · · · Å ¥» ¯ m´ BER 粯³ ¥´ n¯ ¶ §´ ¯   ¯¥q21

(SER: sector-error rate) Ä ¤ ·Ê “0.5 iteration” ­£´¤ ¸ ¬£¥¥ ² ¯ ¥² ·Ê n´ ´¯¯ ¯ © ¥ ¥© ­´Ã ¯¡ qÅ ¥¯ Ã¥ ( m¯ ¬m §§³ qÆ ¤³ © ¥ ¯ ¥­³¬Ã¯§ · · ·) ´ ¥» ² ©m´

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¥» ·Ê 4.20 ç²¥» ·Ê 4.21  ¥·¤  ·¤ ¬£¥¥ ² ¯ © ¥ ¥© ­´ BCJR ç² SOVA

¥² £·¬£¥¥ ² · ¸Ë £¹Ê¯ Ï´ © ¥¯ ¯ ´¥ ¯ ¥­³¬Ã © Ï´Ë Â ¶Ê£ ¸ Ë Ã§²¥² ·ÊÅ n© ¥ ¥© ­´ BCJR £·¬£¥¥ ² · ©m´¥² ·ÊÅ n© ¥ ¥© ­´ SOVA ³ Ë ·ËÂ É Â ¥´²©m´¯³§ ¯¥¶ ¸£ BCJR ²Å­n

m´ LLR ¶ n¯£»§ ·Ê£· º ¢´ £´ ©m´¯³§ ¯¥¶ ¸£ SOVA ( ´£ ·Ê¯ ¶ ´¤Å ·Ê 3) ¯ ´ ·Ë

4

บทที่ 21

¯³ ¥´ n¯ ¶ §´ ¯   ¯¥q (SER) ­£´¤ ¸ ­ ¸Ê   ¯¥q ² ¹¯©m´£· n¯ ¶ §´  ¶ ¸Ë É m¯Â£¹Ê¯£· ¶ ¶ §´  ¶ ¸Ë ¢´¤Å   ¯¥q ³Ë £´ ©m´­¥¹¯Â m´ ³ 1 ¶

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151

¥» ·Ê 4.20  ¥·¤  ·¤ ¬£¥¥ ² ¯ © ¥ ¥© ­´ BCJR ç² SOVA Å ¥» ¯ m´ BER

¥» ·Ê 4.21  ¥·¤  ·¤ ¬£¥¥ ² ¯ © ¥ ¥© ­´ BCJR ç² SOVA Å ¥» ¯ m´ SER

¬n ¥´¡ “0.5 iteration” ¤³ ¬´£´¥ Å nà ¬£¥¥ ² ¯ ¥² ·ÊÆ£m »  n´¥­³¬ (uncoded system) Æ n n©¤ ¸Ê Ï´Å­nÂ­É ©m´¥² ·Ê »  n´¥­³¬ ²£·¬£¥¥ ² · ©m´¥² ·ÊÆ£m »  n´¥­³¬Â¬£¯ ³ ³ Ë ¸ ¬¥º Æ n©m´¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë ¬´£´¥ m©¤Â ¶Ê£¬£¥¥ ² ¯ ¥² Å­n ·¤Ê ¶ ¸Ë Æ n

¥» ·Ê 4.22  ¥·¤  ·¤ ¬£¥¥ ² ¯ © ¥ ¥© ­´ BCJR ç² SOVA ´¥© Ï´Ë Å

¥¯ m´ È ¸Ê ì Å­nÂ­É ©m´¥² ·ÊÅ n© ¥ ¥© ­´ BCJR £·¬£¥¥ ² · ©m´¥² ·ÊÅ n© ¥ ¥© ­´

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¥» ·Ê 4.22 ¬£¥¥ ² ¯ © ¥ ¯ ¥­³¬Ã¯§ · · · ´¥© Ï´Ë Å ¥¯ m´ È

SOVA Å º ¥¯ ¯ ´¥© Ï´Ë Å Ï´ ¯  ·¤© ³ £¹Ê¯ Ï´ © ¥¯ ¯ ´¥ ¯ ¥­³¬Ã © Ï´Ë Â ¶Ê£ ¸Ë É ² Ï´Å­n¥² £·¬£¥¥ ² ·Ê · ¸Ë ¬£¯

4.7 ¬¥º n´¤ ¥­³¬Ã¯§ · · · (LDPC: low-density parity-check) ¹¯¥­³¬Ã nÆ n¯ ¶ §´ ·Ê ·¬º Å ³ º ³ [2, 5, 8] ¸Ê Æ n£· ´¥ Ï ´Å n ´ ¥¶ Å ­§´¤È ´ ¥²¤º q ¥©£ ³ Ë Å °´¥q ¶¬ qÆ ¥¡q n©¤

 ¹Ê ¯ ´ ¥­³¬Ã¯§ · · ·Â É ¥­³¬ §É¯  ¶ ¬n ¥²Â¢ ­ ¸Ê ³ ³ Ë Å ·Ë ¸ Â¥¶Ê£ n n©¤

´¥¯ ¶ ´¤ ³ Ë ¯ ´¥Â n´¥­³¬Ã§² ¯ ¥­³¬ ¯ ¥­³¬ §É¯  ¶ ¬n ¥©£ ³ Ë ©´£­£´¤ ¯ £ ¥¶ q

¯ ´¥Â n´¥­³¬Ã§² ¯ ¥­³¬Ã¯§ · · · Ä ¤ ´ ´¥ §¯ ©m´¬£¥¥ ² ¯ ¥­³¬Ã¯§ · · · ² ¸Ë ¯¤m» ³ £ ¥¶ q ´¥¶ ·Â É ·ÊÅ n ¸Ê Å ­³© n¯ ·Ê 4.5 ÉÆ nì ³©¯¤m´ ´¥¬¥n´ £ ¥¶ q ´¥¶ ·Â É Ã

m´ È Ä ¤Â£ ¥¶ q ´¥¶ ·Â É ·Ê · ² n¯ Æ£m©³ ³ ¥ ·Ê£· ©´£¤´©Â m´ ³ 4 ç² ©¥£· ´¥ ¥² ´¤ ³© ¯

รหัสแอลดีพีซี

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§ 1 (¢´¤Å £ ¥¶ q ´¥¶ ·Â É ) Â É Ã ¬mº£Å­n£´ ·Ê¬º  ¹Ê¯Å­n¥­³¬Ã¯§ · · ·£·¬£¥¥ ²¬» ¬º [17] ¯ ´ ·Ë¤³ Æ nì ³©¯¤m´ ´¥ Ï ´¥­³¬Ã¯§ · · ·Æ Å nÅ ¥² ´¥ ¯ ¥­³¬Ã © Ï´Ë ¯

m¯ ¬³ ´ °´¥q ¶¬ qÆ ¥¡q ¸Ê § ´¥ §¯ ì Å­nÂ­É ©m´ ´¥ ¯ ¥­³¬Ã © Ï´Ë ¬´£´¥ m©¤

 ¶Ê£¬£¥¥ ² ¯ ¥² Å­n ·¤Ê¶ ¸Ë Æ n Ä ¤¥² £·¬£¥¥ ² · ¸Ë £¹Ê¯ Ï´ © ¥¯ ¯ ´¥ ¯ ¥­³¬

4

บทที่

à © Ï´Ë Â ¶Ê£ ¸Ë

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153

4.8 Ã ¸ ­³ n´¤ 1.

¯ ¶ ´¤ ©´£­£´¤ ¯ m´©¬´¥¯¶ ¥¶ ¶ ç² m´©¬´¥Â¯ q ¥¶ ¶

2.

¯ ¶ ´¤­§³ ´¥ ¯ ¥­³¬Ã ¶ Ä ¥£Å ­³© n¯ 4.1.5 ¥n¯£ ³ Ë ¤ ³©¯¤m´ ´¥ Ï´ ©

3.

4. 5. 6.

1 0 1 1 0¯ ° ­´Â£ ¥¶ q ´¥¶ ·Â É Ï´­ Å­n¥­³¬Ã¯§ · · ·£·Â£ ¥¶ q ³© Ï´Â ¶ G ¡ ¡ 0 1 1 0 1° ¢ ± H 粩´ ¥´¡Ã  ¯¥q ¯ £ ¥¶ q H  n´¥­³¬ n¯£»§ m = [1101] ç² m = [1011] Ä ¤Å n£ ¥¶ q ´¥¶ ·Â É H ¸Ê ¬¯ §n¯

³ £ ¥¶ q ³© Ï´Â ¶ G Å ¬£ ´¥ (4.25)

´ £ ¥¶ q ´¥¶ ·Â É H Å ¬£ ´¥ (4.74)  n´¥­³¬ n¯£»§ m = [101011] ç² m =

[111010]

´ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 4.5 n´ Ï´­ Å­n ¶ n¯£»§¯¶ º mn = {1, 1, 0}, ¥­³¬

ï§ · · · Ê·Å n£·Â£ ¥¶ q ³© Ï´Â ¶ G ´£¬£ ´¥ (4.4), ¬³ ´ ¥ © wn = {0.2, 0.3,

–0.1, –0.2, 0.5, –0.4} ç²£· ©´£Ã ¥ ¥©  m´ ³ V2 = 0.5 ­´ m´ LLR à ¯²Ä ¬ Ë ¬º ´¥© Ï´Ë ¥¯ ·Ê 3  ¯¥¶¯¯¥¶ \M1 , M2 , M3 , M4 , M5 , M6 ^ £¹Ê¯¬¶

7.

´ à ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 4.19 n´ Ï´­ Å­n§Ï´ ³ n¯£»§¯¶ º mn = {1, 1}, ¥­³¬

ï§ · · · ÊÅ· n£·Â£ ¥¶ q ³© Ï´Â ¶

1 0 1 1 0¯ °, G ¡ ¡ 0 1 1 0 1° ¢ ± m¯ ¬³ ´ H(D) = 1 + D, ¬³ ´ ¥ © wn = {0.3, –0.2, 0.1, 0.2, –0.4, –0.5}

ç²£· ©´£Ã ¥ ¥©  m´ ³ V2 = 0.5 ¯ ¥­³¬§Ï´ ³ n¯£»§ rn Ä ¤Å n¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Â£¹Ê¯¬¶ Ë ¬º ´¥© Ï´Ë ¥¯ ·Ê 3 Ä ¤ ·Ê© ¥ ¯ ¥­³¬Ã¯§ · · · ·ÊÅ n£· ´¥© Ï´Ë ¢´¤Å ¯³§ ¯¥¶ ¸£ MP Ï´ © 3 ¥¯ 粯· ©¯Æ§Â ¯¥qà SISO ·ÊÅ n¬¥n´ £´ ´

7.1) ¯³§ ¯¥¶ ¸£ BCJR 7.2) ¯³§ ¯¥¶ ¸£ Max-Log-MAP 7.3) ¯³§ ¯¥¶ ¸£ Log-MAP 7.4) ¯³§ ¯¥¶ ¸£ SOVA

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·Ê 5 ´¥ ¥²¤º qÅ n ´ ´¥ ¯ ¥­³¬Ã © Ï´Ë Å ·Ë ²Ã¬ ³©¯¤m´ ´¥ Ï ´Â ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë £´ ¥²¤º qÅ nÅ ´¥Ã n ³ ­´Â¥¹Ê¯

´¥Â n´ ³ ­©² (synchronization) © ¥ ³ ³©¯¤m´ ³ ¯ ¬³ ´ ï ²§É¯ ·ÊÆ n¥³ ç²Â¥¹Ê¯ ´¥Ã nÆ ©´£ ¥º ¥²Â ¶ ©´£¥n¯ (TA: thermal asperity) ·Ê Å ¥² ´¥ ¥²£©§ §¬³ ´

¯ °´¥q ¶¬ qÆ ¥¡q ¸Ê £· § m©¤ Ï´Å­n°´¥q ¶¬ qÆ ¥¡q £·¬£¥¥ ²Ã§² ©´£ m ´Â ¹Ê¯ ¹¯Â ¶Ê£ ¸ Ë

5.1 Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë ´ ·Ê §m´©Å ·Ê 2 ¯ [10] Æ ££¶Ê ¥¶ ³¡Â©¯¥· (timing recovery) Ï´­ n ´ ·ÊÅ ´¥Â n´ ³ ­©² ·¬º ¯¯ £´ m¯ ¬m n¯£»§Ã £Â ¶ §Â­§m´ ³ Ë Æ ¥²£©§ §Å ³ Ë ¯ m¯Æ  m ¬m Æ ¤³ ¯· ©¯

Ƨ ¯¥q 粩 ¥ ¯ ¥­³¬ Â É n ³ ³ Ë Æ ££¶Ê ¥¶ ³¡Â©¯¥· ¹¯©m´Â É ¯ q ¥² ¯ ·Ê£· ©´£¬Ï´ ³

£´ ¯¤m´ ­ ¸Ê Å ¥² ¬¹Ê¯¬´¥ ¶ ¶ ³§  ¥´² n´© ¥ ³ ³©¯¤m´ Ï´ ´ Æ£m · É ² Ï´Å­n n¯£»§Ã £Â ¶ §

·ÊÆ nÆ£m£· º ¢´ ç²Â£¹Ê¯¬m n¯£»§Ã £Â ¶ §Â­§m´ ·ËÆ ¤³ ¯· ©¯Æ§Â ¯¥q粩 ¥ ¯ ¥­³¬ É ² Ï´Å­n

§§³ q ÊÆ· n£· n¯ ¶ §´ Ï´ © £´

Ä ¤ ³Ê©Æ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ (conventional timing recovery) ¸Ê ¯¤m»

¹Ë ´ ¯ © ¥Â¡¬§É¯ §» (PLL: phase-locked loop) [11] ¬´£´¥ Ï´ ´ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ £¹Ê¯ Ï´ ´ Å ¬¢´©² ·Ê m´¯³ ¥´¬m© Ï´§³ ¯ ¬³ ´ m¯ Ï´§³ ¯ ¬³ ´ ¥ © (SNR) ¬»

¯¤m´ Æ¥ É ´£Â É ·Ê ¥´ ³ ©m´¥­³¬Ã nÆ n¯ ¶ §´ (ECC)  m ¥­³¬Â ¯¥qÄ [3] ­¥¹¯¥­³¬Ã¯§ · · · (LDPC) [17] Â É n £·¯³ ¥´ ¤´¤ ¯ ´¥Â n´¥­³¬ (coding gain) ¬» ¸ m©¤Å­n¥²

¬´£´¥ Ï´ ´ ·Ê m´ SNR ÏÊ´È Æ n¯¤m´ m ´Â ¹Ê¯ ¹¯ ³ ³ Ë ¥­³¬ ECC ¸ Æ n » Ï ´£´Å nÅ ­§´¤ ´

¥²¤º q  m Ä ¥ª³ q §¹Ê¯ ·Ê, ¥² ¬¹Ê¯¬´¥ m´ ´©Â ·¤£ ç²°´¥q ¶¬ qÆ ¥¡q Â É n ¸Ê §

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

รหัสแอลดี การประยุ พีซี กตใชงานการถอดรหัสแบบวนซ้ำ

© ¥ ³ ³©¯¤m´ (sampler) ³ ¬³ ´ ï ²§É¯ ·ÊÆ n¥³  ¹Ê¯Å­nÆ n n¯£»§Ã £Â ¶ § (sample) ·Ê

54

บทที่ บทที่

155

§¯¤Æ n Ê· ´££´ ´ ´¥ ³ ´ ·Ë É ¹¯ ¥² Æ ££¶Ê ¥¶ ³¡Â©¯¥· ² n¯ Ï´ ´ ¥² ³ m´ SNR ·Ê n ¯¤ ©m´ ·Ê ¤Å n ´ Å ¯ ·  ¥´² ² ³ Ë ¥² Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ ·Ê Ï´ ´  É

¯¶¬¥² ´ ¥­³¬ ECC ² Ï´ ´ Æ nÆ£m · £¹Ê¯ Ï´ ´ ·Ê ´m SNR ÏÊ´ ¯¤m´ Æ¥ É ´£Å ³ º ³ ³ ©¶ ³¤Æ n

£· ´¥ Ï ´Â¬ ¯¥² Æ ££¶Ê ¥¶ ³¡Â©¯¥· Ê·¬´£´¥ Ï´ ´ ·Ê m´ SNR ÏÊ´È Æ n¯¤m´ £· ¥²¬¶ ¶¢´ ­§´¤ ¥» à [34–36, 56–59]

Å ­³© n¯ ·Ë ²¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë ·Ê¯¤m» ¹Ë ´ ¯

PSP (per-survivor processing) [60] ¸Ê Â É Â ¶ Å ´¥ ¥²£´ m´¥m©£ ³ ¥²­©m´ §Ï´ ³ n¯£»§

·Ê n¯ ´¥ ¯ ¥­³¬Ã§² ´¥´£¶Â ¯¥q Ê·Æ£m ¥´ m´ Ä ¤Â¥¶Ê£ n ´ ´¥¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯

Æ ££¶Ê ¥¶ ³¡Â©¯¥· Ê·¯¤m» ¹Ë ´ ¯ PSP ¬Ï´­¥³ m¯ ¬³ ´ à § ¯ ¬ ¯ ´ ¬m© (PR:

partial response) [61] ·ÊÆ£m »  n´¥­³¬ (uncoded PR channel) ¸Ê Å ·Ê ·Ë ²Â¥·¤ ©m´ “ ¯Â ¯¥q

Ʃ©¯¥qÆ ££¶Ê ¥¶ ³¡Â©¯¥· (PS-TR: per-survivor timing recovery)” [62] ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã§²¯· ©¯Æ§Â ³ à ©¥ ²Â É ¬» ¬º (ML: maximum likelihood) Ä ¤¬´£´¥ ¬¥n´ ¸Ë Æ n ´ ´¥ Ï ´© ¥ PLL Ŭm n´Æ Å Ã m§²Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» (survivor path) ¢´¤Å ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [13] Ä ¤ ´ ´¥ §¯ ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR £·

¬£¥¥ ² · ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ £¹Ê¯ Ï´ ´ Å ¥² ·Ê£· ¶  ¯¥q ´ ©§´22 (timing

jitter) ¬» ­¥¹¯ Ï´ ´ Å ¥² ·Ê n¯ ´¥Å­n£· ´¥§m»Â n´Â¥É© (fast convergence) ¯ ´ ·Ë n¯ · ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR É ¹¯¬´£´¥ Ï´ ´ à ©§´ ¥¶ (real time) Æ n

à © ¶ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ¬´£´¥ Ï ´£´Å n¥m©£ ³ © ¥ ¯ ¥­³¬ ECC

 ¹Ê¯ ³ ´Â É “ ¯Â ¯¥qƩ©¯¥qÆ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë (PS-ITR: per-survivor iterative

timing recovery)” [63, 64] ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥· ¯· ©¯Æ§Â ³ à ML ç² ´¥ ¯ ¥­³¬ ECC Ä ¤Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ²£·¬£¥¥ ² · ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥· à PS-TR £´ à m£· ©´£ ³ n¯ ¬» ç²Æ£m¬´£´¥ Ï´ ´ à ©§´ ¥¶ Æ n ( n¯ ¥²£©§ §

Ã Â É §mº£ (batch processing)  m´ ³ Ë ) Å ´ ¶ ³ ¶Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¬¥n´ ¸Ë

Æ nÄ ¤ ´¥Å¬m ¥² © ´¥Æ ££¶Ê ¥¶ ³¡Â©¯¥·Â n´Æ Å ¯³§ ¯¥¶ ¸£ BCJR [18] Ä ¤¯´ª³¤Â ¶ PSP

Ï´Å­nÆ nÂ É “¯· ©¯Æ§Â ¯¥q BCJR à  ¯Â ¯¥qƩ©¯¥q (per-survivor BCJR equalizer)” ­¥¹¯

Â¥·¤ ©m´ “PSP-BCJR” [63] ¸Ê Ï´­ n ´ ·Êç  §·Ê¤ m´©¬´¥Ã ¯¡ q ³ © ¥ ¯ ¥­³¬ ECC  m  ·¤© ³ ­§³ ´¥ ¯ ¯· ©¯Æ§Â ³ à  ¯¥qÄ [21] ´£ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 2.4 Ä ¤ ´

´¥ §¯ ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR £·¬£¥¥ ² ·£´ £¹Ê¯Â ·¤ ³ Æ ££¶Ê ¥¶ ³¡Â©¯¥· à © Ï´Ë Ã ¯¹Ê È [35]

22

Æ ££¶Ê ¶  ¯¥q ¹¯ ¬³ ´ ¥ © ¢´¤Å © ¥ ³ ³©¯¤m´ ¸Ê £· § Ï´Å­n ³ ­©² ¯ ©§´ ·Ê ² Ï´ ´¥ ³ ³©¯¤m´ ¬³ ´ à m§² ¥³ Ë Â ¶ ©´£ §´  §¹Ê¯ Æ ´ ϴí m ·Ê n¯ ´¥

156

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

Per-survivor timing recovery

n t

ak \o1^

H D

rk

q t

p t

Uk

LPF

yk y kT Uˆk

y t

tk kT Uˆk

z d

aˆk

Viterbi detector

aˆk

Symbol detector

rˆk d Loop Filter

VCO

Fˆk

TED

¥» ·Ê 5.1 à ϴ§¯ m¯ ¬³ ´ ¯º £ ¶Ã§²Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ

5.1.1 à ϴ§¯ m¯ ¬³ ´ ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ ¯º £ ¶Å ¥» ·Ê 5.1 §Ï´ ³ n¯£»§¯¶ º ak {r1} ¸Ê £· ´ ©§´ ¯ ¶ T » ¬m m´ Æ ¤³ m¯ ¬³ ´ H(D) =

O

h D k £¹Ê¯ hk ¹¯ m´¬³£ ¥²¬¶ ¶ Î ³© ·Ê k

k 0 k

¯ m¯ ¬³ ´ , D ¹¯ ³© Ï´Â ¶ ´¥­ m © ©§´­ ¸Ê ­ m ©¤ (unit delay operator), ç² Q ¹¯ ­ m ©¤ ©´£ Ï´ ¯ m¯ ¬³ ´ ³ ³ Ë ¬³ ´ ¯m´ §³ ¬´£´¥  ·¤ Â É ¬£ ´¥Æ n ¹¯ p t

r q t kT U n t

k

(5.1)

k

Ä ¤ ·Ê rk = ak hk

a i

h ¹¯ n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ ·Ê ¥´ª ´ ¬³ ´ ¥ © ,

k i i

q(t) = sin(St/T) / (St/T) ¹¯¡³ q ³ ¶ q (sinc function) [4], Wk ¹¯¯¯¡Â ´ ©§´ ·ÊÆ£m ¥´ m´ (unknown timing offset) ³© ·Ê k, ç² n(t) ¹¯¬³ ´ ¥ ©  ´¬q¬· ´©Ã © (AWGN)

·Ê£· ©´£­ ´Ã m ¬Â ¥³£ Ï´§³ à ¬¯ n´  m´ ³ N0/2 Å ­³© n¯ ·Ë ² Ï´§¯ ¯¯¡Â ´ ©§´

Wk Å­n£·§³ « ²Â É “ ´¥Â ¶ à ¬mº£23 (random walk)” ¸Ê ¶ ¤´£Ä ¤ [66] Uk 1 Uk wk

(5.2)

£¹Ê¯ wk ¹¯ ³©Ã ¥¬mº£Â ´¬q ·¤ à i.i.d. (independent and identically distributed) ·Ê£· m´Â §·Ê¤  m´ ³ ª» ¤qç²£· m´ ©´£Ã ¥ ¥©  m´ ³ Tw2 ­¥¹¯Â ·¤ Ã Æ n n©¤ wk N 0, Tw2 Ä ¤ m´ Tw

²Â É ³© Ï´­ ¥² ³ ©´£¥º Ã¥ ¯ Æ ££¶Ê ¶  ¯¥q 23

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

k

5

บทที่

à ϴ§¯ ´¥Â ¶ à ¬mº£Æ n » Ï ´Å n ¥´²Â É Ã Ï´§¯ ·Ê m´¤ 粬´£´¥ Å nà §³ « ² ¯ m¯ ¬³ ´ m´ È Æ n m´¤ Ä ¤ ´¥Â §·Ê¤ à § m´ ´¥´£¶Â ¯¥q Tw  ·¤ ³©Â ·¤©Â m´ ³ Ë 2

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157

© ¥¢´ ¥³ ¬³ ´ ¯m´ §³ ² » ¬m m´ Æ ¤³ © ¥ ¥¯ m´ ÏÊ´ (LPF) ·Ê£· §

¯ ¬ ¯ ¯¶£ ³§¬q m´ ³ q(t)/T ³Ê ¹¯£· ©´£ ·Ê ³ (cut-off frequency)  m´ ³ 1/(2T)  ¹Ê¯

Ï´ ³ ¬³ ´ ¥ © ·Ê¯¤m» ¯ à ©´£ ·Ê ´ ³ Ë ² Ï´ ´¥ ³ ³©¯¤m´ ¬³ ´ ·Ê©§´ kT Uˆk  ¹Ê¯ Ï´Å­nÆ nÂ É n¯£»§Ã £Â ¶ § yk y kT Uˆk

i riq kT Uˆk iT Ui nk

(5.3)

£¹Ê¯ Uˆk ¹¯ m´ ¥²£´ ¯ Wk ­¥¹¯ ·ÊÂ¥·¤ ©m´ “¯¯¡Â ´ ¡¬ (phase offset)” ³© ·Ê k ¯ ´¥ ³ ³©¯¤m´ , nk N 0, Tn2 ¹¯¬³ ´ ¥ © AWGN, ç² Tn2 N 0 / 2T

5.1.2 Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ Å ´ ¶ ³ ¶Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ ²¯¤m» ¹Ë ´ ¯ © ¥Â¡¬§É¯ §» (PLL) ¸Ê ¥² ¯ n©¤© ¥ ¥© ­´ n¯ ¶ §´ ´ ©§´ (TED: timing error detector), © ¥ ¥¯ §»

(loop filter), 粩 ¥ VCO (voltage-controlled oscillator) ´£ ·Êì Å ¥» ·Ê 5.1 Ä ¤© ¥ TED ² Ï´­ n ´ ·Ê Ï´ © ­´ m´ ¥²£´ ¯ n¯ ¶ §´ ´ ©§´ Fk Uk Uˆk ¸Ê É ¹¯ m´ ©´£

Æ£m ¥ ³ (misalignment) ¥²­©m´ ¡¬ ¯ ¬³ ´ ¯m´ §³ ·ÊÆ n¥³ ³ ¡¬ ¯ ¬³ ´ ´®¶ ´ ¯ © ¥ PLL Å ´ ¶ ³ ¶© ¥ TED £·­§´¤ ¥²Â¢ [11] ¸Ê Ä ¤ ³Ê©Æ ¬£¥¥ ² ¯ Æ ££¶Ê

¥¶ ³¡Â©¯¥· ² ¸Ë ¯¤m» ³ º ¢´ ¯ © ¥ TED Å ·Ê ·Ë ² ¶ ´¥ ´Â ´²© ¥ TED à Mueller

and Müller ­¥¹¯Â¥·¤ ©m´ M&M TED [67] ¸Ê Â É ·Ê ¶¤£Å n ´ Å ­§´¤È ´ ¥²¤º q Ä ¤ ² Ï´ © m´ ¥²£´ ¯ n¯ ¶ §´ ´ ©§´ ´

Fˆk KT \yk rˆk 1 yk 1rˆk ^

(5.4)

Ä ¤ ·Ê rˆk ¹¯ m´ ¥²£´ ¯ rk ¸Ê Æ n£´ ´ © ¥ ¥© ­´¬³ §³ « q (symbol detector), KT ¹¯ m´ ³© ·Ê » Å n ¹Ê¯ Ï´Å­n£³Ê Å Æ n©m´ E < Fˆk | F > F £¹Ê¯ SNR £· m´¬» ­¥¹¯¯´ §m´©Æ n©m´ m´ KT m©¤ Ï´Å­n ©´£ ³ ¯ ¬n Ä n ¥» ³©Â¯¬ (S-curve) [11] £· m´Â m´ ³ ­ ¸Ê º Ï´Â ¶ , ç² E[.] ¹¯ ³© Ï´Â ¶ ´¥ m´ ´ ­£´¤ (expectation operator) ´ ¬£ ´¥ (5.4) ²Â­É Æ n©m´¬£¥¥ ²

¯ © ¥ TED ¸Ë ¯¤m» ³ m´ ³ ¬¶ Å rˆk ³ ³ Ë ¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥· ²Â É ¡³ q ³ ¯ ©´£ m ´Â ¹Ê¯ ¹¯ ¯ m´ ³ ¬¶ Šç² SNR ·ÊÅ n ¸ Â É Â­ º §©m´ Ï´Æ£© ¥ ¥© ­´¬³ §³ « q Ê·Å n

Å Æ ££¶Ê ¥¶ ³¡Â©¯¥· ¹¯© ¥ ¥© ­´©·Â ¯¥q ¶ [13] ·Ê£· ¥¶£´ ´¥­ m © ©§´¬Ï´­¥³ ´¥ ³ ¬¶ Å

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(decision delay)  m´ ³ dT ­ m ©¤ (£¹Ê¯ d ¹¯Â§ Ï´ ©  ɣ © ·Ê£· m´ n ¯¤  m d = 4) à ´¥Å n© ¥ ¥© ­´ · Â¥¶Ê£Â §·Ê¤ à ­§´¤¥² ³ (multi-level threshold detector) [32]

´ ³ Ë m´ ¥²£´ ¯ n¯ ¶ §´ ´ ©§´ Fˆk ² » ¬m m´ Æ ¤³ © ¥ ¥¯ §»  ¹Ê¯ Ï´ ³

¬³ ´ ¥ © ·Êà ¯¤m»Å ¬³ ´ n¯ ¶ §´ ´ ©§´ 粯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ (sampling phase offset) ³© ³ Æ Uˆk 1 É ² » ¥³ m´ n©¤© ¥ PLL ¯³ ³ ·Ê¬¯ (2nd-order PLL) ´£ ©´£¬³£ ³ q ³ ·Ë [11]

Rˆk 1 Rˆk LFˆk

(5.5)

Uˆk 1 Uˆk YFˆk Rˆk 1

(5.6)

£¹Ê¯ Rˆk ¹¯ m´ ¥²£´ ¯ n¯ ¶ §´ ´ ©´£ ·Ê (frequency error) [32], ç² Y ç² L ¹¯ ´¥´£¶Â ¯¥q ¯ © ¥ PLL [11] ¸Ê Â É ³© Ï´­ à q©¶ q ¯ §» (loop bandwidth) ç²

¯³ ¥´ ´¥§m»Â n´ (convergence rate) §m´© ¹¯ n´ ´¥´£¶Â ¯¥q ¯ © ¥ PLL £· m´£´ à q©¶ q

¯ §» É ² ©n´ ¸Ê £· § Ï´Å­n¯³ ¥´ ´¥§m»Â n´Â¥É© ¸Ë à m¬³ ´ ¥ © ·Ê n´£´Å © ¥ PLL É ² £·£´  m ³ ¬Ï´­¥³ Å ¥ · Ê·¥² £·Â ´² n¯ ¶ §´ ´ ¡¬Â m´ ³ Ë © ¥¢´ ¥³ ¯´ Å n ´

© ¥ PLL ¯³ ³ ·Ê­ ¸Ê (1st-order PLL) à © ¥ PLL ¯³ ³ ·Ê¬¯ ÉÆ n Ä ¤¯¯¡Â ´ ¡¬

(5.7)

Uˆk 1 Uˆk YFˆk

Å ´ ¶ ³ ¶Æ ££¶Ê ¥¶ ³¡Â©¯¥· ² Ï´ ´ Â É 2 ¢´©² (mode) ¹¯ 1) ¢´©² ´¥Æ n£´ (acquisition mode) ² Ï´ ´ Å ¯ Â¥¶Ê£ n ¯ ¥² © ´¥Â n´ ³ ­©² n©¤

©´£ m©¤Â­§¹¯ ¯ à n¯£»§ (data pattern) ·ÊÂ¥·¤ ©m´ “preamble” [32]  ¹Ê ¯ ´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·¥n»Ã m ¯ çn©©m´ preamble £·§³ « ²Â É ¯¤m´ Æ¥ ¸ Ï´Å­n¬´£´¥ ¥´ Æ n©m´ m´ rk

·Ê » n¯ ¹¯ m´¯²Æ¥  ¥´² ² ³ Ë Å m© ¢´©² ´¥Æ n£´ ·Ë 24 © ¥ PLL ²Å n m´ rˆk rk Å ´¥

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

¯ ´¥ ³ ³©¯¤m´ ³© ³ Æ ² » ¥³ m´ ´£ ©´£¬³£ ³ q m¯Æ ·Ë [11]

Ï´ © ­´ m´ Fˆk ´£¬£ ´¥ (5.4) ¸Ê Ï´Å­nÆ n §§³ q Ê· » n¯ ³ ³ Ë ¥² © ´¥Æ ££¶Ê ¥¶ ³¡Â©¯¥·Å m© ·Ë ¸ £· ©´£ m ´Â ¹Ê¯ ¹¯£´ Ä ¤ º ¥²¬ q­§³ ¯ ¢´©² ´¥Æ n£´ É ¹¯ ´¥­´

m´Â¥¶Ê£ n ¯ ¯¯¡Â ´ ¡¬Ã§²¯¯¡Â ´ ©´£ ·Ê (frequency offset) ·Êà ¯¤m»Å ¬³ ´

ï ²§É¯ ·Ê ² Ï´ ´¥ ³ ³©¯¤m´

24

5

บทที่

© ¥ ¥© ­´¬³ §³ « q Ê·Å nÅ Æ ££¶Ê ¥¶ ³¡Â©¯¥· ²Æ£m » Ï ´£´Å n ´ Å m© ¢´©² ´¥Æ n£´

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

159

2) ¢´©² ´¥ ¶ ´£ (tracking mode) ² Ï´ ´ m¯ ´ ¢´©² ´¥Æ n£´ Ä ¤Å ³ Ë ¯ ·Ë m´ rˆk ·ÊÅ nÅ ´¥ Ï´ © ­´ m´ Fˆk ´£¬£ ´¥ (5.4) ²Æ n£´ ´ © ¥ ¥© ­´¬³ §³ « q Ê·Å nÅ Æ ££¶Ê ¥¶ ³¡Â©¯¥· ( ¸Ê ¯´ £· º ¢´ Æ£m · £¹Ê¯Â ·¤ ³ ´¥Å n m´ rk ¥¶ ) ³ ³ Ë º ¥²¬ q­§³

¯ ¢´©² ´¥ ¶ ´£ É ¹¯ ´¥Ã nÆ Ã§² ¥³ ¥º m´Â¥¶Ê£ n ¯ ¯¯¡Â ´ ¡¬Ã§²¯¯¡Â

´ ©´£ ·Ê Ê­ · ´Æ n ´ ¢´©² ´¥Æ n£´

²Â­É Æ n©m´Å m© ¢´©² ´¥Æ n£´ © ¥ PLL ¥´ à m ¯ ©m´ preamble ¹¯¯²Æ¥ ³ ³ Ë © ¥ PLL

¸ ¬´£´¥ Å n m´ Y ç² L ·Ê£· m´£´ Æ n  ¹Ê¯ m©¤ Ï´Å­nÆ ££¶Ê ¥¶ ³¡Â©¯¥·£·¯³ ¥´ ´¥§m»Â n´ ·Ê¥© ¥ɩ ¯¤m´ Æ¥ É ´£ m´ Y ç² L ·ÊÅ n ©¥£· m´§ § £¹Ê¯Æ ££¶Ê ¥¶ ³¡Â©¯¥·Â n´¬m» m© ¢´©² ´¥ ¶ ´£  ¹Ê¯ § § ¥² ¯ ¬³ ´ ¥ © ·Ê ²Â n´£´Å © ¥ PLL [68] ³ ³ Ë ´¥¯¯ à m´ ´¥´£¶Â ¯¥q Y ç² L ² n¯ ¥² · ¥² ¯£¥²­©m´ à q© ¶ q ¯ §» 粯³ ¥´ ´¥§m» n´© ¯ © ¥ PLL

¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ PR4 Å ¥» ·Ê 5.1 £¹Ê¯ H(D) = 1 – D2 ç² KT = 3T/16 [56]

¸Ê Â­É Æ n©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã§²© ¥ ¥© ­´©·Â ¯¥q ¶ Ï´ ´ ä ´ ³ Ä ¤¯¶¬¥² ³ ³ Ë ¬£¥¥ ² ¯ ¥² ·ÊÆ£m »  n´¥­³¬ (uncoded system) ² ¸Ë ¯¤m» ³ º ¢´ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Â É ­§³ ¯ ´ ·Ë n´ Ï´­ Å­n© ¥ ¥© ­´¬³ §³ « q Ê·Å nÅ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Â É © ¥ ¥© ­´ · Â¥¶Ê£

 §·Ê¤ ·ÊÆ£m£·­ m ©¤ ©´£ Ï´ (memoryless threshold detector) à 3 ¥² ³ Ä ¤£·¥² ³ · Â¥¶Ê£  §·Ê¤ ·Ê m´ r1 ³Ê ¹¯

£¦2, if yk 1 ¦¦ rˆk ¦¤ 2, if yk 1 ¦¦ else ¦¦¥0,

(5.8)

¬Ï´­¥³ ¥² © ´¥ ¥© ­´ n¯£»§ §Ï´ ³ n¯£»§ {yk} ² » ¬m Æ ¤³ © ¥ ¥© ­´©·Â ¯¥q ¶ Ê·£· ¥¶£´ ­ m © ©§´¬Ï´­¥³ ´¥ ³ ¬¶ Å Â m´ ³ 60T  ¹Ê¯­´§Ï´ ³ n¯£»§¯¶ º ·Ê ©¥ ²Â É ¬» ¬º ¯ ´ ·Ë

m´¯³ ¥´ n¯ ¶ §´ ¯ ¶ (BER) ² Ï´ © Ä ¤Å n n¯£»§­§´¤Â  ¯¥q (  ¯¥q§² 4096 ¶ ) ¥² ³ Ê £· n¯ ¶ §´ ¥©£ ³ Æ£m n¯¤ ©m´ 1000 ¶  ¹Ê¯Å­n §§³ q ÊÆ· n£· ©´£ m ´Â ¹Ê¯ ¹¯ ´ ¬ ¶ ¶

¬Ï´­¥³ ¥² ·ÊÆ£m£·¯¯¡Â ´ ©´£ ·Ê © ¥¢´ ¥³ ¬´£´¥ Å n© ¥ PLL ¯³ ³ ·Ê­ ¸Ê Æ n

Å ¥ · ·Ë ²¬££º ¶Å­n¥² £· ´¥Â n´ ³ ­©²Å m© ¢´©² ´¥Æ n£´Ã ¬£ »¥ q (perfect acquisition) ¸Ê Ï´Æ nÄ ¤ ´¥ Ï´­ Å­n W0 = 0 Å ¬£ ´¥ (5.2)  ¹Ê¯ ²Æ nÆ£m n¯ Å n n¯£»§ preamble ¥» ·Ê 5.2  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² ·ÊÅ nÆ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ m´ Vw /T m´ È Ä ¤

m´ ´¥´£¶Â ¯¥q Y ·ÊÅ n ² » ¯¯ à £´Â ¹Ê¯Å­n¬´£´¥ ¶ ´£ ´¥Â §·Ê¤ à § ´ ¡¬Æ n¢´¤Å

160

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 5.2 ¬£¥¥ ² ¯ ¥² Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ m´ Vw /T m´ È (£¹Ê¯¥² Æ£m£·¯¯¡Â

´ ©´£ ·Ê)

100 ¶ ´£ ·ÊÆ n¯ ¶ ´¤Å ­³© n¯ ·Ê 2.3.1 ¯ [10] ç² m´ SNR ·ÊÅ n ¶¤´£ ´£¬£ ´¥ (4.85) Ä ¤Å ·Ê ·Ë Eb k hk

2

´ ¥» ·Ê 5.2 ©m´¥² ²£· BER § § £¹Ê¯ Eb/N0 £· m´£´ ¸Ë

粬£¥¥ ² ¯ ¥² ² n¯¤§ £¹Ê¯ ¶  ¯¥q ´ ©§´ Vw /T £· ©´£¥º Ã¥ £´ ¸Ë

´¥ ³ ´¥ ³ ¯¯¡Â ´ ©´£ ·Ê Å ·Ê ·Ë ² ¶ ´¥ ´¥² ·Ê Ï´ ´ Å ¬¢´©² ´ §´ ³Ê ¹¯£· m´

Vw /T = 0.5% 粯¯¡Â ´ ©´£ ·Ê m´ ³ 0.2% Å Ï´ ¯  ·¤© ³ ´¥´£¶Â ¯¥q Y ç² L

·ÊÅ n ² » ¯¯ à £´Â ¹Ê¯Å­n¬´£´¥ ¶ ´£ ´¥Â §·Ê¤ à § ´ ¡¬Ã§² ´ ©´£ ·ÊÆ n¢´¤Å C

¶ ´£ ·ÊÆ n¯ ¶ ´¤Å ­³© n¯ ·Ê 2.3.2 ¯ [10] ¯ ´ ·Ë ² ¶ ´¥ ´Â ´² ¥ · Ê·© ¥ PLL Å n

m´ Y ç² L  ·¤© ³ ³ Ë Å m© ¢´©² ´¥Æ n£´Ã§²¢´©² ´¥ ¶ ´£ Ä ¤ n¯£»§­ ¸Ê §mº£ ¥² ¯ n©¤

preamble Ï´ © C ¶ ç² ¶ m´©¬´¥ Ï´ © 4096 ¶ (¥©£ C + 4096 ¶ ) ¥» ·Ê 5.3 ì ¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ £¹Ê¯Å n ´¥´£¶Â ¯¥q ¯ © ¥ PLL ·Ê¯¯ Ã

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

¬Ï´­¥³ ¥² ·Ê£·¯¯¡Â ´ ©´£ ·Ê © ¥¢´ ¥³ ² n¯ Å n© ¥ PLL ¯³ ³ ·Ê¬¯ Å

¬Ï´­¥³ à m§² C Ä ¤Â¬n ¥´¡ “Perfect timing” ­£´¤ ¸ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ ·ÊÅ n

Uˆk Uk Å ´¥ ³ ³©¯¤m´ ¬³ ´ y(t) ¸Ê ²Â­É Æ n©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ Ï´ ´

Æ nÆ£m · £¹Ê¯ Ï´ ´ Å ¥² ·Ê n¯ ´¥¯³ ¥´ ´¥§m»Â n´ ·Ê¥ɩ (­¥¹¯Â£¹Ê¯Å n ´ ³ m´ ´¥´£¶Â ¯¥q ¯ © ¥ PLL ·Ê » ¯¯ à ¬Ï´­¥³ C n ¯¤È)

5

บทที่

´ §§³ q Êà · ¬ Å ¥» ·Ê 5.2 ç² 5.3 ¬¥º Æ n©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ ²

Ï´ ´ Æ nÆ£m · n´¥² £· n¯ ¶ §´ ´ ©§´£´ ­¥¹¯Â£¹Ê¯ Ï´ ´ Å ¥² ·Ê n¯ ´¥¯³ ¥´ ´¥§m»Â n´

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

161

¥» ·Ê 5.3 ¬£¥¥ ² ¯ ¥² ¬Ï´­¥³ Vw /T = 0.5 粯¯¡Â ´ ©´£ ·Ê 0.2%

·Ê¥© ¥ɩ ©¶ · ´¥Ã nÆ ³ ­´ ·Ê m´¤ ·Ê¬º Å ´¥Â ¶Ê£¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ É ¹¯ ´¥Â §·Ê¤ © ¥ ¥© ­´¬³ §³ « q ÊÅ· nÅ Æ ££¶Ê §» ´ © ¥ ¥© ­´ · Â¥¶Ê£Â §·Ê¤ à °´¥q

(hard threshold detector) Â É © ¥ ¥© ­´ · Â¥¶Ê£Â §·Ê¤ à ¯¡ q (soft threshold detector)

[56] ­¥¹¯¯´ Å n© ¥ ¥© ­´©·Â ¯¥q ¶ Ê·£· ¥¶£´ ­ m © ©§´¬Ï´­¥³ ´¥ ³ ¬¶ Å dT n ¯¤È ÉÆ n

[32] ¯¤m´ Æ¥ É ´£©¶ · ´¥ ·Ê §m´©£´Â­§m´ ·Ë ¬´£´¥ m©¤Â ¶Ê£¬£¥¥ ²Æ n ·¤ 夃 n ¯¤Â m´ ³ Ë [35] ³ ³ Ë Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã Å­£m Ê£ · ·¬£¥¥ ²£´ ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ ¸ Â É ¬¶Ê

Ï´Â É ¯¤m´ ¤¶Ê Å ­³© n¯ m¯Æ ² Ï ´Â¬ ¯ ´¥ Ï ´Â ¶ PSP £´Å nÅ ´¥ ³ ´Æ ££¶Ê ¥¶ ³¡Â©¯¥·

¥» à ŭ£m Ê£ · ·¬£¥¥ ² · ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ

5.1.3  ¯Â ¯¥qƩ©¯¥qÆ ££¶Ê ¥¶ ³¡Â©¯¥· Å ´ ¶ ³ ¶¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã Å n ³ ³Ê©Æ ² ¸Ë ¯¤m» ³ m´ ³ ¬¶ Å \rˆk ^ ·ÊÅ nÅ ¬£ ´¥ (5.4)  ¥´² ² ³ Ë ´¥Â ¶Ê£¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥· Ï´Æ nÄ ¤ ´¥Å n m´ \rˆk ^ ·Ê£· ©´£ » n¯ m ´Â ¹Ê¯ ¹¯ ç²Æ£m£· ´¥­ m © ©§´ ¸Ê ¬´£´¥ ­´Æ n ´ Ä ¥ ¬¥n´ ¯ à ¢´  ¥§§¶¬

(trellis diagram) [13] §m´© ¹¯Ã m§² ´¥Â §·Ê¤ ¬ ´ ²¢´¤Å à ¢´  ¥§§¶¬ ²¬¯ §n¯ ³ m´ \rˆk ^ ·ÊÂ É ­ ¸Ê  ·¤© ³Ê ì ©m´ ²£·¯¤m´ n ¯¤­ ¸Ê ´¥Â §·Ê¤ ¬ ´ ²Å à m§² m© ©§´ ¯ à ¢´  ¥§§¶¬ ·Ê ¥ ³ m´ ³ ¬¶ Å ·Ê » n¯ ³ ³ Ë ´¥Å n m´ \rˆk ^ ·Ê » n¯ ´ à ¢´  ¥§§¶¬Å ´¥ ¥³ m´ Uˆk 1 ²¬´£´¥ m©¤Â ¶Ê£¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Æ n à © ¶ Å ´¥

162

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

Ï ´ n¯£»§ ·Êà ¯¤m»Å à ¢´  ¥§§¶¬£´Å nÅ ´¥ ¥²£´ m´ ´¥´£¶Â ¯¥q ÊÆ· £m ¥´ m´ ¥n» ³ ³ Å ¹Ê¯©m´ “ ´¥ ¥²£©§ §Ã  ¯Â ¯¥qƩ©¯¥q (PSP: per-survivor processing)” [60] ¸Ê Æ n »

Ï ´£´Å nÅ ­§´¤ ´ ¥²¤º q  m ´¥¥² º m¯ ¬³ ´ (channel identification), ´¥ ¥© ­´

§Ï´ ³ n¯£»§ ©¥ ²Â É ¬» ¬º à ¥³ m´Æ n (adaptive ML sequence detection), ç² ´¥ n»Â¡¬ ç² §¹Ê ´­q (phase/carrier recovery)

¯´ª³¤Ã © ¶ ¯ PSP Ï´Å­nÆ nÆ ££¶Ê ¥¶ ³¡Â©¯¥·Ã Å­£m ·ÊÂ¥·¤ ©m´ “ ¯Â ¯¥qƩ©¯¥q

Æ ££¶Ê ¥¶ ³¡Â©¯¥· (PS-TR: per-survivor timing recovery)” [62] ­¥¹¯Â¥·¤ ¬³ Ë È ©m´ “Æ ££¶Ê

¥¶ ³¡Â©¯¥·Ã PS-TR” ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã§²© ¥ ¥© ­´©·Â ¯¥q ¶

Ë ¯ Å ´ ¶ ³ ¶Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ² Ï´ ´ §n´¤ ³ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶  ·¤ à m£· ³

Æ ££¶Ê ¥¶ ³¡Â©¯¥·Â ¶Ê£Â n´Æ Å Ã m§²¬ ´ ² ¯ à ¢´  ¥§§¶¬ (trellis state) Ä ¤Ã © ¶ ·Ê¬Ï´ ³

É ¹¯ ´¥ ³ ³©¯¤m´ ¬³ ´ ï ²§É¯ ·ÊÆ n¥³ n©¤ m´ Uˆk ·Ê m´ ³ ¸Ê ¬¯ §n¯ ³ à m§² ´¥Â §·Ê¤

¬ ´ ² ¯ ´ ·Ë à m§²Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» (survivor path) ²£·© ¥ PLL Â É ¯ ¯ ¥² Ï´¯¤m»Å à m§²¬ ´ ²  ¹Ê¯Å nÅ ´¥ ¥³ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ ³© ³ Æ

¯³§ ¯¥¶ ¸£ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ¥» ·Ê 5.4 ì ¯³§ ¯¥¶ ¸£ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR Ä ¤ ¥¥ ³ ·Ê ¸Ë n n©¤Â ¥¹Ê¯ ­£´¤ ¯ ³ ¥q (*) Â É ³ Ë ¯ ·Ê ¶Ê£ ¸Ë £´ ´ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [62] ¬m© m´ ³© 3T/16 Å

Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ¯ ¶ ´¤Æ n ³ ·Ë

¶ ´¥ ´Ã ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ PR4 Å ¥» ·Ê 5.5 n´Å­n : k \ak 1ak 2 ^

à ¬ ´ ² (state) ©§´ k Ä ¤£· Ï´ © ¬ ´ ² ³ Ë ­£ Q = 2Q = 4 ¬ ´ ² ( ¸Ê Å ·Ê ·Ë¥² º

¬ ´ ² 0 ¸ ¬ ´ ² 3) £¹Ê¯ Q ¹¯­ m ©¤ ©´£ Ï´ ¯ m¯ ¬³ ´ PR4 n´ Ï´­ Å­n p , q à ´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² p Æ ¤³ ¬ ´ ² q ç²Å­n Qk p ¹¯ ³© Ï ´­ n ´ (predecessor) ·Ê ¬ ´ ² p ©§´ k ¸Ê Â É m´¬ ´ ² m¯ ­ n ´ ( ©§´ k – 1) ·Ê Ï´Å­n ¶ ´¥Â §·Ê¤ ¬ ´ ² ·Ê

·¬º £´¤³ ¬ ´ ² p ©§´ k Ä ¤ ´¥Â §·Ê¤ ¬ ´ ² ·Ë ¹¯Â É ¬m© ­ ¸Ê ¯ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m»

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

Ë ¯ ´¥ Ï´ ´ ¯ ³ Ë ¯ (A-10) Å n ³ m¯ ¬³ ´ PR4  m´ ³ Ë ¬Ï´­¥³ ¥´¤§²Â¯·¤ ¯ ³

Sk p ¯ ´ ·Ë n´Å­n Uˆk p ¹¯ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ §Ï´ ³ ·Ê k ¬Ï´­¥³ ¬ ´ ²

p ©§´ k ¸Ê ² » Ï ´£´Å nÅ ´¥ ³ ³©¯¤m´ ¬³ ´ y t Å ¥²¤² ·Ê k (k-th stage) ¬Ï´­¥³ ´¥Â §·Ê¤ ¬ ´ ² ·Ê¯¯ ´ ¬ ´ ² p ©§´ k ³Ê ¹¯ yk p y kT Uˆk p

£¹Ê¯ yk p

5

บทที่

¹¯ n¯£»§Â¯´ q º ¯ ´¥ ³ ³©¯¤m´ §Ï´ ³ ·Ê k ¯ ¬ ´ ² p ©§´ k ¯ ´ ·Ë ¤³ Ï´­ Å­n Rˆk p ¹¯ n¯ ¶ §´ ´ ©´£ ·Ê§Ï´ ³ ·Ê k ¯ ¬ ´ ² p ©§´ k ¸Ê ² » Ï ´Æ Å nÅ ´¥ ¥³ Ë ¯ ·Ê (A-12) Å ¥» ·Ê 5.4 m´ Uˆk p ´£ ³

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¥» ·Ê 5.4 ¯³§ ¯¥¶ ¸£ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR Ä ¤ ¥¥ ³ ·Ê ¸Ë n n©¤Â ¥¹Ê¯ ­£´¤ * Â É ³ Ë ¯ ·Ê ¶Ê£ ¸ Ë £´ ´ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ [62] ©§´ k – 1

(0) –1 –1

k

k+2

k+1

rˆ 0,1

Qk (1) 'k (1) Uˆk (1) Rˆk (1)

(1) 1 –1

Sk 1, 2

(2) –1 1

Sk 3, 2

(3) 1 1

Uˆk (3)

yk ( p ) ¥²¤² ·Ê k (k-th stage)

Qk 1 (2) 'k 1 (2) Uˆ (2) Rˆ (2) k 1

k 1

aˆ 1 aˆ 1

¥» ·Ê 5.5 à ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ PR4 ·ÊÅ n¯ ¶ ´¤ ´¥ Ï´ ´ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¶ ´¥ ´¥²¤² ·Ê k ¯ à ¢´  ¥§§¶¬ ¸Ê £· ´¥Â §·Ê¤ ¬ ´ ²¬¯ ¬n ´ £´ ¸ ¬ ´ ²

(2) ©§´ k + 1 ³Ê ¹¯ (1, 2) ç² (3, 2) Â¥¶Ê£ n ² Ï´ ´¥ ³ ³©¯¤m´ ¬³ ´ y t n©¤ ´¥ Å n Uˆk 1 ç² Uˆk 3  ¹Ê¯Å­nÆ n yk 1 ç² yk 3 ´£§Ï´ ³ ´ ³ Ë ² Ï´ © m´Â£ ¥¶ ¬´ ´ Sk 1, 2 ç² Sk 3, 2 ´£ ³ Ë ¯ (A-6) Ä ¤ ·Ê rˆ p , q ¹¯ n¯£»§Â¯´ q º ¯ m¯ ¬³ ´ ·Ê

Ë ¯ (A-7) Å ´¥Â§¹¯ ¬ ´ ² ¥´ª ´ ¬³ ´ ¥ © ¸Ê ¬¯ §n¯ ³ p , q ´ ³ Ë ²Å n ³ Â¥¶Ê£ n ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ·Ê£´ ¸ ¬ ´ ² (2) ©§´ k + 1

¬££º ¶©m´ (1,2) ¹¯ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ·Ê£´ ¸ ¬ ´ ² (2) ©§´ k + 1 ¸Ê ²Æ n

Qk 1 2 1 Å­n Ï´ ´¥ ¥³ m´Â£ ¥¶ ¬n ´ ¬Ï´­¥³ ¬ ´ ² (2) ©§´ k + 1 ­¥¹¯ 'k 1 2 ´£

³ Ë ¯ (A-8) ç² ¥³ m´Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Ê·£´ ¸ ¬ ´ ² (2) ©§´ k + 1 ­¥¹¯ Sk 1 2

´£ ³ Ë ¯ (A-9) ´ ³ Ë ²Å n n¯£»§ Sk 1 2 Å ´¥ ¥³ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ Ë ¯ (A-10) ¸ (A-12) Ä ¤ ·Ê m´ Uˆk 1 2 ² » Ï ´Æ Å nÅ ´¥ ³ ³© ³ Æ Uˆk 1 2 ´£ ³ ³©¯¤m´ ¬³ ´ y t Å ¥²¤² ·Ê k + 1 ¯ ´¥Â §·Ê¤ ¬ ´ ² ·Ê¯¯ £´ ´ ¬ ´ ² (2) ©§´

k + 1 ´ ³ Ë Å­n Ï´ ´£ ³ Ë ¯ m´ È Â­§m´ ·Ë ³ ¬³ ´ y t ·ÊÆ n¥³ ³ Ë ­£  ¹Ê¯ Ï´ ´¥ ¯ ¥­³¬ §Ï´ ³ n¯£»§ ´ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Ê£ · · m´Â£ ¥¶ ¬n ´ n ¯¤¬º

Ä ¤¬¥º çn©¯³§ ¯¥¶ ¸£ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR à m´ ´ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶

³ ·Ë Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR n¯ ´¥­ m ©¤ ©´£ Ï´¬Ï´­¥³ ³ Â É n¯£»§ m´ È Æ nà m ¯¯¡Â ¯¤m´ Æ¥ É ´£Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ¬´£´¥ ³ Â É Â ´² n¯£»§Å ©§´ ³ º ³ ç²Â©§´

m¯ ­ n ´Â m´ ³ Ë Â ¹Ê¯ m©¤§ ¥¶£´ ­ m ©¤ ©´£ Ï´ ·Ê n¯ Å n ¯ ´ ·Ë ²Â­É Æ n©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·

à PS-TR n¯ Å n© ¥ PLL ­ ¸Ê © ¥¬Ï´­¥³ à m§²Â¬n ´ ·Ê¤³ £· ·©¶ ¯¤m»25 ( ¸Ê £· Ï´ ©  m´ ³

Ï´ © ¬ ´ ² ³ Ë ­£ Q ¬ ´ ²) ³ ³ Ë ¬Ï´­¥³ m¯ ¬³ ´ PR4 ¸Ê £· Q = 4 ¬ ´ ² Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ²Å n© ¥ PLL 4 © ¥ ¸ Ï´Å­n£· ©´£ ³ n¯ £´ ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥· à ·ÊÅ n ³ ³©Ê Æ ¥²£´ ¬·Ê m´

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ , n¯ ¶ §´ ´ ©´£ ·Ê, ç² n¯£»§Â¯´ q º ·ÊÆ n ´ ´¥ ³ ³©¯¤m´

¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ Å ¥» ·Ê 5.1 £¹Ê¯ H(D) = 1 – D2 粬££º ¶©m´£·¢´©² ´¥Æ n£´

à ¬£ »¥ q Ä ¤ ´¥ Ï´­ Å­n U 0 0 Å ¬£ ´¥ (5.2)  ¹Ê¯Å­n¬´£´¥ Å n© ¥ PLL ¯³ ³ ·Ê ­ ¸Ê Æ n 25

5

บทที่

Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ²Å n¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ ·Ê m´ ³ ¸Ê ¬¯ §n¯ à m§² ´¥Â §·Ê¤ ¬ ´ ² Å ´¥ ³ ³©¯¤m´ ¬³ ´ y t Å Ã m§² m© ©§´

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11 Conventional timing recovery with hard decision (d = 0) Conventional timing recovery with tentative decision (d = 4) PS-TR (d = 0) Genie-aided detector (d = 0)

Eb/N0 required to achieve BER = 10 (in dB)

10.8

-4

10.6 10.4 10.2 10 9.8 9.6 9.4 9.2 9 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Vw /T (%)

¥» ·Ê 5.6 ¬£¥¥ ² ¯ ¥² Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã m´ È

¥» ·Ê 5.6  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È Ä ¤ ·Ê¬n à y ¯ ¸ ¥¶£´ Eb /N0

(£·­ m ©¤Â É dB) ·Ê¥² n¯ ´¥Â ¹Ê¯ Ï´Å­n¥² £· BER = 10–4 ­¥¹¯¯· ³ ¤­ ¸Ê É ¹¯Â¬n à y ¯ ¸ Ï´§³ ´ ·Ê© ¥¢´ ¬m n¯ Å nÅ ´¥¬m n¯£»§Â ¹Ê¯ Ï´Å­n© ¥¢´ ¥³ £· BER = 10–4 ç²

´¥´£¶Â ¯¥q d ì ¸ ¥¶£´ ­ m © ©§´ ³ Ë ­£ ·Ê ¶ ¸Ë Æ ££¶Ê §» (£·­ m ©¤Â É ´ ©§´ ¯ ¶ ) ¯ ´ ·Ë¬n ¥´¡ “Genie-aided detector” ­£´¤ ¸ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ ·Ê© ¥ PLL Å n rˆk rk ¬Ï´­¥³ º k ( »¥» ·Ê 5.1) Å ´¥ ¥³ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ ³©

³ Æ , ç² m´ ³ ¬¶ Å Â ¹Ë¯ n ­¥¹¯ “tentative decision (d = 4)” ­£´¤ ¸ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ ·Ê© ¥ ¥© ­´¬³ §³ « q ÊÅ· nÅ Æ ££¶Ê §» ¹¯ © ¥ ¥© ­´©·Â ¯¥q ¶ Ê·£· ¥¶£´ ­ m © ©§´Â m´ ³ 4T Ä ¤ m´ ³ ¬¶ Å Â ¹Ë¯ n rˆk d ­´Æ n ´ ´¥ n ­´Ã ¤n¯ §³ ´£Â¬n ´ ·Ê¤³

£· ·©¶ ¯¤m» Ê£ · ´ ¸ ¬ ´ ² ³ Ë È

´ ¥» ·Ê 5.6 ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR £·¬£¥¥ ² · ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã

·ÊÅ n ³ ³Ê©Æ  ¥´²Å n Eb /N0 n ¯¤ ©m´  ¹Ê¯ Ï´Å­n¥² £· BER = 10–4  m´ ³ Ä ¤Â ´²¯¤m´ ¤¶Ê

£¹Ê¯ Ï´ ´ Å ¥² ·Ê£· ©´£¥º Ã¥ ¯ Æ ££¶Ê ¶  ¯¥q Vw /T ¬» ¸ ãn©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·Ê Å n ³ ³©Ê Æ ·ÊÅ n m´ ³ ¬¶ Å Ã °´¥q (hard decision) ´£¬£ ´¥ (5.8) »Â­£¹¯ ²£·¬£¥¥ ²

Å §n ·¤ ³ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ ·ÊÅ n m´ ³ ¬¶ Å Â ¹Ë¯ n à m ²Æ£mÂ É ¥¶ £¹Ê¯ Ï ´Æ Å n

Å m¯ ¬³ ´ ·Ê£· ©´£ ³ n¯ ( m m¯ ¬³ ´ ·Ê£·­ m ©¤ ©´£ Ï´£´ ) ³ ³ Ë ¸ Â É Â­ º §©m´

Ï´Æ£Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ ·ÊÅ n ´ ¥¶ Å ´ ¶ ³ ¶ ¸ ¶ ¤£Å n m´ ³ ¬¶ Å Â ¹Ë¯ n [32]

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

0

10

C = 50 -1

10

-2

10

C = 100

BER

Perfect timing -3

10

Conventional timing recovery with hard decision (d = 0) -4

Conventional timing recovery with tentative decision (d = 4)

10

PS-TR -5

10

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

Eb/N0 (dB)

¥» ·Ê 5.7 ¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã m´ È Â£¹Ê¯Å n ´¥´£¶Â ¯¥q ¯ PLL ·Ê » ¯¯ à ¬Ï´­¥³ à m§² C

¯ ´ ·Ë¤³ ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR £·¯³ ¥´ ´¥§m»Â n´Â¥É© ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·

à ·ÊÅ n ³ ³Ê©Æ ´£ ·Êì Å ¥» ·Ê 5.7 ¸Ê  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È Å ¬¢´©²

´ §´ (£¹Ê¯ Vw /T = 0.5% 粯¯¡Â ´ ©´£ ·Ê m´ ³ 0.2%) Ä ¤Å n ´¥´£¶Â ¯¥q ¯ PLL

Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ £¹Ê¯ Ï´ ´ ·Ê m´ Eb /N0 ¬» Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ C £· m´ n ¯¤

( ³Ê ¹¯Â£¹Ê¯¥² Ï´ ´ Å ¬ ´©² ·Ê n¯ ´¥ ´¥§m»Â n´ ·Ê¥© ¥ɩ)

5.1.4  ¯Â ¯¥qƩ©¯¥qÆ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë Ä ¤ ³©Ê Æ ³ ­´Â¥¹Ê¯ ¥² © ´¥Â n´ ³ ­©² (synchronization) ²Æ£m ³ n¯ n´Æ ££¶Ê ¥¶ ³¡Â©¯¥· Ï´ ´  ·¤ §Ï´ ³ ¯¤m´ Æ¥ É ´£© ¥¢´ ¥³ ·ÊÅ n ´ ¥¶ ² n¯ Ï´ ¥² © ´¥ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥· ¯· ©¯Æ§Â ³ ç² ´¥ ¯ ¥­³¬ ECC  ¹Ê¯ ¯ ¥­³¬ n¯£»§¯¯ £´Å n ´ ¯ ´ ·Ë Æ ££¶Ê ¥¶ ³¡

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

·Ê » ¯¯ à ¬Ï´­¥³ à m§² C [10] ´ ¥» ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR £·¬£¥¥ ² · ©m´

©¯¥· Ê· · ©¥ ²¬´£´¥ Ï´ ´ Å ¬¢´ é §n¯£ ·Ê£·¬³ ´ ¥ © m´ È ¥©£ ³ Ë ´¥Ã ¥ ¬¯

¥²­©m´ ¬³ §³ « q (ISI: intersymbol interference) Æ n¯¤m´ £· ¥²¬¶ ¶¢´

´ ·Ê §m´©£´Å ·Ê 2 ç² 4 ¥­³¬ ECC  m ¥­³¬Â ¯¥qÄ [3] ç²¥­³¬ LDPC [17]

m©¤Å­n¥² ¬¹Ê¯¬´¥ ¶ ¶ ³§¬´£´¥ Ï´ ´ ·Ê m´ SNR ÏÊ´È Æ n¯¤m´ m ´Â ¹Ê¯ ¹¯ ¸Ê ­£´¤ ©´£©m´Æ ££¶Ê

5

บทที่

¥¶ ³¡Â©¯¥· Ê·Å nÅ ¥² ¬¹Ê¯¬´¥ É ² n¯ Ï´ ´ ·Ê m´ SNR ÏÊ´ ©m´ ¶ Å ´ ¶ ³ ¶© ¥¢´ ¥³ Ã

·ÊÅ n ³ ³Ê©Æ (conventional receiver) ² Ï´ ¥² © ´¥Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã§² ´¥ ¯ ¥­³¬ ECC

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

167

ä ´ ³ Ä ¤¯¶¬¥² ­¥¹¯¯´ §m´©Æ n©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Æ£mÆ nÅ n ¥²Ä¤ q ´ ¥­³¬ ECC £´ m©¤ Å ´¥ Ï´ ´ ¸ ¬m § Ï´Å­nÆ ££¶Ê ¥¶ ³¡Â©¯¥·Æ£m¬´£´¥ Ï´ ´ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ £¹Ê¯ Ï´ ´ Å ¥² ·Ê£· m´ SNR ÏÊ´

Å ´ ¦« · ´¥ ¥²£´ m´Ã ML ¥m©£ ³ ¥²­©m´ ¯¯¡Â ´ ©§´Ã§² ¶ m´©¬´¥

¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥· ¯· ©¯Æ§Â ³ ç² ´¥ ¯ ¥­³¬ ECC Â É ©¶ · ´¥

·Ê ·¬º Å ´¥Ã n ³ ­´Â¥¹Ê¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã m£· ©´£ ³ n¯ ¬» £´ [69] ¯¤m´ Æ¥ É ´£ Nayak,

Barry, ç² McLaughlin [56] Æ n ϴ¬ ¯©¶ · ´¥Ã n ³ ­´Â¥¹Ê¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥· Ê·£·¬£¥¥ ²Ã§² £· ©´£ ³ n¯ Å §n ·¤ ³ © ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ ¸Ê Å ·Ê ·Ë ²Â¥·¤ ©m´ “©¶ · ´¥ NBM”

Ä ¤©¶ · ´¥ ·Ë ² Ï ´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Â n´Æ à ¥ Å ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ [21]  ¹Ê¯ Ï´ ¥² © ´¥ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥· ¯· ©¯Æ§Â ³ ç² ´¥ ¯ ¥­³¬ ECC ¥m©£ ³ ¯¤m´ Æ¥ É ´£©¶ · ´¥ NBM ¤³ n¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë (iteration) ­§´¤¥¯  ¹Ê¯Å­n¥² £·¬£¥¥ ² ·Ê · Ä ¤Â ´²

¯¤m´ ¤¶Ê £¹Ê¯¥² £·Æ ££¶Ê ¶  ¯¥q Ê¥· º Ã¥

Å ´¥Â ¶Ê£¬£¥¥ ² ¯ ©¶ · ´¥ NBM Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë ·ÊÂ¥·¤ ©m´ “ ¯Â ¯¥q

Ʃ©¯¥qÆ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë (PS-ITR: per-survivor iterative timing recovery)” ¸ Æ n »

Ï ´Â¬ ¯Å [63] ¸Ê ¬¥n´ Æ nÄ ¤ ´¥ Ï ´Ã © ¶ ¯ PSP Æ ¥²¤º qÅ n ³ ¯³§ ¯¥¶ ¸£ BCJR [18]

Ï´Å­nÆ nÂ É £¯ »§ “PSP-BCJR” ´ ³ Ë Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ²Ã§  §·Ê¤ m´©¬´¥ à ¯¡ q¥²­©m´ PSP-BCJR 粩 ¥ ¯ ¥­³¬ ECC

à ϴ§¯ m¯ ¬³ ´ ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ PR4 ·Ê »  n´¥­³¬Å ¥» ·Ê 5.8 £¹Ê¯ ¶ m´©¬´¥ xk {0,1} »

¬m Æ ¤³ © ¥Â n´¥­³¬ ECC, © ¥¯¶  ¯¥q§·¡Â©¯¥qà ¬mº£ S (S-random interleaver) [27] ­¥¹¯ §É¯ Q , 粩 ¥Â n´¥­³¬ m¯ (precoder) 1 / 1 D 2 [10] ´ ³ Ë ² »  n´ m» (mapping)

Å­nÂ É §Ï´ ³ n¯£»§ bk {r1} ¬³ ´ ¯m´ §³ p(t)  ·¤ Æ n ´£¬£ ´¥ (5.1) ² » ¬m Æ ¤³ © ¥ ¥¯ m´ Ïʴç² » ³ ³©¯¤m´ ¬³ ´ ·Ê©§´ kT Uˆk Ï´Å­nÆ nÂ É n¯£»§Ã £Â ¶ § yk ´£

¬£ ´¥ (5.3) ¯ ´ ·Ë n´¬££º ¶©m´¥² £·¢´©² ´¥Æ n£´Ã ¬£ »¥ q ( Ï´Å­n Ï´­ m´ U 0 0 Å ¬£ ´¥ (5.2) Æ n) ç²Â ¹Ê ¯ ´ Å ¥² Æ£m£·¯¯¡Â ´ ©´£ ·Ê ¸ ¬´£´¥ Å n© ¥ PLL ¯³ ³ ·Ê­ ¸Ê Å ´¥ ¥³ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ ³© ³ Æ ³ ·Ë Uˆk 1 Uˆk KT \yk r k 1 yk 1r k ^

(5.9)

£¹Ê¯ KT = 3T/16 ¬Ï´­¥³ m¯ ¬³ ´ PR4 ç² r k ¹¯ m´ ¥²£´ à ¯¡ q (soft estimate) ¯ rk {0, r2} ¸Ê ­´Æ n ´ [56]

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n t

xk

^0,1`

p t

ECC encoder

LPF

Q

ak

y t

1 1 D 2

yk

kT Uˆk

bk

^r1`

1 D

2

rk

h t

SISO equalizer

PLL

p t

Uk

q(t)

Q 1

Mk

SISO decoder

xˆk

Q

¥» ·Ê 5.8 à ϴ§¯ m¯ ¬³ ´ PR4 ·Ê »  n´¥­³¬ 粩 ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ

r k E <rk | yk >

2sinh 2yk / Tn2

(5.10)

cosh 2yk / Tn2 e 2/ Tn

2

Å ·Ê ·Ë ²Å n m´ ¥²£´ à ¯¡ q  ¥´² m´ ¥²£´ à ¯¡ qÅ­n¬£¥¥ ² · ©m´ m´ ¥²£´ à °´¥q Å ¬£ ´¥ (5.8) [56]

¬m §§³ q Ê·Æ nÆ ¤³ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ( »¥» ·Ê 5.8) ¸Ê ²Ã§  §·Ê¤ m´©¬´¥Ã ¯¡ q ¥²­©m´ ¯· ©¯Æ§Â ¯¥qà SISO (Å n ¯ ¥­³¬ n¯£»§ ·Ê m´ m¯ ¬³ ´ PR4 à ·Ê »  n´¥­³¬ m¯ ) 粩 ¥ ¯ ¥­³¬Ã SISO (Å n ¯ ¥­³¬ n¯£»§ ·Ê m´ © ¥Â n´¥­³¬ ECC)

¯³§ ¯¥¶ ¸£ PSP-BCJR PSP-BCJR ¬¥n´ Æ nÄ ¤ ´¥ Ï ´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Â n´Æ Ï´ ´ ¥m©£ ³ ³ ¯· ©¯Æ§Â ¯¥q BCJR ( ³Ê ¹¯© ¥ ¥© ­´ ·Ê¬¥n´ ´ ¯³§ ¯¥¶ ¸£ BCJR) Ä ¤¯´ª³¤Ã © ¶ ¯ PSP Ä ¤ ³Ê©Æ Ï´ ´ ¯

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

Å © ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ Â£¹Ê¯Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³©Ê Æ Ï´ ´ ¬¥É É ²

PSP-BCJR ² §n´¤ ³ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ¯¤m´ Æ¥ É ´£¯¯¡Â ´ ¡¬ ¯ ´¥ ³

³©¯¤m´ ³© ³ Æ Uˆk 1 ² » ¥³ m´Å à m§²¬ ´ ² ³ Ë ¬¯ ¶ª ´ (à n´ ­ n ´Ã§²Ã ¤n¯ §³ )

´£¯³§ ¯¥¶ ¸£ BCJR Ä ¤¯´ª³¤ n¯£»§ ´ ¬n ´ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ·Ê£´ ¸ ¬ ´ ² ³ Ë ¥» ·Ê 5.9 ì ¯³§ ¯¥¶ ¸£ PSP-BCJR Ä ¤ ¥¥ ³ ·Ê ¸Ë n n©¤Â ¥¹Ê¯ ­£´¤ ¯ ³ ¥q (*)  É

5

บทที่

Ë ¯ (B-9) ç² (B-12) ³ Ë ¯ ·Ê ¶Ê£ ¸Ë £´ ´ ¯³§ ¯¥¶ ¸£ BCJR ¬m© m´ ³© 3T/16 Å ³

²Å n ³ m¯ ¬³ ´ PR4  m´ ³ Ë ( ¸Ê ¬´£´¥ ¥©£Â n´ ³ ´¥´£¶Â ¯¥q ¯ © ¥ PLL Æ n m ³ ) ¬Ï´­¥³ ³ Ë ¯ ´¥ Ï´ ´ ¯ PSP-BCJR ¯ ¶ ´¤Æ n ³ ·Ë

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¥» ·Ê 5.9 ¯³§ ¯¥¶ ¸£ PSP-BCJR Ä ¤ ·Ê ¥¥ ³ ·Ê ¸Ë n n©¤Â ¥¹Ê¯ ­£´¤ * Â É ³ Ë ¯ ·Ê ¶Ê£ ¸ Ë £´ ´ ¯³§ ¯¥¶ ¸£ BCJR

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rˆ 0,1

aˆ 0,1

Rˆk (1) Uˆk (1) Qk (1)

Hk 1, 2

Hk 3, 2

Uˆk (3)

yk ( p )

Uˆk 1 (2) Rˆk 1 (2) Qk 1 (2)

aˆ 1 aˆ 1

¥» ·Ê 5.10 à ¢´  ¥§§¶¬ ·ÊÅ n¯ ¶ ´¤ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ PSP-BCJR Å m© ´¥Â©·¤  ¶ à n´ ­ n ´

´¥Â©·¤  ¶ à n´ ­ n ´ (forward recursion) ¶ ´¥ ´Ã ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ PR4 Å ¥» ·Ê 5.10 n´Å­n : k \bk 1bk 2 ^ à £¹Ê¯ Q = 2 ¹¯­ m ©¤ ©´£ Ï´ ¯ m¯ ¬³ ´ PR4 ·Ê£· ´¥Â n´¥­³¬ m¯ Ï´­ Å­n p , q Ã

´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² p Æ ¤³ ¬ ´ ² q ç²Å­n Qk p ¹¯ ³© Ï ´­ n ´ ·Ê¬ ´ ² p ©§´ k ¸Ê Â É m´¬ ´ ² m¯ ­ n ´ ( ©§´ k – 1) ·Ê Ï´Å­n ¶ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º £´¤³ ¬ ´ ² p

©§´ k ¯ ´ ·Ë n´Å­n Uˆk p ¹¯ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ §Ï´ ³ ·Ê k ¬Ï´­¥³ ¬ ´ ²

p ©§´ k ¸Ê ² » Ï ´£´Å nÅ ´¥ ³ ³©¯¤m´ ¬³ ´ y t Å ¥²¤² ·Ê k (k-th stage) ¬Ï´­¥³ ´¥Â §·Ê¤ ¬ ´ ² ·Ê¯¯ ´ ¬ ´ ² p ©§´ k ³Ê ¹¯ yk p y kT Uˆk p

£¹Ê¯ yk p

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

¬ ´ ² ©§´ k Ä ¤£· Ï´ © ³ Ë ­£ Q = 2Q = 4 ¬ ´ ² (Â¥¶Ê£ ´ ¬ ´ ² 0 ¸ ¬ ´ ² 3)

¹¯ n¯£»§Â¯´ q º ¯ ´¥ ³ ³©¯¤m´ §Ï´ ³ ·Ê k ¯ ¬ ´ ² p ©§´ k ç²Å­n Rˆk p ¹¯ n¯ ¶ §´ ´ ©´£ ·Ê§Ï´ ³ ·Ê k ¯ ¬ ´ ² p ©§´ k ¸Ê ² » Ï ´Æ Å nÅ ´¥ ¥³ m´ Uˆk p ´£ ³ Ë ¯ ·Ê (B-11) Å ¥» ·Ê 5.9

¶ ´¥ ´¥²¤² ·Ê k ¯ à ¢´  ¥§§¶¬ ¸Ê £· ´¥Â §·Ê¤ ¬ ´ ²¬¯ ¬n ´ £´ ¸ ¬ ´ ²

5

บทที่

(2) ©§´ k + 1 ³Ê ¹¯ (1,2) ç² (3,2) Â¥¶Ê£ n ² Ï´ ´¥ ³ ³©¯¤m´ ¬³ ´ y t n©¤ ´¥Å n Uˆk 1 ç² Uˆk 3  ¹Ê¯Å­nÆ n yk 1 ç² yk 3 ´£§Ï´ ³ ´ ³ Ë ² Ï´ © m´Â£ ¥¶ Hk 1, 2

ç² Hk 3, 2 ´£ ³ Ë ¯ (B-6) £¹Ê¯ aˆ p , q ¹¯ m´ ¥²£´ ¯ n¯£»§Â¯´ q º ¯ © ¥Â n´¥­³¬ เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

171

m¯ (precoder) ·Ê¬¯ §n¯ ³ p , q ç² Ma ak ¹¯ m´ LLR à ¯² ¶¥¶¯¯¥¶ ¯ ak ´ ³ Ë ²Å n ³ Ë ¯ (B-7) Å ´¥ ¥³ m´ Bk 2

¬ ´ ²Â¥¶Ê£ n ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ·Ê£´ ¸ ¬ ´ ² (2) ©§´ k + 1

² » §¹¯ ´£ ³ Ë ¯ (B-8) ¬££º ¶©m´ (1,2) ¹¯ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ·Ê£´ ¸ ¬ ´ ² (2)

©§´ k + 1 ¸Ê ²Æ n Qk 1 2 1 ´ ³ Ë Ï´ ´¥ ¥³ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ ³© ³ Æ Uˆk 1 2 ´£ ³ Ë ¯ (B-9) – (B-11) Ä ¤ m´ Uˆk 1 2 ² » Ï ´Æ Å nÅ ´¥ ³ ³©¯¤m´ ¬³ ´ y t Å ¥²¤² ·Ê k + 1 ¯ ´¥Â §·Ê¤ ¬ ´ ² ·Ê¯¯ £´ ´ ¬ ´ ² (2) ©§´ k + 1

´¥Â©·¤  ¶ à ¤n¯ §³ (backward recursion) ¥² © ´¥ ¥³ m´ ´ ©§´Å ¶ª ´ ¤n¯ §³ £·©³ º ¥²¬ q ¹Ê¯ ¥³ ¥º º ¢´ ¯ n¯£»§Ã £Â ¶ §

{yk} Å­n ·£´ ¸Ë ¸Ê ²¬m §Å­n º ¢´ ¯ m´Â£ ¥¶ ¬´ ´ · ¸Ë n©¤ ¥» ·Ê 5.11 ì à ¢´

 ¥§§¶¬ ·ÊÅ n¯ ¶ ´¤ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ PSP-BCJR Å m© ´¥Â©·¤  ¶ à ¤n¯ §³ Ä ¤

Å ·Ê ·ËÆ n ¶¤´£Â¬n ´ “ ´¥Â §·Ê¤ ¬ ´ ²Ã ¤n¯ §³ (backward transition)” Å Ã ¢´

 ¥§§¶¬ ¸Ê ì n©¤Â¬n §» ª¥¬·Â ´ n´ Ï´­ Å­n Qkb 1 q ¹¯ ³© ´£­§³ (successor) ·Ê¬ ´ ²

q ©§´ k + 1 ¸Ê Â É m´¬ ´ ² m¯ ­ n ´ ( ©§´ k + 2) ·Ê Ï´Å­n ¶ ´¥Â §·Ê¤ ¬ ´ ²Ã

¤n¯ §³ ·Ê ·¬º £´¤³ ¬ ´ ² q ©§´ k + 1 ¯ ´ ·Ë n´Å­n Uˆkb 1 q ¹¯ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ à ¤n¯ §³ §Ï´ ³ ·Ê k ¬Ï´­¥³ ¬ ´ ² q ©§´ k + 1 ¸Ê ² » Ï ´£´Å nÅ

´¥ ³ ³©¯¤m´ ¬³ ´ y t Å ¥²¤² ·Ê k Å m© ´¥ Ï´ ´ à ¤n¯ §³ ³Ê ¹¯ ykb q

y kT Uˆkb 1 q

ç²Å­n Rˆkb 1 q ¹¯ n¯ ¶ §´ ´ ©´£ ·Êà ¤n¯ §³ §Ï´ ³ ·Ê k ¯ ¬ ´ ²

q ©§´ k + 1 ¸Ê ² » Ï ´Æ Å nÅ ´¥ ¥³ m´ Uˆkb 1 q ´£ ³ Ë ¯ ·Ê (B-24) Å ¥» ·Ê 5.9 ¶ ´¥ ´Ã ¢´  ¥§§¶¬Å ¥» ·Ê 5.11 Å ¥²¤² ·Ê k ¸Ê £· ´¥Â §·Ê¤ ¬ ´ ²Ã ¤n¯ §³

¬¯ ¬n ´ £´ ¸ ¬ ´ ² (1) ©§´ k ³Ê ¹¯ (1,2) ç² (1,3) Â¥¶Ê£ n ² Ï´ ´¥ ³ ³©¯¤m´

¬³ ´ y t n©¤ ´¥Å n Uˆkb 1 2 ç² Uˆkb 1 3  ¹Ê¯Å­nÆ n ykb 2 ç² ykb 3 ´£§Ï´ ³ ´ ³ Ë

Ë ¯ (B-19) ç² ¥³ m´ Ck 1 ´£ ³ Ë ¯ É Ï´ © m´Â£ ¥¶ Hkb 1, 2 ç² Hkb 1,3 ´£ ³ (B-20) Å Ï´ ¯  ·¤© ³ ¬ ´ ²Â¥¶Ê£ n ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ²Ã ¤n¯ §³ ·Ê ·¬º ·Ê

Ë ¯ (B-21) ¬££º ¶©m´ (1,2) ¹¯ ´¥Â §·Ê¤ ¬ ´ ² £´ ¸ ¬ ´ ² (1) ©§´ k ² » §¹¯ ´£ ³

à ¤n¯ §³ ·Ê ·¬º ·Ê£´ ¸ ¬ ´ ² (1) ©§´ k ¸Ê ²Æ n Qkb 1 2 ´ ³ Ë Ï´ ´¥ ¥³ m´¯¯¡Â Ë ¯ (B-22) – (B-24) Ä ¤ m´ ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ à ¤n¯ §³ ³© ³ Æ Uˆkb 1 ´£ ³ Uˆkb 1 ² » Ï ´Æ Å nÅ ´¥ ³ ³©¯¤m´ ¬³ ´ y t Å ¥²¤² ·Ê k – 1 ¯ ´¥Â §·Ê¤ ¬ ´ ²Ã

¤n¯ §³ ·Ê¯¯ £´ ´ ¬ ´ ² (1) ©§´ k ¬º n´¤ Ï´ ´¥ Ï´ © ­´ m´ LLR ¯ ak ³Ê ¹¯

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

©§´ k – 1

(0) –1 –1

Qkb (1) Uˆkb (1) Rˆkb (1)

(1) 1 –1

rˆ 2, 0

aˆ 2, 0

Hbk 1, 2

(2) –1 1

(3) 1 1

k+2

k+1

k

Hbk 1, 3

aˆ 1 aˆ 1

ykb q

¥²¤² ·Ê k (k-th stage)

Uˆkb 1 (2) Rˆkb 1 (2) Qkb 1 (2)

Uˆkb 1 (3)

¥» ·Ê 5.11 à ¢´  ¥§§¶¬ ·ÊÅ n¯ ¶ ´¤ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ PSP-BCJR Å m© ´¥Â©·¤  ¶ à ¤n¯ §³

Mp ak ´£ ³ Ë ¯ (B-27) ¯ ´ ·Ë  ¹Ê¯Â§·Ê¤ ´¥Â ¶ Æ Â ¶§¬§¶ 26 (cycle clip) [10, 11] £¹Ê¯ Uˆkb 1 Â¥¶Ê££· m´Ã m´ ´ Uˆk 1 Å ·Ê ·ËÆ n¬ ¯ ´¥Ã n ³ ­´Ä ¤ ´¥­´ m´Â §·Ê¤¥²­©m´ Uˆkb 1

Æ ´ Uˆk 1 Ä ¤Å ·Ê ·Ë ²Å n ' = 0.1T  ¥´² n¯ ´¥¥³ «´Å­n \Uˆkb ^ £· m´Å §n ·¤ ³ \Uˆk ^

¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¬¥n´ Æ n ´ ´¥ ³ ¶ Ë © ¥ PLL Å ¥» ·Ê 5.8 ç²Ã ¯· ©¯Æ§Â ¯¥q à SISO n©¤£¯ »§ PSP-BCJR

¶ ´¥ ´¥² ·Ê »  n´¥­³¬ (coded system) ·Ê£·¯³ ¥´¥­³¬Â m´ ³ 8/9 ¸Ê §É¯ n¯£»§ ·Ê

£· Ï´ © 3636 ¶ »  n´¥­³¬ n©¤© ¥Â n´¥­³¬ ¯ Ä©§» ³ à £·¥² ©·¤  ¶ (RSC: recursive 3 4 systematic convolutional encoder) ·Ê£· ­º ´£ ³© Ï´Â ¶ ¹¯ ¡1, 1 D D 4D ¯° ç²£·¯³ ¥´¥­³¬ ¢ 1 D D ±  m´ ³ 1/2 ´ ³ Ë É ² » ¬m  n´Æ ¤³ © ¥Â ´² (puncturer) [2]  ¹Ê¯Â ¶Ê£¯³ ¥´¥­³¬ ´ 1/2 Â É 8/9 Ä ¤ ³ ¶ ´¥¶ · Ï´ © 7 ¶ Ã¥ ¶ Ë Å º È 8 ¶  ¹Ê¯ Ï´Å­nÆ nÂ É §Ï´ ³ n¯£»§ ´ 4095

26

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

ç² Uˆk 1 ´£ ³ Ë ¯ (B-25) £¹Ê¯ ' ¹¯ m´ · Â¥¶Ê£Â §·Ê¤ (threshold) ·Ê¤¯£Å­n Uˆkb 1 £· m´ m´

5

บทที่

Æ Â ¶§¬§¶ (cycle slip) £· § Ï´Å­n ´¥ Ï´ ´ ¯ © ¥ PLL  ¶ ´¥Â §·Ê¤ ¬ ´ ² ´ º ¬£ º§ º ­ ¸Ê Æ ¤³ º ¬£ º§ ¯· º ­ ¸Ê ¸Ê ² m¯Å­n ¶ n¯ ¶ §´ Ï´ © £´ ·Ê© ¥ ¥© ­´ ( »§³ « ² ¯ Æ Â ¶§¬§¶ Å ¥» ·Ê 2.9 ¯ [10])

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173

¶ m¯­ ¸Ê   ¯¥q ´ ³ Ë ¸ ¬m m¯Æ ¤³ © ¥¯¶  ¯¥q§·¡Â©¯¥qà ¬mº£ S ·Ê£· S = 16 É ²Æ n

Â É §Ï´ ³ n¯£»§ ak ¯ ´ ·Ë ¯· ©¯Æ§Â ¯¥qà SISO 粩 ¥ ¯ ¥­³¬Ã SISO ¬¥n´ Ä ¤

¯³§ ¯¥¶ ¸£ BCJR ¬m© m´ ´¥´£¶Â ¯¥q ¯ © ¥ PLL ·ÊÅ nÅ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã m´ È ² »

2 ¯¯ à  ¹Ê¯ Ï´Å­n¥´ Ï´§³ ¬¯  §·Ê¤ ¯ n¯ ¶ §´ ´ ©§´ TF E ¡ Uk Uˆk ¯° £· m´ n ¯¤¬º ¢ ±

¥² ³ Eb /N0 = 5 dB ç² m´ BER à m§² m´Æ n£´ ´ ´¥¬m n¯£»§¯¶ º  n´Æ Å ¥² ­§´¤È   ¯¥q ¥² ³ Ê £· n¯ ¶ §´  ¶ ¸Ë ¥©£Æ£m n¯¤ ©m´ 100   ¯¥q ´¥© Ï´Ë Å ¥¯ ·Ê 100

¥» ·Ê 5.12 (a)  ¥·¤  ·¤ ¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã m´ È Vw/T = 0.5%

¸Ê ­£´¤ ¸ ©´£ m ´ ²Â É ·Ê ²Â ¶ Æ Â ¶§¬§¶ Å ¥² £· n¯¤ ¯ ´ ·Ë ³©Â§ ·Ê¯¤m»Å © Â§É Ã¬ Ï´ © ¥¯ ¯ ´¥© Ï´Ë ·ÊÅ n ¹Ê¯ Ï´Å­n ¶ ¬n ¥´¡Ã m§²Â¬n Ä ¤Â¬n ¥´¡ “Perfect timing”

­£´¤ ¸ © ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ ¸Ê Å n Uˆk Uk Å ´¥ ³ ³©¯¤m´ ¬³ ´ y t Å ² ·Ê

¬n ¥´¡ “Genie-aided receiver” ­£´¤ ¸ © ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ ¸Ê © ¥ PLL ²Å n m´ ³ ¬¶ Å ·Ê » n¯ ³ Ë ­£ ( rˆk rk ) Å ´¥ ¥³ m´¯¯¡Â ´ ¡¬ ¯ ´¥ ³ ³©¯¤m´ ³© ³ Æ

³ ³ Ë © ¥¢´ ¥³ à Genie-aided ¸ Ï´­ n ´ ·Ê¬£¹¯ Â É Â q ¥·¤  ·¤ ¬£¥¥ ²¬Ï´­¥³

Æ ££¶Ê ¥¶ ³¡Â©¯¥· º à ·Ê Ï´ ´ Ä ¤Å n© ¥ PLL ´ ¥» ² ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR

£·¬£¥¥ ² · ©m´©¶ · ´¥ NBM 夃 n ¯¤ ´¥© Ï´Ë Å ¥¯ ·Ê 50 ç² ³ Ë ¬¯ à ·Ë £·¬£¥¥ ²

· ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ 27 ¥²£´ 0.45 dB BER = 10-5 ¯ ´ ·Ë Æ ££¶Ê ¥¶ ³¡

©¯¥·Ã PS-ITR £·¬£¥¥ ²Å §n ·¤ ³ © ¥¢´ ¥³ à Genie-aided ç²£·¬£¥¥ ² n¯¤ ©m´ “Perfect timing”  ·¤ 0.35 dB BER = 10-5

Å ¬m© m¯Æ ² ¶ ´¥ ´¥² ·Ê£· Vw/T = 1% ¸Ê ­£´¤ ¸ ©´£ m ´ ²Â É ·Ê ²Â ¶ Æ Â ¶§

¬§¶ Å ¥² £·£´ ¥» ·Ê 5.12 (b)  ¥·¤  ·¤ ¬£¥¥ ² ¯ Æ ££¶Ê ¥¶ ³¡ ©¯¥·Ã m´ È

Vw/T = 1% ¸Ê ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR £·¬£¥¥ ² · ©m´©¶ · ´¥ NBM m¯ n´ £´ ç² ³ Ë ¬¯ à ɣ·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ £´ Å Ï´ ¯  ·¤© ³ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR £·¬£¥¥ ²Å §n ·¤ ³ © ¥¢´ ¥³ à Genie-aided ç²£·¬£¥¥ ² n¯¤ ©m´ “Perfect timing”  ·¤ 0.35 dB BER = 10-5

¬´Â­ º ÊÆ· ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR £·¬£¥¥ ² · ©m´©¶ · ´¥ NBM Ä ¤Â ´²¯¤m´ ¤¶Ê

£¹Ê¯ Vw/T £· m´£´ Â É Â ¥´²©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¬´£´¥ à nÆ Æ Â ¶§¬§¶ Æ n¯¤m´

¯³ Ä £³ ¶Ã§²¥© ¥ɩ£´ ©m´©¶ · ´¥ NBM ¸Ê ¯ ¶ ´¤Æ n n©¤¥» ·Ê 5.13 ¸Ê ì m´ ¥²£´ ¯

¯¯¡Â ´ ¡¬ Uˆk ·ÊÆ n ´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR 粩¶ · ´¥ NBM ¯ n¯£»§¬¯   ¯¥q 27

Å ·Ê ·Ë¤³ ©m´¬£¥¥ ² ¯ © ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ ´¥© Ï´Ë Å ¥¯ ·Ê 50 ç² 100 Æ£m£· ©´£Ã m´ ³ [34] (Æ£mÆ nì Å ¥» ·Ë )

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

¥» ·Ê 5.12  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È Â£¹Ê¯ (a) Vw/T = 0.5% ç² (b) Vw/T = 1% [34]

·Ê m´ ³ £¹Ê¯Â¬n ¥´¡¬·Â ´Ã¬ ¯¯¡Â ´ ©§´ ¥¶ Uk ·Ê ¶ ¸Ë Å ¥² ´ ¥» ·Ê 5.13 (a) ©m´©¶ · ´¥ NBM n¯ Å n ´¥© Ï´Ë £´ ©m´ 150 ¥¯ Å ´¥Ã nÆ Æ Â ¶§¬§¶ ç²Æ ££¶Ê ¥¶ ³¡Â©¯¥·

à PS-ITR Å n ´¥© Ï´Ë Â ·¤ 1 ¥¯  m´ ³ Ë Å ² ·Ê ´ ¥» ·Ê 5.13 (b) ©m´©¶ · ´¥ NBM

n¯ Å n ´¥© Ï´Ë ¥²£´ 50 ¥¯ Å ´¥Ã nÆ Æ Â ¶§¬§¶ ç²Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR Å n

5

บทที่

´¥© Ï´Ë Â ·¤ 5 ¥¯  m´ ³ Ë ³ ³ Ë Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¸ ­£´²¬Ï´­¥³ ´¥ Ï ´£´Å n Å ¥² ·Ê£·¯³ ¥´ ´¥Â ¶ Æ Â ¶§¬§¶ ¬»  m ¥² ·Ê£· ©´£¥º Ã¥ ¯ ¬³ ´ ¥ © £´

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T 0.8T

Timing Estimate

0.6T

50

0.4T

100

1

0.2T

150

NBM scheme 0 -0.2T -0.4T -0.6T -0.8T

Actual W 0

500

1000

1500

Per-survivor iterative timing recovery (1) 2000

2500

3000

3500

4000

3500

4000

(a) Time (in bit periods) 2.5T

Timing Estimate

2T

Actual W

1.5T

5

T

2

0.5T

0

-0.5T

1 Per-survivor iterative timing recovery 0

500

1000

1500

NBM scheme (50) 2000

2500

3000

(b) Time (in bit periods)

¥» ·Ê 5.13 ´¥Ã nÆ Æ Â ¶§¬§¶ ¯ n¯£»§¬¯   ¯¥q Ê · m´ ³ (Eb /N0 = 5 dB ç² Vw /T = 1%)

©´£ ³ n¯ 粬£¥¥ ² ¯ ¥² ¸ ãn©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ²£·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ Ã§²©¶ · ´¥

NBM Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ Vw/T £· m´£´ à mÆ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR £· ©´£ ³ n¯

¬» £´ ³ ³ Ë ´¥Â ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È Â£¹Ê¯ º ¥² £· ©´£ ³ n¯ (complexity)  m´ ³ ¸ Â É ¬¶Ê ·Ê m´¬ Å Ä ¤Å ·Ê ·Ë ² ¶ ´¥ ´ ©´£ ³ n¯ Å ¥» ¯ Ï´ © ³© Ï´Â ¶ ´¥ ©

(addition operator) ç² ³© Ï´Â ¶ ´¥ » (multiplication operator)

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´¥´ ·Ê 5.1 ©´£ ³ n¯ ¯ © ¥¢´ ¥³ (£¹Ê¯¥©£ ©´£ ³ n¯ ¯ © ¥ ¯ ¥­³¬Ã SISO) [35] Ï´ © ³© Ï´Â ¶ ´¥ ´ ¶ ª´¬ ¥q ( m¯­ ¸Ê ¶ )

© ¥¢´ ¥³

´¥ ©

´¥ »

¥©£

86 + 330N

27 + 595N

113 + 925N

NBM

416N

622N

1038N

PS-ITR

1010N

787N

1797N

Genie-aided

85 + 330N

24 + 595N

109 + 925N

Perfect timing

83 + 330N

21 + 595N

104 + 925N

Conventional receiver

´ ·ÊÆ nª¸ «´Å [34, 35] ©´£ ³ n¯ ¯ © ¥¢´ ¥³ à m§²Ã (£¹Ê¯¥©£ ©´£ ³ n¯

¯ © ¥ ¯ ¥­³¬Ã SISO) ¬´£´¥ ì Æ nÅ ´¥´ ·Ê 5.1 £¹Ê¯ N ¹¯ Ï´ © ¥¯ ¯ ´¥

© Ï´Ë n´¬££º ¶©m´ ³© Ï´Â ¶ ´¥ © ç² ³© Ï´Â ¶ ´¥ » £· ©´£ ³ n¯  m´ ³ ç²Â Ä Ä§¤· Å ³ º ³ ¬´£´¥ ¥¯ ¥³ ©´£ ³ n¯ ¥©£ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ·Ê Ï´ ´ ¥ 5

¥¯ ³ ³ Ë ´ ´¥´ ·Ê 5.1 ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ·Ê Ï´ ´ ¥ 5 ¥¯ ²£· ©´£

³ n¯ ( Ï´ © ¥©£ ¯ ³© Ï´Â ¶ ´¥ © ç² ´¥ » )  m´ ³ © ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ ·Ê

Ï´ ´ 10 ¥¯ , ©¶ · ´¥ NBM ·Ê Ï´ ´ 9 ¥¯ , © ¥¢´ ¥³ à Ginie-aided ·Ê Ï´ ´ 10 ¥¯ ,

¥² m´ È Â£¹Ê¯ º ¥² £· ©´£ ³ n¯  m´ ³ ç² Vw/T = 1% ¸Ê ² ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã

PS-ITR ¤³ £·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ 粩¶ · ´¥ NBM ³ Ë ·Ë Â É Â ¥´²©m´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¬´£´¥ à nÆ Æ Â ¶§¬§¶ Æ n¯¤m´ ¥© ¥ɩç²£· ¥²¬¶ ¶¢´

´¥ ¥²¤º qÅ n ´ Å m¯ ¬³ ´ °´¥q ¶¬ qÆ ¥¡q ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ Å ¥» ·Ê 5.8 Ä ¤Â ¶Ê£ §É¯ 'tk  n´Æ ¥²­©m´ §É¯ h(t) ç² Wk

£¹Ê¯ Ï´­ Å­n h(t) = {g(t) – g(t – T)}/2 Ä ¤ ·Ê g(t) ¹¯¬³ ´ ³§¬q §·Ê¤ ¬ ´ ² ¯ ¥²

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

粩 ¥¢´ ¥³ à Perfect timing ·Ê Ï´ ´ 10 ¥¯ ¥» ·Ê 5.14  ¥·¤  ·¤ ¬£¥¥ ² ¯

´¥ ³ ¸ à à © ³ Ë ´£¬£ ´¥ (1.3) ³ ³ Ë ¬³ ´ ¯m´ §³ ¬´£´¥  ·¤ Æ nÂ É [35]

\

^

p t bk g t kT %tk Uk g t k 1 T %tk 1 Uk n t

(5.11)

k

5

บทที่

£¹Ê¯ 'tk ¹¯¬³ ´ ¥ © ¶  ¯¥q ¯ ¬¹Ê¯ ³ ¸ (media jitter noise) ¸Ê » Ï´§¯ Å­n£·§³ « ²

Â É ´¥Â§¹Ê¯ à ¬mº£ ( ϴí m ·Ê£· ´¥Â §·Ê¤ ¬ ´ ² ¯ ¬¢´ ©´£Â É Ã£m­§É Å ¬¹Ê¯ ³ ¸ ) ·Ê£·¡³ q ³ ©´£­ ´Ã m ©´£ m ´ ²Â É Ã Â ´¬q ·¤ ·Ê£· m´Â §·Ê¤Â m´ ³ ª» ¤qç² ©´£Ã ¥ ¥©

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¥» ·Ê 5.14  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È Â£¹Ê¯ º ¥² £· ©´£ ³ n¯  m´ ³ ç² Vw/T = 1%

 m´ ³ bk bk 1 / 2 T j2 ç² » Ï´ ³ Å­n£· m´Æ£m ¶ T/2 Ä ¤ ·Ê Vj ² » Ï´­ Â É Ï´ ©  ¯¥qÂ É q ¯ ¶  §§q T ç² x ¹¯ m´¬³£ »¥ q ¯ x ¯ ´ ·Ë ²Å¬m© ¥¯· ©¯Æ§Â ¯¥qà  ¶ ¬n  n´Æ ¯¤m»¥²­©m´ © ¥ ³ ³©¯¤m´ 粯· ©¯Æ§Â ¯¥qà SISO  ¹Ê¯ Ï´­ n ´ ·Ê ¥³ ¥» ¥m´ ¯ ¬³ ´ ¯m´ §³ ·ÊÆ n¥³ Å­nÂ É Æ ´£ ´¥qÂ É (target) ·Ê n¯ ´¥ Ä ¤ ·Ê ´¥qÂ É Ã§²© ¥¯· ©¯

Ƨ ¯¥q ² » ¯¯ à ¹Ë ´ ¯ à © ¶ ´¥ Ï´Å­n n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤£· m´ n ¯¤¬º

(MMSE: minimum mean-squared error) [10, 14] ¸Ê ´¥qÂ É ·ÊÆ n ·Ë ² Ï ´£´Å n¬¥n´ à ¢´  ¥§§¶¬ ·ÊÅ nÅ ¯· ©¯Æ§Â ¯¥qà SISO

Å ´¥ §¯ ²Å n m´ SNR (£·­ m ©¤Â É dB) ¸Ê ¶ ¤´£Ä ¤ V 2 ¬­ p SNR 10 log10 2 ­­­ Tn ®­

(5.12)

£¹Ê¯ Vp ¹¯ m´Ã¯£ §¶ » ¬» ¬º ¯ ¬³ ´ ³§¬q ´¥Â §·Ê¤ ¬ ´ ²Â¯  ª (isolated transition

pulse) ç² Tn2 N 0 / 2T ¹¯ Ï´§³ ´ ¯ ¬³ ´ ¥ © n(t) ¯ ´ ·Ë n¯£»§­ ¸Ê   ¯¥q

¥² ¯ n©¤ preamble Ï´ © 256 ¶ ç² n¯£»§¯¶ º Ï´ © 4096 ¶ Ä ¤ ·Ê preamble

² » Ŭm n´Æ Å §Ï´ ³ n¯£»§ bk m¯ ¬m §§³ q ÊÆ· n n´Æ Å m¯ ¬³ ´ h(t) Å ² ·Ê © ¥

¢´ ¥³ preamble ·Ë ² » ³ ¶ Ë ·Ê n´ ´¯¯ ¯ © ¥¯· ©¯Æ§Â ¯¥qà  ¶ ¬n m¯ ¬m §§³ q ·ÊÆ nÆ ¤³ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ¯ ´ ·Ë¤³ ¬££º ¶©m´Å ¥² Æ£m£·¯ q ¥² ¯ ¯ ¯¯¡Â

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 5.15  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È ¬Ï´­¥³ m¯ ¬³ ´ ´¥ ³ ¸ à à © ³ Ë ND = 2, Vj /T = 3%, Vw /T = 0.5%, 粯¯¡Â ´ ©´£ ·Ê m´ ³ 0.4%

´ ©´£ ·Ê­§³ ´ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Ï´ ´ ¥ ´¥© Ï´Ë ­ ¸Ê ¥¯ ¸Ê ­£´¤ ©´£©m´©¶ · ´¥

NBM ç²Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¬´£´¥ Å n© ¥ PLL ¯³ ³ ·Ê­ ¸Ê Å ´¥ ¥³ à m n¯£»§ à £Â ¶ §Æ n ­§³ ´ Ï´ ´ ¥ ´¥© Ï´Ë ­ ¸Ê ¥¯

粯¯¡Â ´ ©´£ ·Ê m´ ³ 0.4% ¥² ²Å n ´¥qÂ É ·Ê£· 3 Ã É Ã§²¯· ©¯Æ§Â ¯¥q Ê·£· 21 à É

¸Ê » ¯¯ à m´ SNR ·Ê Ï´Å­n ¶ BER = 10–5 Ä ¤ ´¥qÂ É ·ÊÆ n ¹¯ H(D) = 1 + 1.148D +

0.475D2 ¯ ´ ·Ë ²Å nà ϴ§¯  ¶ ¬n ¯ © ¥ PLL ¯³ ³ ·Ê¬¯ [10, 11] Å ´¥¯¯ Ã

m´ ´¥´£¶Â ¯¥q ¯ PLL Å­n¬´£´¥ ¶ ´£ ´¥Â §·Ê¤ à § ¯ ¡¬Ã§² ©´£ ·ÊÆ n ³ ¢´¤Å 256 ¶ Ä ¤ m´ ´¥´£¶Â ¯¥q ¯ PLL ·ÊÆ n ² » Ï ´£´Å n ³ Ë m© ¢´©² ´¥Æ n£´Ã§² m© ¢´©² ´¥ ¶ ´£

¥» ·Ê 5.15  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È ¸Ê ² ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-

ITR £·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ 粩¶ · ´¥ NBM Ä ¤Â ´²¯¤m´ ¤¶Ê ·Ê m´

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

¶ ´¥ ´ m¯ ¬³ ´ ´¥ ³ ¸ à à © ³ Ë ·Ê ND = 2, Vj /T = 3%, Vw /T = 0.5%,

SNR ¬» È §m´© ¹¯Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR £·¬£¥¥ ² · ©m´©¶ · ´¥ NBM ¥²£´ 1 dB £¹Ê¯ Ï´ ´ ¥ 10 ¥¯ m´ BER = 10-4 ¯¤m´ Æ¥ É ´£Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¤³ £·

¬£¥¥ ² n¯¤ ©m´¥² Perfect timing £´ ³ Ë ·Ë ¯´ Â É Â ¥´²©m´¥²  ¶ ³ ¯¯¡Â ´

©´£ ·Ê Ê·¥º Ã¥ Å ¬m© m¯Æ ² Ï´ ´¥Â ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È Â£¹Ê¯ º ¥² £· ©´£

5

บทที่

³ n¯  m´ ³ ( ¶ ´¥ ´ ´ Ï´ © ³© Ï´Â ¶ ´¥ © ç² ³© Ï´Â ¶ ´¥ » ) ´£ ·ÊÆ nª¸ «´Å

[35] ©´£ ³ n¯ ¯ © ¥¢´ ¥³ à m§²Ã (£¹Ê¯¥©£ ©´£ ³ n¯ ¯ ¯· ©¯Æ§Â ¯¥qà  ¶ ¬n )

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´¥´ ·Ê 5.2 ©´£ ³ n¯ ¯ © ¥¢´ ¥³ (£¹Ê¯¥©£ ©´£ ³ n¯ ¯ ¯· ©¯Æ§Â ¯¥qà  ¶ ¬n ) [35] © ¥¢´ ¥³

Ï´ © ³© Ï´Â ¶ ´¥ ´ ¶ ª´¬ ¥q ( m¯­ ¸Ê ¶ ) ´¥ ©

´¥ »

¥©£

106 + 330N

48 + 595N

154 + 925N

NBM

436N

643N

1079N

PS-ITR

1170N

955N

2125N

103 + 330N

42 + 595N

145 + 925N

Conventional receiver

Perfect timing

¥» ·Ê 5.16  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È Â£¹Ê¯ º ¥² £· ©´£ ³ n¯  m´ ³

ì Å ´¥´ ·Ê 5.2 £¹Ê¯ N ¹¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Å Ï´ ¯  ·¤© ³ ²¬££º ¶©m´ ³© Ï´Â ¶ ´¥ © ç² ³© Ï´Â ¶ ´¥ » £· ©´£ ³ n¯  m´ ³ ç²Â Ä Ä§¤·Å ³ º ³ ¬´£´¥ ¥¯ ¥³

©´£ ³ n¯ ¥©£ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ·Ê Ï´ ´ ¥ 4 ¥¯ ¸Ê ¹¯©m´£· ©´£ ³ n¯

 m´ ³ © ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ ·Ê Ï´ ´ 10 ¥¯ , ©¶ · ´¥ NBM ·Ê Ï´ ´ 8 ¥¯ , 粩 ¥

¢´ ¥³ à Perfect timing ·Ê Ï´ ´ 10 ¥¯ ¥» ·Ê 5.16  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È

£¹Ê¯ º ¥² £· ©´£ ³ n¯  m´ ³ ¸ ãn©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR »Â­£¹¯ ²£·¬£¥¥ ²

n¯¤ ©m´©¶ · ´¥ NBM £¹Ê¯ SNR £· m´ n ¯¤ à m ² ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR £·¬£¥¥ ²

¬» ©m´©¶ · ´¥ NBM £´ £¹Ê¯ SNR £· m´£´ ³Ê ¹¯Â£¹Ê¯¥² Ï´ ´ ¥² ³ SNR ·Ê¬»  ·¤ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ²¬´£´¥ Ï´ ´ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ Ä ¤Å n ´¥© Ï´Ë Æ£m Ê·¥¯

180

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³ ³ Ë ¥² ³ ©´£ ³ n¯ ·Ê n¯¤ ¸ ´ §´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¹¯©m´£·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ 粩¶ · ´¥ NBM Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ SNR £· m´¬» ³ Ë ·Ë

Â É Â ¥´²©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¬´£´¥ à nÆ Æ Â ¶§¬§¶ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ ç² ¥© ¥ɩ£´ ©m´©¶ · ´¥¯¹Ê È

¬¥º ç² n¯Â¬ ¯Ã ² ´ ·Ê §m´©£´Å ­³© n¯ ·Ê 5.1 ²Â­É Æ n©m´ ´¥ Ï ´Â ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë £´ ¥²¤º qÅ n¥m©£ ³

Æ ££¶Ê ¥¶ ³¡Â©¯¥· Ï´Å­nÆ nÂ É © ¥¢´ ¥³ ¥» à ŭ£m Ê·Â¥·¤ ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¸Ê ç  §·Ê¤ m´©¬´¥Ã ¯¡ q¥²­©m´ PSP-BCJR 粩 ¥ ¯ ¥­³¬ ECC Ä ¤ ´ ´¥ §¯ ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR £·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ 粩¶ · ´¥

NBM à m É£· ©´£ ³ n¯ ¬» £´ ( ¹Ê ¯ £´ ´ £¯ »§ PSP-BCJR)

´ ©¶ ³¤Å [65] Æ n ϴ¬ ¯©¶ · ´¥§ ©´£ ³ n¯ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR

Ä ¤ ´¥ Ï ´Ã © ¶ ¯ PSP £´ ¥²¤º qÅ n ³ ¯³§ ¯¥¶ ¸£ SOVA [19] Ï´Å­nÆ nÂ É ¯· ©¯Æ§Â ¯¥q

SOVA à  ¯Â ¯¥qƩ©¯¥q (per-survivor SOVA equalizer) ­¥¹¯Â¥·¤ ©m´ “PSP-SOVA” [65] ´ ³ Ë Â ¯Â ¯¥qƩ©¯¥qÆ ££¶Ê ¥¶ ³¡Â©¯¥·Ã © Ï´Ë ·Ê£· ©´£ ³ n¯ n ¯¤ (RC-PS-ITR: reducedcomplexity per-survivor iterative timing recovery) ²Ã§  §·Ê¤ m´©¬´¥Ã ¯¡ q¥²­©m´ PSP-SOVA 粩 ¥ ¯ ¥­³¬ ECC  m  ·¤© ³ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¸Ê Å n PSP-

´ §´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã RC-PS-ITR ²£·¬£¥¥ ² · ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ç²Æ ££¶Ê ¥¶ ³¡Â©¯¥· ³ Ë ¬¯ à ·Ë ɤ³ £·¬£¥¥ ²¬» ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³ ³Ê©Æ

Ë ¯ ´¥ Ï´ ´ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã m¯ n´ £´ n»¬ Å ¬´£´¥ ª¸ «´¥´¤§²Â¯·¤ ¯ ³

RC-PS-ITR Æ n ´ [35, 65]

5.2 ´¥§ § ¥² ¯ ©´£ ¥º ¥²Â ¶ ©´£¥n¯ à © Ï´Ë

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

BCJR Ä ¤ ´ ´¥ §¯ ©m´ [65] £¹Ê¯ ©´£ ³ n¯ ¯ ¥² » Ï´ ³ Å­n¯¤m»Å ¥² ³ n ¯¤ ¸

Å ¥² © ´¥¯m´ n¯£»§ ¯ ¯º ¥ q°´¥q ¶¬ qÆ ¥q¡ ­³©¯m´ à MR (magneto-resistive) ²

Ï´ ´¥ ¥© ³ ´¥Â §·Ê¤ à § ¯ ¡§³ qãm­§É (magnetic flux) ·Ê ¶ ¸Ë ¥¶Â© ·Ê£· ´¥  §·Ê¤ à § ¬ ´ ² ¯ ¬ ´£Ã£m­§É ¯ ¶ n¯£»§ ·Ê »  ·¤  n´Æ Å ¬¹Ê¯ ³ ¸ ¸Ê Â É § Ï´Å­n Æ nÂ É ¬³ ´ ³§¬q ´¥Â §·Ê¤ ¬ ´ ² (transition pulse) ·Ê n´ ´¯¯ ¯ ­³©¯m´ ³ ³ Ë Â£¹Ê¯

5

บทที่

­³©¯m´  §¹Ê¯ ·Ê n´£´ ³ ©´£ ¥º ¥² (asperity) ¹Ë ¶© ¯ ¬¹Ê¯ ³ ¸ ·Ê ¶ ´ ¯ º¢´ ­¥¹¯ ¬¶Ê à § §¯£Â n´Æ ³ ¶© ¯ ¬¹Ê¯ ³ ¸ É Ï´Å­n ¶ ¬³ ´ Ã¥ ³ Æ¡¡n ´ ³Ê© ² (transient

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181

voltage) £´ ¬£ ³ ¬³ ´ ¯m´ §³ ¸Ê ¬m §Å­n¬n  ¹Ê¯£ ´ (baseline) ¯ ¬³ ´ ¯m´ §³ £· m´Â §·Ê¤ Æ ´£§³ « ² ¯ ¬³ ´ TA (thermal asperity) Ä ¤¬³ ´ Ã¥ ³ Æ¡¡n ´ ³Ê© ²

·Ê ¶Ê£ ¸Ë £´ ·ËÂ¥·¤ ³ ³©Ê Æ ©m´ “¬³ ´ TA” [70]

Ä ¤ ³©Ê Æ ¬³ ´ TA Â É ¬³ ´ ·Ê£· ©´£ ·Ê ÏÊ´, ï£ §¶ » ¬» ¬º ¥²£´ 2 – 3  m´

¯ ï£ §¶ » ¬» ¬º ¯ ¬³ ´ ¯m´ §³ , m© ©§´Â ¶Ê£¥² ³ (rise time) ¥²£´ 60 – 150

´Ä ©¶ ´ · ·Ê£·§³ « ² ´¥Â ¶Ê£¥² ³ à  ¶ ¬n , ç² m© ©§´§ ¥² ³ (decay time) ¥²£´ 1 – 5 Æ£Ä ¥©¶ ´ · ·Ê£·§³ « ² ´¥§ ¥² ³ à § · Ë Ï´§³ (exponential decay) [70] Å ´

¶ ³ ¶¬³ ´ TA ²¬m § Ï´Å­n ¶ n¯ ¶ §´ Â É Ï´ © £´ ¸Ê  ¶ · ©´£¬´£´¥ ¯ ¥­³¬

ECC ·Ê ² ³ ´¥Æ n Ä ¤ ³©Ê Æ ¥² © ´¥ §¶ °´¥q ¶¬ qÆ ¥q¡£· ³ Ë ¯ ´¥ ¥© ­´ ©´£ ¥º ¥²

·Ê ¶ ¸Ë ¬¹Ê¯ ³ ¸ Ä ¤Â£¹Ê¯ ©´£ ¥º ¥² ¬¹Ê¯ ³ ¸ É ² Ï´Â ¥¹Ê¯ ­£´¤ ϴí m ·Ê£· Ë ¯ ·Ë ©´£ ¥º ¥² ³ §m´©  ¹Ê¯Æ£mÅ­n­³©Â ·¤ £´ ³ ¸ n¯£»§ ϴí m ³ Ë ¯¤m´ Æ¥ É ´£ ³

Æ£m¬´£´¥ Ï´Æ n ¥ º ϴí m ·Ê£· ©´£ ¥º ¥²Â ¶ ¸Ë 28 [71] ³ ³ Ë Â ¶ ´¥ ¥© ­´Ã§²Ã nÆ

TA ¸ Â É ¬¶Ê Ï´Â É ¯¤m´ ¤¶Ê ¬Ï´­¥³ ¥² ´¥ ³ ¸ n¯£»§Â ¶ ãm­§É

§ ¥² ·Ê ¶ ´ TA Â É ³ ­´ ·Ê¬Ï´ ³ £´ Å °´¥q ¶¬ qÆ ¥q¡  ¥´²¯´ £· § Ï´Å­n

Æ ££¶Ê ¥¶ ³¡Â©¯¥·Â ¶ ´¥¬» ¬·¤ ´¥Â n´ ³ ­©² ­¥¹¯ Ï´Å­n ¶ ´¥¯m´ n¯£»§ n´£Ã ¥É (off-track)

³ ³ Ë n´Æ£m£· ´¥§ § ¥² ¯ TA É ² Ï´Å­n¬£¥¥ ² ¯ ¥² n¯¤§ £´ ç² Ï´Å­n ¶

n¯ ¶ §´ Â É Ï´ © £´ Å ­ ¸Ê Â É Â ¯¥qÆ n ¯ ´ ·Ë £¹Ê¯°´¥q ¶¬ qÆ ¥q¡£· ©´£ º¬» ¸Ë É£·

§ Ï´Å­n¥²¤²­m´ ¥²­©m´ ­³©¯m´ 粬¹Ê¯ ³ ¸ (fly height) n ¯¤§ ¤¶Ê ¸Ë ( ³ º ³ n ¯¤ ©m´ 10

´Ä £ ¥) ¸Ê ­£´¤ ©´£©m´Ä¯ ´¬ ·Ê­³©¯m´ ²Â §¹Ê¯ ·Ê£´ ³ ¯ º¢´ Å È ¬¹Ê¯ ³ ¸ É£·

©´£Â É Æ Æ n¬» £´ ¸Ë  ¥´² ² ³ Ë ´¥Ã nÆ ³ ­´Â¥¹Ê¯ TA ¸ Â É ¬¶Ê ·Ê n¯ Ï´ ¸ ¸ ¯¤m´ £´

¬Ï´­¥³ °´¥q ¶¬ qÆ ¥q¡¥mº Å­£m Ê£ · · ©´£ º n¯£»§¬»

Å ³ º ³ ´ ©¶ ³¤ ·Ê ·Ê¤© ³  ¶ ´¥ ¥© ­´Ã§²Ã nÆ TA £· Ï´ © £´  ¹Ê ¯ ´

¬³ ´ ¯m´ §³ ·ÊÆ£m£· § ¥² ¯ ¬³ ´ TA ²£· m´Â §·Ê¤ ¯ ¬³ ´ ¯m´ §³ (­¥¹¯

¬n  ¹Ê¯£ ´ ) £· m´Â m´ ³ ª» ¤q  ¥´² ² ³ Ë Klaassen ç² Peppen [72] Æ n ϴ¬ ¯Â ¶ ´¥

¥© ­´ ´¥Â ¶ ¯ ¬³ ´ TA Ä ¤Å n ¶ ´¥­´ · Â¥¶Ê£Â §·Ê¤ (threshold-based approach)

¸Ê ²Â ¥·¤  ·¤ ¬³ ´ ¯m´ §³ ç² m´Â §·Ê¤ ¯ ¬³ ´ ¯m´ §³ ´ ³ Ë É Ï´ ´¥§ § ¥²

¯ TA Ä ¤ ´¥ Ï ´¬³ ´ ¯m´ §³ Æ m´ © ¥ ¥¯ m´ ¬» Å ² ·Ê Dorfman ç² Wolf [73] Æ n¬ ¯Â ¶ ´¥§ § ¥² ¯ TA Ä ¤ ´¥ Ï ´¬³ ´ ¯m´ §³ Æ m´ © ¥ ¥¯ (1 – D)

£¹Ê¯ D ¹¯ ³© Ï´Â ¶ ´¥­ m © ©§´­ ¸Ê ­ m ©¤ ¸Ê £¹Ê¯ Ï ´Â ¶ ·Ë Æ §¯ ³ m¯ ¬³ ´ ´¥ 28

Å ¥²­©m´ ´¥Å n ´ °´¥q ¶¬ qÆ ¥¡q ¬¹Ê¯ ³ ¸ ¯´ ²Â ¶ ©´£ ¥º ¥² ¸Ë £´Å­£m¯ ­¥¹¯£·¬Ê¶ ¬ ¥ § Æ ¬¹Ê¯ ³ ¸ ÉÆ n

182

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³ ¸ à à © ¯ (longitudinal recording) ·ÊÅ n ´¥qÂ É EPR4 ©m´¬£¥¥ ² ¯ ¥² · ¸Ë £´ à m ɤ³ £· ³ ­´Â ·Ê¤© ³ ¬­¬³£ ³ q ¯ ¬³ ´ ¥ © ·Ê ¶ ¸Ë Å ¥² ¸Ê m¯£´Æ n

£· ´¥ ¥³ ¥º ¬£¥¥ ²Ä ¤¥©£ ³ Ë ­£ ¯  ¶ ·ËÄ ¤¯´ª³¤© ¥ Ï´ ´¤¬³ ´ ¥ © (noise

predictor) Å [74] ¯¤m´ Æ¥ É ´£Â ¶ ·Ê ϴ¬ ¯Å [73, 74] Æ£m­£´² ·Ê ² Ï ´£´Å nÅ m¯ ¬³ ´

´¥ ³ ¸ à à © ³ Ë Â ¹Ê ¯ ´ m¯ ¬³ ´ ´¥ ³ ¸ à à © ³ Ë £·¯ q ¥² ¯ Æ¡¡n ´ ¥²Ã¬ ¥

£´ ³ ³ Ë ¬Ï´­¥³ m¯ ¬³ ´ ´¥ ³ ¸ à à © ³ Ë Erden ç² Kurtas [71] Æ n ϴ¬ ¯©¶ · ´¥

§ § ¥² ¯ ¬³ ´ TA Ä ¤¯´ª³¤© ¥ ¥¯ m´ Ïʴ粩 ¥ ¥¯ m´ ¬» Å ² ·Ê Mathew ç² Tjhia [75] Æ n¬ ¯©¶ · ´¥ ¥© ­´Ã§²Ã nÆ TA à m´¤ ·ÊÆ£m ³ n¯ Ä ¤ ´¥­´ m´Â §·Ê¤ ¯ ¬³ ´ ¯m´ §³  ¹Ê¯ Ï ´£´Å nÅ ´¥ ¥© ­´ ϴí m ´¥Â ¶ TA ´ ³ Ë ´¥Ã nÆ TA Ï´Æ n

Ä ¤ ´¥ Ï ´ m´Â §·Ê¤ ·ÊÆ n£´§ ¯¯ ´ ¬³ ´ ¯m´ §³ ·Ê£· § ¥² ¯ TA É ²Æ n¬³ ´

¯m´ §³ ·Ê£· § ¥² ¯ TA n ¯¤§ ¯¤m´ Æ¥ É ´£¬³ ´ TA ·Ê¬¥n´ ¸Ë £´Ä ¤©¶ · ·Ë¤³ Æ£m ·

 m´ ·Ê ©¥  ¥´² ² ³ Ë Kovintavewat ç² Koonkarnkhai [76] Æ n¬ ¯Â ¶ ´¥ ¥²£´ m´ ¬³ ´ TA Ä ¤Å n ¶ ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£ (curve fitting technique)  ¹Ê¯Å nÅ ´¥

¬¥n´ ¬³ ´ TA ¸Ë £´Å­£m ¸Ê ©¶ · ·Ë£·¬£¥¥ ² · ©m´Â ¶ à ·ÊÅ n ³ ³Ê©Æ £´ ¯ ´ ·Ë ¤³ £· ©´£ ´ m¯ ´¥Â §·Ê¤ à § ¯ ï£ §¶ » ¬» ¬º ¯ ¬³ ´ TA n©¤

Å ­³© n¯ ·Ë ²Ã¬ ©¶ · ´¥ Ï ´Â ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë £´ ¥²¤º qÅ n¥m©£ ³ ¯³§ ¯¥¶ ¸£

¥© ­´Ã§²Ã nÆ TA ·Ê ϴ¬ ¯Å [76] Ï´Å­nÆ nÂ É “©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë ” TA 粯· ©¯Æ§Â ³ à  ¯¥qÄ Ä ¤ ´ § ´¥ §¯ ©m´©¶ · ´¥§ § ¥² ¯ TA Ã

© Ï´Ë £·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ ( ¸Ê Ï´ ¥² © ´¥ ¥© ­´Ã§²Ã nÆ TA 粯· ©¯Æ§Â ³ à  ¯¥qÄ Ã¤ ´ ³ ¯¤m´ ¯¶¬¥²) m¯ n´ £´

5.2.1 à ϴ§¯ m¯ ¬³ ´ ¥» ·Ê 5.17 ì à ϴ§¯ m¯ ¬³ ´ ·Ê »  n´¥­³¬ £¹Ê¯ H D k hk D k

1 2D D 2

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

(iterative TA suppression) [77] ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ ¥² © ´¥ ¥© ­´Ã§²Ã nÆ

¹¯ m¯ ¬³ ´ à PR2 §Ï´ ³ n¯£»§ xk {0, 1} ² » ¬m  n´© ¥Â n´¥­³¬ LDPC ç² »

 n´ m» (mapping) Ï´Å­nÆ nÂ É §Ï´ ³ n¯£»§ ak {r1} ·Ê£· ´ ©§´ ¯ ¶  m´ ³ T  ¥´² ² ³ Ë

¬³ ´ ¯m´ §³ p(t)  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯

p t k rk s t kT n t u t

(5.13)

5

บทที่

º ¯ m¯ ¬³ ´ ·Ê ¥´ª ´ ¬³ ´ ¥ © , Ä ¤ ·Ê rk = ak hk {0, r2, r4} ¹¯ n¯£»§Â¯´ q

¹¯ ³© Ï´Â ¶ ´¥ ¯ Ä©§» ³ , s(t) = sin(St/T)/(St/T) ¹¯¬³ ´ ³§¬qÆ ©¶ ¬q¯º £ ¶ [16],

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

183

xk

yk

rk

ak

tk kT

yk

xˆk

zk

r k

Mk

¥» ·Ê 5.17 à ϴ§¯ m¯ ¬³ ´ ¥n¯£ ³ Ë ©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë

n(t) ¹¯¬³ ´ ¥ © AWGN ·Ê£· ©´£­ ´Ã m ¬Â ¥³£ Ï´§³ à ¬¯ n´ N0/2, ç² u(t) ¹¯¬³ ´ TA

© ¥¢´ ¥³ ¬³ ´ ¯m´ §³ ² » ¥¯ n©¤© ¥ ¥¯ m´ ÏÊ´¯º £ ¶ (ideal LPF)

·Ê£· § ¯ ¬ ¯ ¯¶£ ³§¬q m´ ³ s(t)/T  ¹Ê¯ Ï´ ³ ¬³ ´ ¥ © ·Ê¯¤m» ¯ à ©´£ ·Ê ´ ³ Ë

É ² » Ï´ ´¥ ³ ³©¯¤m´ ¬³ ´ n©¤¯³ ¥´Â¥É© 500 £ ² ¶ m¯©¶ ´ · [75] Ä ¤¬££º ¶©m´£· ´¥Â n´ ³ ­©²¯¤m´ ¬£ »¥ q §Ï´ ³ n¯£»§ yk ·ÊÆ n ² » ¬m m¯Æ ¤³ © ¥ ¥© ­´Ã§²Ã nÆ TA  ¹Ê¯Å­nÆ n

Â É §Ï´ ³ n¯£»§ zk ·Ê£· § ¥² ´ TA § §

¬Ï´­¥³ © ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ ¸Ê Å n ´¥ ¯ ¥­³¬Ã © Ï´Ë ( ³Ê ¹¯¥» ·Ê 5.17 ²

Æ£m£· §É¯ “Soft decision” ç²Â¬n §» ª¥¬·Â ´) Ä ¤Â£¹Ê¯ Ï´ ´¥§ § ¥² ´ TA çn© §Ï´ ³ n¯£»§ zk ² » ¬m  n´Æ ¤³ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ¸Ê ² Ï´ ´¥Ã§  §·Ê¤ n¯£»§¥²­©m´ ¯· ©¯

Ƨ ¯¥q SOVA ( ³Ê ¹¯© ¥ ¥© ­´ ·Ê¬¥n´ ´ ¯³§ ¯¥¶ ¸£ SOVA) [19] 粩 ¥ ¯ ¥­³¬ LDPC [17] ç² ² Ï´ ´¥¬m m´©¬´¥Ã ¯¡ q {Ok} §³ Æ ¤³ ¯· ©Æ§Â ¯¥q SOVA ¯· ¥³ Ë ´£ Ï´ ©

¥¯ ¯ ´¥© Ï´Ë ·Ê Ï´­ Æ©n m¯ ²Å­n §§³ qÂ É m´ ¥²£´ ¯ §Ï´ ³ n¯£»§ xˆk  ¥´² ² ³ Ë ²Â­É Æ n©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ ²Æ£m£· ´¥Å n ¥²Ä¤ q ´ m´©¬´¥Ã ¯¡ q£´ m©¤§

§ ¥² ´ TA

5.2.2 à ϴ§¯ ¬³ ´ TA Å ¬m© ·Ë ²¯ ¶ ´¤Ã Ï´§¯ ¬³ ´ TA ·Ê ¶¤£Å n ³ ³©Ê Æ ¸Ê Ï ´Â¬ ¯Ä ¤ Stupp et al. [70]

 ¹Ê ¯ ´ £· ©´£¬¯ §n¯ ³ ¬³ ´ ·ÊÆ n ´ ­³©¯m´ ¯ °´¥q ¶¬ qÆ ¥q¡ ¥» ·Ê 5.18 ì Ã

184

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

A0

t Tr

Tf

¥» ·Ê 5.18 à ϴ§¯ ¬³ ´ TA

Ï´§¯ ¯ ¬³ ´ TA ¸Ê £· m© ©§´Â ¶Ê£¥² ³ ¯¤m´ ¥© ¥ɩç²£· m© ©§´§ ¥² ³ ¯¤m´ n´È à § · Ë Ï´§³ Ä ¤¬´£´¥  ·¤ Å­n¯¤m»Å ¥» ¯ ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯ [75]

£¦A t / Tr , 0 b t b Tr u (t ) ¦¤ 0 ¦¦¥A0 exp( (t Tr ) / Td ), Tr t b Tf Ä ¤ ·Ê A0 = N

k

(5.14)

hk ¹¯Ã¯£ §¶ » ¬» ¬º ¯ ¬³ ´ TA, N ¹¯ ³© ¥² ¯ m´¬» ¬º (peak

¬³ ´ TA ³ Ë ­£ ¸Ê Å ·Ê ·Ë Ï´­ Å­n Tf = Tr + 4Td £¹Ê¯ m© ©§´§ ¥² ³ £· m´Â m´ ³ 4Td

¸Ê  ·¤ ¯ ·Ê ² Ï´Å­nï£ §¶ » ¯ ¬³ ´ TA § § ­§¹¯Â ·¤ 1.8% ¯ ï£ §¶ » ¬» ¬º ¯

¬³ ´ TA

5.2.3 ©¶ · ´¥ ¥© ­´Ã§²Ã nÆ TA Å ­ ³ ¬¹¯ ·Ë ² ¶ ´¥ ´Â ´²©¶ · ´¥ ¥© ­´Ã§²Ã nÆ TA ·Ê¯¤m» ¹Ë ´ ¯  ¶ ´¥ ¥³

¬n Ä n ·Ê­£´²¬£ ·Ê ϴ¬ ¯Å [76]  ¥´²Æ£m ³ n¯ ´ m¯ ´¥Â §·Ê¤ à § ¯ ï£ §¶ »

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

factor), Tr ¹¯ m© ©§´Â ¶Ê£¥² ³ , Td ¹¯ m´ ³© ¯ ´¥§ ¥² ³ , ç² Tf ¹¯ m© ©§´ ´¥Â ¶

¬» ¬º ¯ ¬³ ´ TA ç²£·¬£¥¥ ² · ©m´©¶ · ´¥ ·Ê ϴ¬ ¯Å [75] Ä ¤ ´¥ ¥© ­´ ´¥Â ¶ ¯ TA ²¯´ª³¤­§³ ´¥ ·Ê©m´Â£¹Ê¯ TA  ¶ ¸Ë Å ¥² ² Ï´Å­n m´Â §·Ê¤ ¯ ¬³ ´ ¯m´ §³ (­¥¹¯Â¬n  ¹Ê¯£ ´ ) £· m´Æ£m m´ ³ m´ª» ¤q ¸Ê m´Â §·Ê¤ ·Ë­´Æ n ´ [75] qk

1 k H yi L i k H

5

บทที่ (5.15)

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185

£¹Ê¯ L ¹¯ ©´£ ©n´ ¯ ­ n ´ m´ ·ÊÅ n­´ m´Â §·Ê¤ (Â É Â§ Ï´ ©  ɣ ·Ê), H = (L – 1)/2, ç² yi ¹¯Ã £Â ¶ § n¯£»§ ³© ·Ê i ¯ ¬³ ´ ¯m´ §³ Ä ¤ ²£· ´¥ ¥© ´¥Â ¶ ¸Ë ¯ TA Å ¥² É m¯Â£¹Ê¯ qk * £¹Ê¯ * ¹¯ m´ · Â¥¶Ê£Â §·Ê¤ (threshold value)

­§³ ´ ·Ê£· ´¥ ¥© ¬³ ´ TA ¥² © ´¥ ¥© ­´ TA É ²­¤º Ï´ ´ ´ ³ Ë

²Â¥¶Ê£ ¥² © ´¥Ã nÆ TA Â É ¥²¤²Â©§´ Tf  ¹Ê¯­´ m´ ¥²£´ ¯ ¬³ ´ TA ³Ê ¹¯ û t

Ä ¤Å n ¶ ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£Ã Ï´§³ ¬¯ n ¯¤¬º (least square) ç² n¯£»§ {qk} [76]

Å ´¥ ¥²£´ m´¬³ ´ TA Å m© ©§´Â ¶Ê£¥² ³ ç² m© ©§´§ ¥² ³ ³ ¥´¤§²Â¯·¤ m¯Æ ·Ë ´¥ ¥²£´ m´¬³ ´ TA Å m© ©§´Â ¶Ê£¥² ³

£¹Ê¯£· ´¥ ¥© ´¥Â ¶ ¯ ¬³ ´ TA É ² Ï´ ´¥Â É Ã £Â ¶ § n¯£»§ ¯ m´Â §·Ê¤ {qk} ³ Ë Ã m

ϴí m ·Ê ¥© TA ¸ m´¬» ¬º ¯ qk  ¹Ê¯Å nÅ ´¥ ¥²£´ m´¬³ ´ TA Å m© ©§´  ¶Ê£¥² ³ Ä ¤Å n©¶ · ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£Ã  ¶ ¬n ¸Ê £·¥» ¬£ ´¥ ¹¯ uˆr t at b

(5.16)

£¹Ê¯ uˆr t ¹¯ m´ ¥²£´ ¯ ¬³ ´ TA Å m© ©§´Â ¶Ê£¥² ³ ç² {a, b} ¹¯ m´¬³£ ¥²¬¶ ¶ Î ¯ ¬£ ´¥Â ¶ ¬n ·ÊÂ É Â§ Ï´ © ¥¶ ¸Ê ­´Æ n ´ ´¥Ã n¬£ ´¥ m t2 ¡ i 1 i ¡ m ¡ ¡¢ i 1 ti

m t ¯° a ¯ ¡ i 1tiqi ¯° °¡ ° ¡ ° m ° ¡¢b °± ¡ ° m ° ¡¢ i 1qi °± ±

m

i 1 i

(5.17)

£¹Ê¯ qi = q(iT) ¹¯ m´Â §·Ê¤§Ï´ ³ ·Ê i ¯ ¬³ ´ ¯m´ §³ , ti ¹¯Â©§´ ·Ê¬¯ §n¯ ³ qi, ç²

m ¹¯ Ï´ © à £Â ¶ § ·ÊÅ nÅ ´¥ ¥²£´ m´ TA Å m© ©§´Â ¶Ê£¥² ³

´¥ ¥²£´ m´¬³ ´ TA Å m© ©§´§ ¥² ³ ´¥ ¥²£´ m´¬³ ´ TA Å m© ©§´§ ¥² ³ ²Å nà £Â ¶ § n¯£»§ qk ³ Ë Ã m qj Æ ¸ q j 4Td £¹Ê¯ j ¹¯ ϴí m m´¬» ¬º ¯ {qk} Ä ¤ ·Ê ´¥ ¥²£´ m´¬³ ´ TA Å m© ©§´§ ¥² ³ ·Ë ²Å n ¶ ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£Ã § · Ë Ï´§³ ·Ê£·¥ » ¬£ ´¥ ¹¯ [76] uˆd t Ae Bt

186

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(5.18)

£¹Ê¯ uˆd t ¹¯ m´ ¥²£´ ¯ ¬³ ´ TA Å m© ©§´§ ¥² ³ ç² {A, B} ¹¯ m´¬³£ ¥²¬¶ ¶ Î ¯ ¬£ ´¥ (5.18) ·ÊÂ É Â§ Ï´ © ¥¶ Ä ¤ m´¬³£ ¥²¬¶ ¶ Î A ­´Æ n ´ A exp Z £¹Ê¯

t q q ln q t q t q ln q

Z q t q t q

n

i 1

n

2 i i

n

i 1

n

i

i

n

i 1

i

i 1

i 1

n

i i n

2 i i

i 1

i i

i 1

i

2

2 i i

(5.19)

ç² m´ m´¬³£ ¥²¬¶ ¶ Î B ­´Æ n ´

B

n i 1

qi i 1 tiqi ln qi i 1 tiqi i 1 qi ln qi

n

n

i 1 qi i 1 ti2qi n

n

n

t q

n

i 1

2 i i

2

(5.20)

£¹Ê¯ n ¹¯ Ï´ © à £Â ¶ § ¯ {qk} ·ÊÅ nÅ ´¥ ¥²£´ m´ ¯ ¬³ ´ TA Å m© ©§´§ ¥² ³

Ä ¤ ·Ê ´¥ ¥²£´ m´ ¯ ¬³ ´ TA Å m© § ¥² ³ ²¬¶ Ë ¬º É m¯Â£¹Ê¯ uˆd t 0.01 ´¥Ã nÆ TA

­§³ ´ ·ÊÆ n m´ ¥²£´ ¯ ¬³ ´ TA Å Ã m§²¬m© çn© ÉÅ­n Ï´£´¥©£ ³ Â É m´ ¥²£´ ¯

£ ˆ ¦ ¦uˆr t , Ty b t b Tp uˆ t ¤ ˆ ˆ ¦ ˆ ¦ ¦ ¥ud t , Tp b t b Tf

(5.21)

Ä ¤ ·Ê Ty ¹¯Â©§´ ·Ê ¥© ¬³ ´ TA, Tˆp ¹¯Â©§´Â£¹Ê¯Ã £Â ¶ § {qk} £· m´¬» ¬º , ç² Tˆf ¹¯ m´ ¥²£´ m© ©§´ ¯ ¬³ ´ TA ³ ³ Ë ¬³ ´ ¯m´ §³ ·Ê£· § ¥² ¯ TA n ¯¤§ ­´ Æ n ´

£yk uˆk , if TA is present ¦ , zk ¦ ¤ ¦ if TA is absent ¦ ¥yk ,

(5.22)

£¹Ê¯ uˆk uˆ kT ¹¯ m´ ¥²£´ ¯ ¬³ ´ TA §Ï´ ³ ·Ê k ´ ³ Ë © ¥¢´ ¥³ à ·ÊÅ n ³

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

¬³ ´ TA ³Ê ¹¯ û t ´£¬£ ´¥ m¯Æ ·Ë

5

บทที่

³©Ê Æ É ²¬m §Ï´ ³ n¯£»§ zk Æ ¤³ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ¸Ê ²Ã§  §·Ê¤ m´©¬´¥¥²­©m´ ¯· ©¯

Ƨ ¯¥q SOVA [19] 粩 ¥ ¯ ¥­³¬ LDPC [17] ´£ Ï´ © ¥¯ ·Ê n¯ ´¥

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187

5.2.4 ©¶ · ´¥ ¥© ­´Ã§²Ã nÆ TA à © Ï´Ë Å ´ ¶ ³ ¶© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ ² Ï´ ¥² © ´¥ ¥© ­´Ã§²Ã nÆ TA Ä ¤Æ£mÆ nÅ n ¥²Ä¤ q ´ ¥­³¬ ECC ¸ Ï´Å­n£·¬£¥¥ ²Æ£m · £¹Ê¯ Ï´ ´ ·Ê m´ SNR ÏÊ´ ³ ³ Ë Â ¹Ê¯Å­n¥²

¬´£´¥ Ï´ ´ ·Ê m´ SNR ÏÊ´Æ n¯¤m´ £· ¥²¬¶ ¶¢´ Kovintavewat ç² Koonkarnkhai [77] ¸ Æ n ϴ¬ ¯ “©¶ · ´¥ ¥© ­´Ã§²Ã nÆ TA à © Ï´Ë ” £¹Ê¯© ¥ ¥© ­´Ã§²Ã nÆ TA, ¯· ©¯

Ƨ ¯¥qà SOVA, 粩 ¥ ¯ ¥­³¬ LDPC ²Ã§  §·Ê¤ m´©¬´¥¥m©£ ³ ´£ ·Êì Å ¥» ·Ê 5.17 ¸Ê ¬´£´¥ ¯ ¶ ´¤ ³ Ë ¯ ´¥ Ï´ ´ Æ n ³ ·Ë

n´ Ï´­ Å­n ¥³ Ë Ã¥ ·Ê© ¥ ¯ ¥­³¬ LDPC Å­n n¯£»§Â¯´ q º Å ¥» m´©¬´¥Ã ¯¡ q

Mk ¯¯ £´ Â¥·¤ ©m´ “ ´¥© Ï´Ë ¥¯ ·Ê­ ¸Ê (first iteration)” ³ ³ Ë ©¶ · ´¥ ·Ê ϴ¬ ¯ ²£· ³ Ë ¯

´¥ Ï´ ´ Å ¥¯ Ã¥ ¯ ´¥© Ï´Ë Â­£¹¯ ³ © ¥¢´ ¥³ ·ÊÅ n ³ ³Ê©Æ ³Ê ¹¯¬³ ´ ¯´ q º

¯ © ¥ ³ ³©¯¤m´ {yk} ² » ¬m  n´Æ ¤³ © ¥ ¥© ­´Ã§²Ã nÆ TA ( ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 5.2.3)

Ï´Å­nÆ nÂ É §Ï´ ³ n¯£»§ {zk} ¸Ê ² » ¬m m¯Æ ¤³ ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ­§³ ´ ´¥© Ï´Ë ¥¯ ·Ê­ ¸Ê ¬¥É m´©¬´¥Ã ¯¡ q {Ok} ² » ¬m §³ Æ ¤³ © ¥ ¥© ­´Ã§²Ã nÆ TA ç²

¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ( »¥» ·Ê 5.17)  ¹Ê¯ Ï ´Æ Å nÅ ´¥­´ m´ ¥²£´ à ¯¡ q ¯ §Ï´ ³ n¯£»§ {rk} [77] ³Ê ¹¯ \r k ^ £¹Ê¯ ( »¢´ © ) r k E <rk | Mk >

C 1 C 2 C 3 2 cosh Mk / 2 cosh Mk 1 / 2 cosh Mk 2 / 2

(5.23)

Ä ¤ ·Ê E[.] ¹¯ ³© Ï´Â ¶ ´¥ ´ ­£´¤, C1 2sinh Mk Mk 1 Mk 2 / 2 , C 2 sinh Mk

Mk 1 Mk 2 / 2 , ç² C 3 sinh Mk Mk 1 Mk 2 / 2

Å ´¥© Ï´Ë ¥¯ ·Ê¬¯ ¸Ë Æ ©¶ · ´¥ ·Ê ϴ¬ ¯ ² Ï ´§Ï´ ³ n¯£»§ \r k ^ ·ÊÆ n ´ ¬£ ´¥ (5.23) Æ § ¯¯ ´ ¬³ ´ ¯m´ §³ {yk} Ï´Å­nÆ n ck yk r k ³Ê ¹¯ n´ \r k ^ £· m´Â m´ ³ {rk} É

² Ï´Å­n {ck} ­§¹¯Â ·¤ ¬³ ´ ¥ © 粬³ ´ TA  m´ ³ Ë 29 ´ ³ Ë ²¬m §Ï´ ³ n¯£»§ ck  n´ ¥² © ´¥ ¥© ­´Ã§²Ã nÆ TA Å­£m¯· ¥³ Ë ¸Ê Ï´Å­n ¶ ´¥ ¥²£´ m´¬³ ´ TA n©¤Â ¶ ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£Ã Ï´§³ ¬¯ n ¯¤¬º [76] Å Ã m§²¥¯ ¯ ´¥© Ï´Ë Ï´ ´ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ £´ ¸Ë ³Ê ¹¯ Ï´Å­n§Ï´ ³ n¯£»§ {zk} ·ÊÆ n£· º ¢´ · ¸Ë ¸Ê É ²

¬m §Å­n¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Ï´ ´ Æ n · ¸Ë ´£Æ n©¤ ³ ³ Ë ²Â­É Æ n©m´¯· ©¯Æ§Â ¯¥qÃ

29

 ¶ ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£Ã Ï´§³ ¬¯ n ¯¤¬º [75] ¬´£´¥ ­´ m´ ¥²£´ ¯ ¬³ ´ TA Æ n¯¤m´ » n¯ n´¬³ ´ ·ÊÆ n¥³ ¥² ¯ n©¤¬³ ´ TA 粬³ ´ ¥ ©  m´ ³ Ë

188

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

 ¯¥qÄ Æ n ¥²Ä¤ q ´ §Ï´ ³ n¯£»§ {zk} ·Ê£· º ¢´ £´ ¸Ë 粩 ¥ ¥© ­´Ã§²Ã nÆ TA É Æ n ¥²Ä¤ q ´ m´ ³ ¬¶ Å Ã ¯¡ q \r k ^ ·Ê£· º ¢´ £´ ¸Ë  m ³

´ ·Ê¯ ¶ ´¤Å n´ n ©m´©¶ · ´¥ ·Ê ϴ¬ ¯ [77] É ¹¯¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ Ã

·ÊÅ n ³ ³©Ê Æ Â ·¤ à m£· ³ Ë ¯ ´¥§ § ¥² ¯ TA à ¥  n´Æ Å Ã m§²¥¯ ¯ ´¥© Ï´Ë

¸Ê §§³ q ÊÆ· n É ¹¯ ¬³ ´ ¯m´ §³ ²£· § ¥² ¯ TA § § £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë Å ´ ¶ ³ ¶© ¥ ¥© ­´Ã§²Ã nÆ TA £· ©´£ ³ n¯ n ¯¤£´ £¹Ê¯Â ·¤ ³ ¯· ©¯Æ§Â ¯¥q

à  ¯¥qÄ ³ ³ Ë ¯´ §m´©Æ n©m´©¶ · ´¥ ·Ê ϴ¬ ¯£· ©´£ ³ n¯ ¥©£Å §n ·¤ ³ © ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ ¸ Ï´Å­n¬´£´¥ £´Å n ´ ¥¶ Å ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q Æ n

5.2.5 § ´¥ §¯ ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ Å ¥» ·Ê 5.17 Ä ¤ ·Ê§Ï´ ³ n¯£»§¯¶ º {xk} Ï´ © 3640 ¶

»  n´¥­³¬ n©¤¥­³¬ LDPC ¥ ¶Ã (3, 27) ·Ê£·¯³ ¥´¥­³¬Â m´ ³ 8/9 [17, 77] Ï´Å­n É

§Ï´ ³ n¯£»§ {ak} Ï´ © 4095 ¶ £¹Ê¯Â£ ¥¶ q ´¥¶ ·Â É Å Ã m§²­§³ £·Â§ ­ ¸Ê Ï´ © 3 ³©

ç²Å à m§²Ã ©£·Â§ ­ ¸Ê Ï´ © 27 ³© Ä ¤ ´¥ ¯ ¥­³¬ LDPC ²Å n¯³§ ¯¥¶ ¸£ ´¥ m´ m´©¬´¥

(Message-Passing) ·Ê£· ´¥© Ï´Ë ¢´¤Å Ï´ © 3 ¥¯ [17]

Å ´¥ Ï´§¯ ¥² ² Ï´­ Å­n­ ¸Ê Â É Â ¯¥q£· n¯£»§ Ï´ © 4095 ¶ ç²£· § ¥²

P = 2, Tr = 60 ´Ä ©¶ ´ ·, ç² Td = 0.5 Æ£Ä ¥©¶ ´ · ¸Ê Ï´Å­nÆ n Ï´ © à £Â ¶ § ³ Ë ­£ ¯

¬³ ´ TA  m´ ³ Tf = 1030T ¸Ê ¹¯©m´Â É ¥ · Ê· n¯¤¬º (worst case) Å ¥ · ·Ë n´Æ£m£·

´¥§ § ¥² ´ TA É ² Ï´Å­n ¶ n¯ ¶ §´ Ï´ © £´ ¯ ´ ·Ë Å ´¥ Ï´ © m´ BER

²Å n n¯£»§ Ï´ © 10000 Â É Â ¯¥q­¥¹¯£· n¯ ¶ §´  ¶ ¸Ë ¯¤m´ n ¯¤ 1000 ¶ ¸Ê ²Â¥·¤ ©m´ “BER given TA” ç² m´ SNR ·ÊÅ n ¶¤´£ ´£¬£ ´¥ (4.85) £¹Ê¯ Eb k hk

2

¬Ï´­¥³ m¯

¬³ ´ PR2 ¥² © ´¥ ¥© ­´ TA ²Å n L = 51 Å ´¥­´ m´ {qk} ç² * = 2.8 ( ¸Ê »

¯¯ à ´ ¥² ·ÊÆ£m »  n´¥­³¬ m´ Eb /N0 = 10.7 dB  ¹Ê¯ Ï´Å­n ¶ BER n ¯¤¬º ·Ê n´

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

´ TA  ¶ ¸Ë ·Ê ϴí m ¶ ·Ê 1000T ¯ º Â É Â ¯¥q Ä ¤ ·Ê¬³ ´ TA £· ´¥´£¶Â ¯¥q

´¯¯ ¯ ¯· ©¯Æ§Â ¯¥q SOVA) Å ´¥ ¥© ­´ TA

¥» ·Ê 5.19  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È ´¥© Ï´Ë Å ¥¯ ·Ê¬¶ £¹Ê¯ “No TA”

¹¯¬£¥¥ ² ¯ ¥² ·ÊÆ£m£· TA, “With TA” ¹¯¬£¥¥ ² ¯ ¥² ·ÊÆ£m£· ´¥§ § ¥² ¯ TA, “Conventional” ¹¯© ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ , “Proposed” ¹¯© ¥¢´ ¥³ ·Ê ϴ¬ ¯

5

บทที่

´£ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 5.2.4, ç² “Trained” ¹¯© ¥¢´ ¥³ ·Ê ϴ¬ ¯ ¸Ê Å n r k rk Å ´¥§ § ¥² ¯ TA ´ ¥» Â­É Æ n ³  ©m´ n´¥² ·ÊÆ£m£· ¥² © ´¥ ¥© ­´Ã§²Ã nÆ TA ²£· ¬£¥¥ ² n¯¤£´ Å ² ·Ê “Proposed” £·¬£¥¥ ² · ©m´ “Conventional” à m£·¬£¥¥ ²

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189

¥» ·Ê 5.19 ¬£¥¥ ² ¯ ¥² m´ È ´¥© Ï´Ë Å ¥¯ ·Ê¬¶

¥» ·Ê 5.20 ¯³ ¥´ n¯ ¶ §´ ¯   ¯¥q (SER)  ·¤ ³ Ï´ © ¥¯ ¯ ´¥© Ï´Ë

n¯¤ ©m´ “Trained” ç² “No TA”  ·¤ 0.6 dB ç² 0.8 dB ´£§Ï´ ³ ¥² ³ BER = 10–4

¯ ´ ·Ë ¥» ·Ê 5.20  ¥·¤  ·¤ ¬£¥¥ ² ¯ “Proposed” ç² “Conventional” Å ¥» ¯

¯³ ¥´ n¯ ¶ §´ ¯   ¯¥q (SER: sector-error rate)  ·¤ ³ Ï´ © ¥¯ ¯ ´¥© Ï´Ë ¸Ê

² ©m´Â£¹Ê¯¯· ©¯Æ§Â ³ à  ¯¥qÄ ¬´£´¥ m©¤Â ¶Ê£¬£¥¥ ² ¯ © ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ

Æ n ¸ ¥¯ ·Ê­ ¯ ´¥© Ï´Ë ´ ³ Ë ¥² ²Â ¶ ³ ³ ­´Â¥¹Ê¯ ¹Ë n¯ ¶ §´ (error floor)

190

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 5.21 m´ MSE ·Ê ¶ ´ © ¥¢´ ¥³ ·Ê ϴ¬ ¯ m´ Eb /N0 m´ È

Å ´ ¥ ³ n´£© ¥¢´ ¥³ ·Ê ϴ¬ ¯­¥¹¯ “Proposed” ¤³ Å­n¬£¥¥ ² ·Ê · ¸Ë Â¥¹Ê¯¤È ´£

Ï´ © ¥¯ ¯ ´¥© Ï´Ë ·Ê ¶Ê£ ¸Ë ¸Ê ­£´¤ ©´£©m´ m´ ¥²£´ ¯ ¬³ ´ TA ­¥¹¯ û t ·Ê Æ n ´  ¶ ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£Ã Ï´§³ ¬¯ n ¯¤¬º [76] £· º ¢´ · ¸Ë ¸Ê ¬m §Å­n ¸Ë Â¥¹Ê¯¤È Å Ã m§²¥¯ ¯ ´¥© Ï´Ë §¬¥º ·Ë¬´£´¥ m´ ³ ¬¶ Å Ã ¯¡ q \r k ^ £· º ¢´ ·

¬³ ´ TA ¥¶ u t ç² û t ´£¥» ·Ê 5.21 Ä ¤ ·Ê 1 MSE 10 log10 Tf

Ty Tf

\u kT uˆ kT ^

k Ty

2

¬­ ­­ ­ ®­

(5.24)

£·­ m ©¤Â É dB ç² Ty ¹¯Â©§´ ·Ê ¥© ¬³ ´ TA ´ ¥» Â­É Æ n ³  ©m´ ©´£Æ£m¬¯ §n¯ ¥²­©m´ u t ç² û t § § £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë ³ ³ Ë ¸ Â É Â­ º §©m´ Ï´Æ£

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

¤¹ ¤³ Æ n ´ ´¥©´ ¥´¡Ã¬ n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤ (MSE: mean-squared error) ¥²­©m´

“Proposed” ¸ £·¬£¥¥ ² · ©m´ “Conventional” Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë £· m´£´

¯ ´ ·Ë¥ » ·Ê 5.22  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² m´ È ·ÊÂ É ¡³ q ³ ¯ ³© ¥² ¯

m´¬» ¬º ´¥© Ï´Ë Å ¥¯ ·Ê¬¶ ç² Eb /N0 = 6.65 dB £¹Ê¯¬£¥¥ ² ¯ ¥² ·ÊÆ£m£· TA ­¥¹¯

5

บทที่

“No TA” £· m´ BER = 10–5 Å Ï´ ¯  ·¤© ³ ¥² ²£·¬£¥¥ ² n¯¤£´ n´¥² Æ£m£· ¥² ©

´¥ ¥© ­´Ã§²Ã nÆ TA ¯ ´ ·Ë¬£¥¥ ² ¯ ¥² à ·ÊÅ n ³ ³©Ê Æ Å ¥¯ ·Ê­ ¸Ê £· m´ ·Ê

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

191

0

10

With TA (10 iterations)

-1

BER given TA

10

1 iteration -2

10

Conventional 10 iterations

-3

10

Proposed (10 iterations)

-4

10

1

1.5

2

2.5

3

Peak factor (P)

¥» ·Ê 5.22 ¬£¥¥ ² ¯ ¥² Å ¥» BER ¬Ï´­¥³ ¥² ³ ©´£¥º Ã¥ ¯ ¬³ ´ TA m´ È

¸Ê ¬¯ §n¯ ³ n¯¬¥º ¯ ¥² ·ÊÅ n ¶ ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£Ã Ï´§³ ¬¯ n ¯¤¬º ·Ê©m´

¥² ²£· ©´£ ´ m¯ ´¥Â §·Ê¤ à § m´Ã¯£ §¶ » ¬» ¬º ¯ ¬³ ´ TA [76] ´ ¥» ² Â­É Æ n©m´¥² m´ È £· m´ BER m¯ n´ ¬» ³ Ë ·Ë Â É Â ¥´²©m´¬³ ´ TA ·ÊŬm n´Æ Å ¥²

¹¯©m´Â É ¬³ ´ TA ·Ê m¯ n´ ¥º Ã¥ §m´© ¹¯ n¯£»§Ã m§²Â  ¯¥q£· TA  ¶ ¸Ë ­ ¸Ê ¥³ Ë

¸Ê £·Ã¯£ §¶ » ¬» ç²£· m© ©§´§ ¥² ³ ·Ê¤´© ´ ¯¤m´ Æ¥ É ´£ “Proposed” ¤³ Å­n¬£¥¥ ² ·Ê · ©m´ “Conventional” ¬Ï´­¥³ º m´Ã¯£ §¶ » ¬» ¬º ¯ ¬³ ´ TA

5.2.6 ¬¥º § ´¥ §¯ ©´£ ¥º ¥²Â ¶ ©´£¥n¯ ­¥¹¯ TA ·Ê ¶ ¸Ë Å °´¥q ¶¬ qÆ ¥¡q ²¬m §Å­n¬£¥¥ ²¥©£ ¯ ¥² n¯¤§ £´ Å ·Ê ·ËÆ n¯ ¶ ´¤Â ¶ ´¥ ¥³ ¬n Ä n ·Ê­£´²¬£Ã Ï´§³ ¬¯ n ¯¤¬º [76]  ¹Ê¯Å n

§ § ¥² ¯ TA ·Ê Å ¬³ ´ ¯m´ §³ Ä ¤©¶ · ´¥ ¥© ­´ ´¥Â ¶ TA ²¯¤m» ¹Ë ´ ¯ ´¥­´ · Â¥¶Ê£Â §·Ê¤ 粩¶ · ´¥Ã nÆ § ¥² ·Ê ¶ ´ TA Ï´Æ nÄ ¤ ´¥­´ m´Â §·Ê¤ ¯

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Å ´ ¶ ³ ¶© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ ( ¸Ê Ï´ ¥² © ´¥ ¥© ­´Ã§²Ã nÆ TA

粯· ©¯Æ§Â ³ à  ¯¥qÄ Ã¤ ´ ³ Ä ¤¯¶¬¥²) ²Æ£m¬´£´¥ Ï´ ´ Æ n · £¹Ê¯ SNR £· m´ n ¯¤

192

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³ ³ Ë Å ­³© n¯ ·Ë Æ n¯ ¶ ´¤©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë [77] ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ ¥² © ´¥ ¥© ­´Ã§²Ã nÆ TA 粯· ©¯Æ§Â ³ à  ¯¥qÄ Ä ¤Å à m§²¥¯ ¯ ´¥© Ï´Ë ©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë ²Å n m´ ³ ¬¶ Å Ã ¯¡ q Ê·Æ n ´ © ¥ ¯

¥­³¬ LDPC £´ m©¤Â ¶Ê£¬£¥¥ ² ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£ ¥© ­´Ã§²Ã nÆ TA [76]  ¹Ê¯Å­n Æ n¬³ ´ ¯m´ §³ ·Ê£· º ¢´ · ¸Ë ¸Ê É ²¬m § Ï´Å­n¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ ¬´£´¥ Ï´ ´

Æ n¯¤m´ £· ¥²¬¶ ¶¢´ £´ ¸Ë Å ¥¯ ³ Æ § ´¥ §¯ ì Å­nÂ­É ©m´©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë £·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ Ï´ © ¥¯

¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë ¯ ´ ·Ë ©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë ·Ë ¹¯©m´£· ©´£ ³ n¯

Å §n ·¤ ³ © ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ ¸ Ï´Å­n¬´£´¥ Ï ´£´Å n ´ ¥¶ Å ¥² ´¥ ¥²£©§ §

¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q Æ n

5.3 ¬¥º n´¤ Å ·Ë Æ n¯ ¶ ´¤©¶ · ´¥ Ï ´Â ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë £´ ¥²¤º qÅ n¥m©£ ³ Æ ££¶Ê ¥¶ ³¡Â©¯¥·

Ĥ¯´ª³¤Â ¶ PSP Ï´Å­nÆ nÂ É © ¥¢´ ¥³ ¥» à ŭ£m Ê· ¥·¤ ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ¸Ê ²Ã§  §·Ê¤ m´©¬´¥Ã ¯¡ q¥²­©m´ PSP-BCJR 粩 ¥ ¯ ¥­³¬ ECC Ä ¤ ´ ´¥

§¯ ©m´Â£¹Ê¯¥² £· ©´£¥º Ã¥ ¯ Æ ££¶Ê ¶  ¯¥q£´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ²£·

¯¤m´ Æ¥ É ´£Å ·Ë ¤³ ì Å­nÂ­É ©m´Â£¹Ê¯ ©´£ ³ n¯ ¯ ¥² » Ï´ ³ Å­n¯¤m»Å ¥² ³ n ¯¤ ¸ ´ §´ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-ITR ɤ³ £·¬£¥¥ ² · ©m´Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã ·ÊÅ n ³

³Ê©Æ 粩¶ · ´¥ NBM ¸ Ï´Å­n¬´£´¥ Ï ´£´Å n ´ ¥¶ Å ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q Æ n

¯ ´ ·Ë¤³ Æ n¯ ¶ ´¤©¶ · ´¥ Ï ´Â ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë £´Å nà n ³ ­´Â¥¹Ê¯ ©´£

¥º ¥²Â ¶ ©´£¥n¯ (TA) Ï´Å­nÆ nÂ É ©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë ¸Ê Â É ´¥ Ï´ ´

¥m©£ ³ ¥²­©m´ ¥² © ´¥ ¥© ­´Ã§²Ã nÆ TA 粯· ©¯Æ§Â ³ à  ¯¥qÄ Ä ¤ ´ § ´¥

การประยุกตใชงานการถอดรหัสแบบวนซ้ำ

¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³ ³Ê©Æ 粩¶ · ´¥ NBM £´ (à m É£· ©´£ ³ n¯ ¬» )

§¯ ©m´©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë £·¬£¥¥ ² · ©m´© ¥¢´ ¥³ à ·ÊÅ n ³

³Ê©Æ ( ·Ê Ï´ ¥² © ´¥ ¥© ­´Ã§²Ã nÆ TA 粯· ©¯Æ§Â ³ à  ¯¥qÄ Â É ¯¶¬¥² m¯ ³ ) Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ Ï´ © ¥¯ ¯ ´¥© Ï´Ë Â ¶Ê£ ¸Ë ¯ ´ ·Ë ©¶ · ´¥§ § ¥² ¯ TA

à © Ï´Ë ·Ë¤³ £· ©´£ ³ n¯ Å §n ·¤ ³ © ¥¢´ ¥³ à ·ÊÅ n ³ ³©Ê Æ ¸ Ï´Å­n¬´£´¥ Ï ´£´Å n

5

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´ ¥¶ Å ¥² ´¥ ¥²£©§ §¬³ ´ ¯ °´¥q ¶¬ qÆ ¥¡q Æ n m ³

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5.4 Ã ¸ ­³ n´¤

194

1.

¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ç² PS-ITR

2.

´ à ϴ§¯ m¯ ¬³ ´ PR4 Å ¥» ·Ê 5.1 £¹Ê¯ H(D) = 1 – D2 ¶¬» q©m´Æ ££¶Ê ¥¶ ³¡

3.

´ à ϴ§¯ m¯ ¬³ ´ PR2 Å ¥» ·Ê 5.1 £¹Ê¯ H(D) = 1 + 2D + D2 ­´ m´ KT ·Ê

4.

¶¬» q m´ ¥²£´ à ¯¡ q r k Å ¬£ ´¥ (5.10)

5.

´ à ϴ§¯ m¯ ¬³ ´ PR2 Å ¥» ·Ê 5.1 £¹Ê¯ H(D) = 1 + 2D + D2 ­´ m´ ¥²£´

6.

¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ PSP-BCJR ç² PSP-SOVA

7.

¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ ©¶ · ´¥§ § ¥² ¯ TA à © Ï´Ë

8.

´ à ϴ§¯ m¯ ¬³ ´ PR4 Å ¥» ·Ê 5.7 £¹Ê¯ H(D) = 1 – D2 ­´ m´ ¥²£´ Ã

©¯¥·Ã PS-TR ²Å n m´ KT = 3T/16 Å ¬£ ´¥ (5.4)

n¯ Å nÅ Æ ££¶Ê ¥¶ ³¡Â©¯¥·Ã PS-TR ´£¬£ ´¥ (5.4)

à ¯¡ q r k E <rk | yk > ¯ m¯ ¬³ ´ PR2

¯¡ q r k E <rk | Mk > m¯ ¬³ ´ PR4

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

·Ê 6 Â Ä Ä§¤· BPMR ³ º ³ ·Ë ´¥Â ¶ Ä ´ n´ ¯¶  ¯¥qÂ É Ã§² ´¥¬¹Ê¯¬´¥ ¶ ¶ ³§Â É Æ ¯¤m´ ¥© ¥ɩ ¸ ¬m § Ï´Å­n£·

©´£ n¯ ´¥ ¯ ¹Ë ·ÊÅ ´¥ ³ Â É n¯£»§Â ¶Ê££´ ¸Ë Â¥¹Ê¯¤È °´¥q ¶¬ qÆ ¥¡q Å ³ º ³ ²Å n¬Ê ¹¯

³ ¸ ·Ê §¹¯ n©¤¡¶ §q£ ´ ¯ ¬´¥Ã£m­§É ¸Ê ¥² ¯ n©¤Â ¥  ¶ ãm­§É 30 (magnetic grain)

´ Â§É Å ¥² ³ ´Ä £ ¥ Ä ¤Ã m§²Â ¥ ²£·¬¢´ ©´£Â É Ã£m­§É (magnetization) Æ Å ¶ª ´ ·Êà m´ ³ ³ ³ Ë ´¥ ³ ¸ n¯£»§ ²¯´ª³¤¬ ´£Ã£m­§É ´ ­³©Â ·¤ (write head)

 ¹Ê¯ Ï´Å­n ¥ ­§´¤È  ¥ £·¬¢´ ©´£Â É Ã£m­§É Æ Å ¶ª ´ ·Ê n¯ ´¥ ( ´ ­¥¹¯ ³ Ë ´

³ ¥² ´ ¯ ¬¹Ê¯ ³ ¸ ) Ä ¤ ³Ê©Æ ´¥Â ¶Ê£ ©´£­ ´Ã m  ¶ ¹Ë ·Ê (areal density) ­¥¹¯ ©´£ º

n¯£»§ Ï´Æ nÄ ¤ ´¥§ ´ ¯  ¥ Å­n夃 § ¯¤m´ Æ¥ É ´£ ´¥§ ´ ¯  ¥  ¹Ê¯Â ¶Ê£ ©´£ Å ´¥Â É n¯£»§  ¹Ê ¯ ´ §³ ´ ©´£¥n¯ ´ ¢´¤ ¯ ² Ï´Å­n¬¢´ ©´£Â É Ã£m­§É ¯

 ¥ £· ¶ª ´  §·Ê¤ Æ Æ n m´¤ ( Ï´Å­n ¶ n¯£»§ “0”  §·Ê¤ Â É “1” ­¥¹¯Å ´ ¥ ³ n´£) ¸Ê

¥´ ´¥ q ·ËÂ¥·¤ ©m´ “ · Ï´ ³ »Â ¯¥q ´¥´Ã£  ¶ 31 (super-paramagnetic limit)” [1, 43]

­¥¹¯ · Ï´ ³ ©´£­ ´Ã m  ¶ ¹Ë ·Ê

³ ³ Ë Â Ä Ä§¤·Å­£m ʬ · ´£´¥ ³ Â É n¯£»§Æ n£´ ©m´Â Ä Ä§¤· ´¥ ³ ¸ n¯£»§Ã ·Ê

Å nÅ ³ º ³ ( ³Ê ¹¯Ã à © ³ Ë ) ¸ Â É ¬¶Ê Ï´Â É ¯¤m´ ¤¶Ê Å ¯ ´  m Â Ä Ä§¤· HAMR

(heat assisted magnetic recording) [78], Â Ä Ä§¤· BPMR (bit-patterned magnetic recording) [79], ç²Â Ä Ä§¤· TDMR (two-dimensional magnetic recording) [80] Â É n ¸Ê

Â Ä Ä§¤·Â­§m´ ·Ë¬´£´¥ ³ Â É n¯£»§Æ n£´ ©m´ 1  ¥² ¶ m¯ ´¥´ ¶Ë© (terabits/in2 ­¥¹¯ Tb/in2) 30 31

 ¥  ¶ ãm­§É Â É ¯ º¢´ ·Ê夃 ¬º Å ¬¹Ê¯ ³ ¸ ·Ê¬´£´¥ » Ï´Å­n£·¬¢´ ©´£Â É Ã£m­§É Æ n¯¤m´ ¯¶¬¥²

การประยุเทคโนโลยี กตใชงานการถอดรหั BPMR สแบบวนซ้ำ

­ ´Ã m  ¶ ¹Ë ·Ê£·Ã ©Ä n £ ·Ê ² Ï´Æ n¤´ ¸Ë  ¥´²Â ¥ ·Ê£· ´ 夃 £´  ¶ Æ ²Æ£m£·Â¬ ·¤¥¢´

65

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»Â ¯¥q ´¥´Ã£  ¶ ¹¯ ¥´ ´¥ q Ê · Ï´Å­n ©´£Â É Ã£m­§É ¯ à m§²Â ¥  ¶ ³ ³ ­´Â¥¹Ê¯ ©´£Æ£m¬ ·¤¥  ¶ ©´£¥n¯ ¸Ê ¬m § Ï´Å­n ©´£Â É Ã£m­§É ¯ à m§²Â ¥  ¶ ´¥Â §·Ê¤ à § ¶ª ´ ¯ ¬ ´£Ã£m­§É

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195

¥» ·Ê 6.1 §³ « ² ¯ ¬¹Ê¯ ³ ¸ ·Ê£· ( )  ¥  ¶ ãm­§É ´ Å­ m ç² ( )  ¥  ¶ ãm­§É ´ §É

Å ·Ë ²¯ ¶ ´¤Â ´² ¹Ë ´ ç²­§³ ´¥ Ï´ ´ ¯ Â Ä Ä§¤· BPMR ¥n¯£ ³ Ë ¬¥º

¢´ ¥©£ ¯ ´ ©¶ ³¤ m´ È ·Ê m´ £´ ·Ê ·Ê¤© n¯ ³ Â Ä Ä§¤· BPMR  ¹Ê¯Å­n n»¯m´ ¬´£´¥ Å n É

º Â¥¶Ê£ n Å ´¥ Ï´©¶ ³¤ ´ n´ ¥² ´¥ ¥²£©§ §¬³ ´ ¯ Â Ä Ä§¤· BPMR Æ n

6.1 Ï ´ Å ¥² ´¥ ³ ¸  ¶ ãm­§É ¬£¥¥ ² ¯ ¥² Å ¥» ¯ ¯³ ¥´ n¯ ¶ §´ ¯ ¶ (BER: bit-

error rate) ² ¸Ë ¯¤m» ³ m´¯³ ¥´¬m© Ï´§³ ¯ ¬³ ´ m¯ Ï´§³ ¯ ¬³ ´ ¥ © (SNR: signal-

to-noise ratio) ¸Ê Å ´ ¶ ³ ¶ m´ SNR Å ¬³ ´ ¯m´ §³ ²¬³£ ³ q ³ Ï´ ©  ¥ m¯ ¶

 §§q (bit cell) ­¥¹¯ n¯£»§­ ¸Ê ¶ Ä ¤ ³Ê©Æ ¬³ ´ ¥ © ´¥Â §·Ê¤ ¬ ´ ² (transition noise) ¹¯©m´Â É ¬³ ´ ¥ © ­§³ ·Ê £´ Å ¥² ´¥ ³ ¸ à à © ³ Ë [79] ¸Ê ©´£¥º Ã¥ ¯

¬³ ´ ¥ © ´¥Â §·Ê¤ ¬ ´ ² ·Ë ¸Ë ¯¤m» ³ ´¥Â §·Ê¤ à § à ¶ à (zig-zag transition)

¥¶Â© ¥¯¤ m¯ ·ÊÂ É ¯  ¯ à m§² ¶  §§q Ä ¤ ´¥Â §·Ê¤ à § à ¶ à ²£· ©´£

¥º Ã¥ £¹Ê¯Â ¥ à m§²Â ¥ £· ´ Å­ m (ç²¥º Ã¥ n ¯¤Â£¹Ê¯Â ¥ £· ´ 夃 ) ³ ì Å ¥» ·Ê

6.1 ³ ³ Ë n´¬¹Ê¯ ³ ¸ ·ÊÅ n ¥² ¯ n©¤Â ¥ ´ Å­ m Ï´ © £´ É ²¬m § Ï´Å­n¥² n¯  ¶

³ ³ ­´Â¥¹Ê¯ ¬³ ´ ¥ © ´¥Â §·Ê¤ ¬ ´ ² ·Ê¥º Ã¥  ¥´² ² ³ Ë ¬¹Ê¯ ³ ¸ ·Ê¬¥n´ ´  ¥ ´ 夃 ¸ Â É ¬¶Ê ·Ê Ï´Â É ¯¤m´ ¤¶Ê ç²­ ¸Ê ¶  §§q É ©¥ ¥² ¯ n©¤Â ¥ ´ Â§É Ï´ © £´  ·¤ ¯Â ¹Ê¯Å­n¥² £· m´ SNR ´£ ·Ê n¯ ´¥

Ä ¤ ³©Ê Æ ´¥Â ¶Ê£ ©´£ º n¯£»§ ¯ °´¥q ¶¬ qÆ ¥¡q Ï´Æ nÄ ¤ ´¥§ ´ ¯ ¶ n¯£»§Å­n

夃 § à m¤³ ¥³ «´¥² ³ SNR Å­n m´Â ¶£ ­¥¹¯ §m´©¯· ³ ¤­ ¸Ê ¹¯ ´¥§ ´ ¯  ¥ Å­n

夃 § à m¤³ £· Ï´ ©  ¥ m¯­ ¸Ê ¶  §§q  ¶£ ¯¤m´ Æ¥ É ´£ ´ ¯  ¥ Æ£m ©¥Â§É  ¶ Æ

 ¥´² §³ ´ ©´£¥n¯ ´ ¢´¤ ¯ ²¬´£´¥  §·Ê¤ ¶ª ´ ¬¢´ ©´£Â É Ã£m­§É ¯  ¥

Æ n ( Ï´Å­nÆ£m£·Â¬ ·¤¥¢´ Å ´¥ ³ Â É n¯£»§) ³Ê ¹¯ Ï´Å­n ¶ ³ ­´Â¥¹Ê¯ »Â ¯¥q ´¥´Ã£  ¶

196

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[1, 43] ¸Ê Â É · Ï´ ³ ·Ê Ï´Å­nÂ Ä Ä§¤· ´¥ ³ ¸  ¶ ãm­§É ·ÊÅ nÅ ³ º ³ Æ£m¬´£´¥  ¶Ê£ ©´£­ ´Ã m  ¶ ¹Ë ·ÊÆ n£´ ©m´ 1 Tb/in2 Å ´ ¶ ³ ¶ ³ ­´Â¥¹Ê¯ »Â ¯¥q ´¥´Ã£  ¶

¬´£´¥ n ¯ ³ Æ nÄ ¤ ´¥Å n¬Ê ¯ ¹ ³ ¸ ·Ê£· m´¯³ ¥´¬m© [1, 43] K uV pC kBT

(6.1)

£¹Ê¯ Ku ¹¯ m´¬³£ ¥²¬¶ ¶ÃÎ ¯ Æ¯Ä ¥¯ · à à  ·Ê¤© ¯ ©³¬ º, V ¹¯ ¥¶£´ ¥ ¯  ¥ ·ÊÅ n

Â É n¯£»§­ ¸Ê ¶ , kB ¹¯ m´ ³©Ä § qã (Boltzmann’s constant) £· m´Â m´ ³ 1.38×10–23

»§ m¯Â §©¶ (joules per kelvin), T ¹¯¯º ­¢»£¶¬³£ »¥ q£·­ m ©¤Â É Â §©¶ , ç² E ¹¯ Ï´ ©

 ɣ © ·Ê£· m´£´ È Â m E = 60 Â É n  ¹Ê ¯ ´ m´ kBT Â É m´ ³© ³ ³ Ë Â ¹Ê¯  ¤ ¥¶£´ ¥ ¯  ¥ ·Ê§ § ¬¹Ê¯ ³ ¸ ² n¯ Å n¬´¥Ã£m­§É ·Ê£· m´ Ku ¬» £´ ¸Ë ¸Ê § ·Ê ´££´ É ¹¯­³©Â ·¤

² n¯ Å n¬ ´£Ã£m­§É ·Ê£· ©´£Â n£¬» £´ Å ´¥Â ·¤ ¶ n¯£»§§ Æ ³ Â É Å ¬¹Ê¯ ³ ¸ Æ n¯¤m´ £·

¬ ·¤¥¢´ ³ ­´ ·Ëà nÆ Æ nÄ ¤Å nÂ Ä Ä§¤· HAMR [78] ( »¥´¤§²Â¯·¤ Å ·Ê 8) à m¯¤m´ Æ¥ É ´£¬¹Ê¯ ³ ¸ ·ÊÅ nÅ ³ º ³ ( ·Ê §¹¯ n©¤¡¶ §q£ ´ ¯ ¬´¥Ã£m­§É ) É Ï´§³ ² ¸ · Ï´ ³ ¯

´¥ ³ Â É n¯£»§Å ¯ ´ ¯³ Å §n ·Ë 2

Â Ä Ä§¤· BPMR ¹¯©m´Â É Â Ä Ä§¤· Ê·¬´£´¥  ¶Ê£ ©´£­ ´Ã m  ¶ ¹Ë ·ÊÆ n£´ ©m´

1 Tb/in ç²Æ£m£· ³ ­´Â¥¹Ê¯ · Ï´ ³ »Â ¯¥q ´¥´Ã£  ¶ [79] Ä ¤Â Ä Ä§¤· BPMR ²Å n

¬¹Ê¯ ³ ¸ ·Ê£· ´¥ Ï´Ã (patterned media) ­¥¹¯¬¹Ê¯ ³ ¸ ·Ê£·¥» à à m ¯ ¸Ê ¬¥n´ ´ ¬´¥ ãm­§É ·Ê£·Ä £ ãm­§É  ·Ê¤© (single magnetic domain) ­¥¹¯£·§³ « ²Â É Æ¯Ã§ q ¶

ãm­§É (non-magnetic material) ¯¤m´ Â É ¥²Â ·¤ ç²£·¥²¤²­m´ ¬£Ïʴ¬£¯ Ä ¤ ¶ª ´ ¯

¬¢´ ©´£Â É Ã£m­§É ¯ Ưç q¯´ ² ´ ­¥¹¯ ³ Ë ´ ³ à m ¥¯ ¥³ ÉÆ n ¥» ·Ê 6.2 ì ³©¯¤m´ ´¥ ³ Â É n¯£»§Å ¬¹Ê¯ ³ ¸ ¯ Â Ä Ä§¤· BPMR

 ¹Ê ¯ ´ Ưç q ¶ ãm­§É ´ ´Ä à ¯  ª (isolated nano-scale magnetic

เทคโนโลยี BPMR

ãm­§É (magnetic island) ´ ´Ä £ ¥ Â¥·¤ ³© ³ à m ¥¯ ¥³ ·Ê Ï´£´ ´ ©³¬ º Ê·Æ£m É

islands) ·Ê » §n¯£¥¯ n©¤©³¬ º ÊÆ· £mÂ É Ã£m­§É ² Ï´­ n ´ ·ÊÂ É Ã “Ä Â£  ·Ê¤© (single domain)”

­¥¹¯ Ï´­ n ´ ·Ê¬£¹¯ Â É Æ¯Ã§ qà  ¥  ·¤©32 ³ ³ Ë ´¥Å n ¥ ´ Â§É Ï´ © £´ m¯­ ¸Ê

¶ n¯£»§ ¸ Â É ¬¶Ê ·ÊÆ£m Ï´Â É ¬Ï´­¥³ Â Ä Ä§¤· BPMR ³Ê ¹¯Æ¯Ã§ q­ ¸Ê Ưç q¯´ ¬¥n´ ´

 ¥  ·¤  ¥  ·¤© ÉÆ n ¯ ´ ·Ë ´¥Å nƯç q ¶ ãm­§É Ã Ä Â£  ·Ê¤©¤³ ¬´£´¥ ³ ´¥

6

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¬ ´ ²Æ n¯· n©¤ [81] 32

Ưç q ¶ ãm­§É à  ¥  ·¤©­£´¤ ¸ Ưç q ¶ ãm­§É ·Ê¬¥n´ ¸Ë ´  ¥  ¶ ãm­§É  ·¤  ¥  ·¤©Â m´ ³ Ë

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¥» ·Ê 6.2 §³ « ² ´¥ ³ Â É n¯£»§Å ¬¹Ê¯ ³ ¸ ¯ Â Ä Ä§¤· BPMR

Å Â Ä Ä§¤· BPMR ϴí m ¯ Ưç q ³ Ë ­£ ² » Ï´­ Æ©nÂ¥·¤ ¥n¯¤Ã§n© ³ Ë Ã m

³ Ë ¯ ´¥ Ï´Ã (­¥¹¯ ´¥¬¥n´ ) ¯ ¬¹Ê¯ ³ ¸ ¸ Ï´Å­n£· n¯ · Ï´ © £´ £¹Ê¯ Ï ´£´Å n ´ ¥¶  m § ³ ­´Â¥¹Ê¯ ¬³ ´ ¥ © ´¥Â §·Ê¤ ¬ ´ ², Ï´ ³ ³ ­´Â¥¹Ê¯ ´¥Â§¹Ê¯ ¶ à ƣm É

 ¶ ¬n (nonlinear bit shift), Ï´Å­n ¥² © ´¥ n» n¯£»§ m´¤ ¸Ë , ç² Ï´Å­n ¥² © ´¥ ¶ ´£ (tracking) ·ÊÅ nÅ ¥²  ¯¥qÄ© (servo system) m´¤ ¸Ë [81, 82] Â É n

6.2 ©¶©³ ´ ´¥ ¯ Â Ä Ä§¤· BPMR ­³© n¯ ·Ë ² §m´© ¸ ©¶©³ ´ ´¥ ¯ Â Ä Ä§¤· BPMR ³ Ë Ã mÂ¥¶Ê£Ã¥ ¸ ³ º ³  ¹Ê¯Å­n n»¯m´

¥´ ¸ ´ ©¶ ³¤ n´ m´ È ·Ê m´¬ Å ·Ê£·¬m© m©¤ Ï´Å­nÂ Ä Ä§¤· BPMR ¬´£´¥ Ï ´£´Å n ´ ¥¶ Å ¯ ´ ¯³ Å §n ·ËÆ n

6.2.1 ¬¹Ê¯ ³ ¸ Å m© Ã¥ ´ ©¶ ³¤ ´ n´ Â Ä Ä§¤· BPMR ²Â n Æ ·Ê ´¥ ³ ´­¥¹¯ ´¥¬¥n´ ¬¹Ê¯ ³ ¸ ·Ê£· ´¥ Ï´Ã Ã © ¶ Å ´¥ Ï´Ã ¯ ¬¹Ê¯ ³ ¸ Â¥¶Ê££´ ³ Ë Ã m · .ª. 1963 [83] Ä ¤£· ´¥Â¬ ¯Å­n

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¥» ·Ê 6.3 ¥² BPMR à à m ­£º

Å n “à ¥É ·Ê£· ´¥ Ï´Ã (patterned track)”  ¹Ê¯§ ³ ­´ ·Ê ¶ ´ ¬³ ´ ¥ © ç² ¥² © ´¥ ¶ ´£Å ¥²  ¯¥qÄ© ´ ³ Ë Å · .ª. 1987 ÉÆ n£· ´¥ª¸ «´ º ¬£ ³ ¶ ¯ ´¥Å n “à ¥É

à à 33 (narrow tracks)” [84] ç²Æ n Ï´ ´¥ª¸ «´Ã§² §¯ ³ ¸ n¯£»§§ Å ¬¹Ê¯ ³ ¸ ·Ê

£· ´¥ Ï´Ã ´ ´Ä Å · .ª. 1991 [85]

³ Ë Ã m · .ª. 1991 Â É n £´ ´ ©¶ ³¤ ´ n´ ¬¹Ê¯ ³ ¸ ·Ê£· ´¥ Ï´Ã Æ n n Æ ·Ê ´¥

¬¹Ê¯ ³ ¸ ·Ê¬´£´¥ ³ Â É n¯£»§Æ n£´  m ´Ä §¶Ä ¥´¡· (nano lithography), ´¥ ³ Â¥·¤ ³©Â¯ (self-assembly), §¶Ä ¥´¡· n©¤§Ï´¯¶Â§É ¥¯ (electron beam lithography), 粧¶Ä

¥´¡· n©¤ ´¥ ¶£ q¥² ³ ´Ä (nano-imprint lithography) Â É n n»¬ Å ´ n´ ´¥¬¥n´

เทคโนโลยี BPMR

¬¥n´ ç² ´¥ª¸ «´ º ¬£ ³ ¶ ¯ ¬¹Ê¯ ³ ¸ Ä ¤Â Ä Ä§¤· m´ È Æ n » ³ ´ ¸Ë £´Â ¹Ê¯Å n¬¥n´

¬¹Ê¯ ³ ¸ ·Ê£· ´¥ Ï´Ã ¬´£´¥ ª¸ «´¥´¤§²Â¯·¤  ¶Ê£Â ¶£Æ n ´ [86 – 89]

6

6.2.2 ¥² ´¥ ³ ¸  ¶ ãm­§É ¬Ï´­¥³ BPMR Ä ¤ ³Ê©Æ ¥² ´¥ ³ ¸  ¶ ãm­§É à BPMR à m ¯¯ Æ nÂ É 2 ¥²Â¢ ­§³ ¹¯ ¥²

บทที่

BPMR à à m ­£º (spinning-disk system) ç²¥² BPMR Ã Ä ¥ (probe-based system) [90] ³ ì Å ¥» ·Ê 6.3 ç² 6.4 ´£§Ï´ ³

33

à ¥É à à ¬¥n´ Æ n n©¤ ¥² © ´¥ ³ ¸Ë ¥¯¤ (etching process) Ä ¤ ´¥Â ´²¥m¯ ¯ ¬¹Ê¯ ³ ¸ Å­nÂ É Ã ¥É

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¥» ·Ê 6.4 ¥² BPMR Ã Ä ¥ [90]

¥» ·Ê 6.3 ì ¥² BPMR à à m ­£º ·ÊÅ n­³©Ã£m­§É à MR (magneto-

resistive) ¥m©£ ³ ¬¹Ê¯ ³ ¸ ·Ê£· ´¥ Ï´Ã ¸Ê £·§³ « ² ´¥ Ï´ ´ §n´¤ ³ ¥² ´¥ ³ ¸ à à © ³ Ë ·ÊÅ n ³ Å ³ º ³ ³ ³ Ë Â Ä Ä§¤· m´ È ·ÊÅ nÅ ¥² ´¥ ³ ¸ à à © ³ Ë ¸ ¬´£´¥

Ï ´£´ ¥²¤º qÅ n ³ ¥² BPMR à à m ­£º ·ËÆ n ¯¤m´ Æ¥ É ´£ ¥² © ´¥Â n´ ³ ­©² (syn-

chronization) ¥²­©m´ ϴí m ¯ ­³©Ã£m­§É ç² ϴí m ¯ Ưç q Ê· ² Ï´ ´¥Â ·¤ ­¥¹¯¯m´

n¯£»§Å ¥² BPMR ²Ã m´ ´ ¥² © ´¥Â n´ ³ ­©² ·ÊÅ nÅ ¥² ´¥ ³ ¸ à à © ³ Ë m¯ n´ £´ [91] ´ ©¶ ³¤Å [91, 92] Æ nª¸ «´ ¥² © ´¥Â ·¤ n¯£»§Å ¥² BPMR ¸Ê

ì Å­nÂ­É ©m´¬ ´£Æ¡¡n ´Â ·¤ (write field) Ï´Â É ¯¤m´ ¤¶Ê ·Ê ² n¯  n´ ³ ­©² ³ ϴí m ¯

Ưç q Ê · n¯ ´¥Â ·¤ ¶ n¯£»§§ Æ §m´© ¹¯Â£¹Ê¯­³©Â ·¤  §¹Ê¯ ·Ê£´¯¤m» ϴí m º ª» ¤q §´

¯ Ưç q ¬ ´£Æ¡¡n ´Â ·¤ n¯ » n ¯  n´Æ ŠƯç q ³ ·¢´¤Å ¥²¤²Â©§´ ·Ê Ï´­ Å­n

 m´ ³ Ë [16, 93, 94] ³ ³ Ë ¥² © ´¥Â n´ ³ ­©² ·ÊÅ nÅ ¥² BPMR n¯ ´¥ ©´£Â ·Ê¤ ¥

¬» £´ ©m´¥² ´¥ ³ ¸ à à © ³ Ë ¯ ´ ·Ë ©¶ ·Å ´¥Â n´ ³ ­©² ´¥Â ·¤ ¯· ©¶ ·­ ¸Ê ¸Ê Å n ´ Æ n · É ¹¯ “ ´¥¯m´ Å ²Â ·¤ (read while write)” [90] £¶ ² ³ Ë ¯´ m¯Å­n ¶ ³ ­´

n¯ ¶ §´ Å ´¥Â ·¤ (written-in error) [91, 95] ¸Ê £· § Ï´Å­n ¶ n¯£»§ ·Ê n¯ ´¥Â ·¤  n´Æ

ŠƯç q ¶ ³ ­´34Â¥¹Ê¯ ´¥Ã ·Ê (sub-stitution), ´¥ ³ (deletion) ç² ´¥Ã ¥ (in-

sertion) ¯ ´ ·Ë ´ ©¶ ³¤Å [96] Æ nª¸ «´Ã n¯£»§ (data pattern) ·ÊÅ nÅ ¥²  ¯¥qÄ© 34

Å ³ ­´ n¯ ¶ §´ Å ´¥Â ·¤ ´¥Ã ·Ê (substitution) ­£´¤ ¸ ¶ n¯£»§ ·Ê n¯ ´¥ ²Â ·¤  n´Æ ŠƯç q ¶ ´¥Ã ·Ê ( ´ ¶ 1  §·Ê¤ Â É ¶ 0 ­¥¹¯Å ´ ¥ ³ n´£), ´¥ ³ (deletion) ­£´¤ ¸  ¶ ´¥¬» ­´¤ ¯ ¶ n¯£»§ ·Ê ·¤  n´Æ ŠƯç q, ç² ´¥Ã ¥ (insertion) ­£´¤ ¸ £· ¶ n¯£»§Â ¶Ê£Â n´£´Å ¬¹Ê¯ ³ ¸ ( m  ·¤ n¯£»§ ­ ¸Ê ¶ à m ¥´ ©m´£· n¯£»§¬¯ ¶ »  ·¤ § Æ Å ¬¹Ê¯ ³ ¸ )

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©m´ ´¥Å n¬Ê ¹¯ ³ ¸ ·Ê£· ´¥ Ï´Ã ² m©¤ Ï´Å­n¬´£´¥ Å nà n¯£»§ ·Ê ³ n¯ Å ¥²  ¯¥qÄ©Æ n

¸Ê £· § Ï´Å­n ©´£Ã ¥ ¥© ¯ ¬³ ´ n¯ ¶ §´ ¯ ϴí m (PES: position error signal)

§ § ¯¤m´ £´ Å ¥² BPMR

¥² ´¥ ³ ¸  ¶ ãm­§É ¬Ï´­¥³ BPMR ¯· à ­ ¸Ê É ¹¯ ¥² BPMR Ã Ä ¥

´£¥» ·Ê 6.4 Ä ¤­³©Ã£m­§É ­§´¤È ­³© ² » ¶ ³ Ë ¯¤m» ¥² ´ ·Ê §¹Ê¯ ·Ê¯¤m»Â­ ¹ ¯¬¹Ê¯ ³ ¸

´ ³ Ë ´¥Â ·¤ n¯£»§ Ï´Æ nÄ ¤ ´¥ n ¯ ¬ ´£Ã£m­§É  n´Æ ¤³ ϴí m ¯ Ưç q Ê · n¯ ´¥ Ä ¤¬ ´£Ã£m­§É ·Ê n¯  n´Æ ² n¯ Æ£mÆ ¥ © Ưç q ϴí m ¯¹Ê È Å Ï´ ¯  ·¤© ³ ´¥

¯m´ n¯£»§ Ï´Æ nÄ ¤ ´¥Å n©¶ · ´¥ ·Ê­£¹¯ ³ ©¶ · MFM (magnetic force microscope) [97] Ä ¤

­³©Ã£m­§É ² ¥© ­´Â ·¤ ©m´Æ¯Ã§ q ³Ë £·¬ ´ ² ¯ ¬¢´ ©´£Â É Ã£m­§É Å ¶ª ´ ·Ê mº ¸ Ë

­¥¹¯ mº §  m´ ³ Ë ¯ ´ ·Ë ´¥¯m´ n¯£»§Å ¥² BPMR Ã Ä ¥ ¤³ ¬´£´¥ Ï´Æ nÄ ¤ ´¥©³

¬ ´£Ã£m­§É Ä ¤ ¥ ´ Ưç q Ä ¤ ´¥Å n­³©¯m´ à MR ´ ¶Í©­¥¹¯Ä ¥  ¶ ì (optical probe) Â É n

¥² BPMR ²Å n ´ Æ n · É m¯Â£¹Ê¯¥² £· m´ SNR ·Ê ·¤ ¯ ¸ ãn©m´ ´¥Å nƯç q

 ¶ ãm­§É Ã Ä Â£  ·Ê¤©¬´£´¥ m©¤§ § ¥² ·Ê ¶ ´ ¬³ ´ ¥ © ´¥Â §·Ê¤ ¬ ´ ² ç² ´¥Â§¹Ê¯ ¶ à ƣmÂ É Â ¶ ¬n [81, 82] à m ©´£Æ£m¬£ »¥ qÅ ´¥¬¥n´ ¬¹Ê¯ ³ ¸ ² Ï´Å­n  ¶ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ (media noise) ¥» à ŭ£m [98, 99] ¸Ê £· § Ï´Å­n¬£¥¥ ² ¯

¥² BPMR § § ¯¤m´ £´ [100] ¸Ê ´ ´¥ª¸ «´ ©m´¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ·Ë  ¶ ´

´¥ ³ © à ¥ ³ (fluctuation) ¯ ´ ç² ϴí m ¯ Ưç q ¶ ãm­§É [99 – 103]

Å m© Ã¥ ¯ ´¥ ³ ´¥² ´¥ ¥²£©§ §¬³ ´ Å ¥² BPMR ³ ©¶ ³¤ ²Â n Æ ·Ê¥² BPMR à à m ­£º ¸Ê £·§³ « ² ´¥ Ï´ ´ §n´¤ ³ ¥² ´¥ ³ ¸ n¯£»§Ã ·ÊÅ n ³ ³Ê©Æ ( ³Ê ¹¯Ã à © ¯ ç²Ã à © ³ Ë ) ³ ³ Ë m¯ ¬³ ´ ¯m´ ¯ ¥² BPMR ¸ ¬´£´¥

เทคโนโลยี BPMR

6.2.3 ´¥ ¥²£©§ §¬³ ´ Å ¥² BPMR

Ï´§¯ Â É Ã ¢´ §É¯ à m´¤Æ n ´£¥» ·Ê 6.5 [10] ¸Ê ¥² ¯ n©¤ m¯ ¬³ ´ (channel),

¯· ©¯Æ§Â ¯¥qà § ¯ ¬ ¯ ´ ¬m© (partial-response equalizer), 粩 ¥ ¥© ­´©·Â ¯¥q ¶ (Viterbi detector) [13]

´ ©¶ ³¤ ´ n´ m¯ ¬³ ´ ¯m´ ¯ ¥² BPMR Æ nÂ¥¶Ê£ n Å · .ª. 1998 [102]

6

บทที่

Ä ¤Å n m¯ ¬³ ´ § ¯ ¬ ¯ ´ ¬m© ©¥ ²Â É ¬» ¬º (PRML: partial-response maximum-

likelihood) Å ´¥©³ ¬£¥¥ ² ¯ ¥² BPMR Ä ¤Å nƯç q Ê·£·¬¢´ ©´£Â É Ã£m­§É à à © ¯ (longitudinal magnetization) ´ ³ Ë ´ ©¶ ³¤ Å [81, 100, 101] Æ nª¸ «´

¥² © ´¥¯m´ ¯ ¥² BPMR ·ÊÅ n¬Ê ¹¯ ³ ¸ ¬Ï´­¥³ Ưç q Ê·£·¬¢´ ©´£Â É Ã£m­§É

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¥» ·Ê 6.5 à ¢´ §É¯ à m´¤¬Ï´­¥³ m¯ ¬³ ´ ¯m´ ¯ ¥² BPMR

à à © ¯ ¯ ´ ·Ë ´ ©¶ ³¤Å [100, 101] Æ nª¸ «´ m¯ ¬³ ´ ¯m´ ¯ ¥² BPMR ·ÊÅ n

¬¹Ê¯ ³ ¸ ¬Ï´­¥³ Ưç q Ê·£·¬¢´ ©´£Â É Ã£m­§É à à © ³ Ë (perpendicular magnetization) Ä ¤¬³ ´ ¯m´ §³ (readback signal) ² » Ï´§¯ ´ à © ¶ à ¬¯ £¶ ¶ ¯ ´¥ Ï´ © ¯¶ ¶ ¥³§ ´¥ ¯ ¬ ¯ (reciprocity integral)

 ¹Ê¯Å­nà ϴ§¯ ¯ ¬³ ´ ¯m´ §³ £· ©´£ » n¯ £´ ¤¶Ê ¸Ë ´ ©¶ ³¤Å [104] Æ n

¬ ¯Ã © ¶ à ¬´££¶ ¶ ¯ ´¥ Ï´ © ¯¶ ¶ ¥³§ ´¥ ¯ ¬ ¯  ¹Ê¯ ¥²£´ m´ § ¯ ¬ ¯

¬³ ´ ³§¬q (pulse response) ¯ ¥² BPMR ç²Æ n Ï´ ´¥ª¸ «´ § ¥² ¯ ¥» ¥ ¯

Ưç q (island geometry) ·Ê£· m¯ § ¯ ¬ ¯ ¬³ ´ ³§¬q ·Ë ¸Ê ©m´ § ¯ ¬ ¯ ¬³ ´ ³§¬q ¯ ¥² BPMR ² ¸Ë ¯¤m» ³ ´ ç²¥» ¥m´ ¯ Ưç q m¯ n´ £´ ¯ ´ ·Ë ´ ©¶ ³¤ Å [105, 106] Æ nª¸ «´ § ¥² ¯ ¥» ¥ ¯ Ưç q m¯¬£¥¥ ² ¯ m¯ ¬³ ´ ¯m´ Å

¥» ¯ ¯³ ¥´ n¯ ¶ §´ ¯ ¶ (BER) Ä ¤ ´ ©¶ ³¤ ·Ë Æ nÅ n ´¥ Ï´ © ¯¶ ¶ ¥³§ ´¥ ¯ ¬ ¯

à ¬´££¶ ¶ (3D reciprocity integral) Å ´¥ ¥²£´ m´ § ¯ ¬ ¯ ¬³ ´ ³§¬q ¯ ¥²

BPMR 粬³ ´ ¯m´ §³ ·ÊÆ n ´ ­³©¯m´  ¶ ´ ´¥ n¯ ³  ¶ ¬n (linear superposition)

¯ § ¯ ¬ ¯ ¬³ ´ ³§¬q ¯ à ¥É ­§³ (main track) ç²Ã ¥É n´  ·¤ (adjacent track) ­¥¹¯¯´ §m´©Æ n©m´¬³ ´ ¯m´ §³ ·ÊÆ n ´ ­³©¯m´ £· § ¥² ·Ê ¶ ´ à ¥É n´  ·¤ ­¥¹¯ ·Ê

Â¥·¤ ©m´ “ ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É (ITI: inter-track interference)” ¸Ê ´ ´¥ §¯ ©m´ ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É £· § Ï´Å­n¬£¥¥ ² ¯ ¥² BPMR n¯¤§ £´ ¯¤m´ Æ¥ É ´£ ´¥§ § ¥² ¯ ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É ¬´£´¥ Ï´Æ nÄ ¤ ´¥Å n¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶

(2D equalizer) [107] 粩 ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ (2D Viterbi detector) [108, 109] Å

´¥ ¥© ­´ n¯£»§ ( »¥´¤§²Â¯·¤ Å ·Ê 7)

¯ ´ ·Ë ³ ­´Â¥¹Ê¯ ¯¯¡Â É ¯ ­³©¯m´ (read head offset) ­¥¹¯Ã ¥É £¶¬Â¥ ¶¬Â ¥ ³

(TMR: track mis-registration) ¥©£ ³ Ë ©´£Æ£mà m ¯ ¯ Ưç q ¶ ãm­§É Å ¬¹Ê¯ ³ ¸ É£· § Ï´Å­n¬£¥¥ ² ¯ ¥² BPMR § § n©¤ [110] Ä ¤ ³Ê©Æ ¥² BPMR ·ÊÅ n¬Ê ¹¯ ³ ¸ ·Ê£·

Ưç q ¶ ãm­§É Â¥·¤ ³©Ã ¥¶ ° ²Ä ³ § (hexagonal grid) ²£·¬£¥¥ ² · ©m´¥²

BPMR ·ÊÅ n¬Ê ¯ ¹ ³ ¸ ·Ê£·Æ¯Ã§ q ¶ ãm­§É Â¥·¤ ³©Ã ¥¶ £º£ ´ (rectangular grid)  ¥´²©m´

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¥» ·Ê 6.6 ´¥Â¥·¤ ³© ¯ Ưç q ¶ ãm­§É à ( ) ¥¶ £º£ ´ ç² ( ) ¥¶ ° ²Ä ³ §

´¥Â¥·¤ ³©Ã ¥¶ ° ²Ä ³ § ² Ï´Å­nƯç q ¯ à ¥É ·Ê¯¤m» ¶ ³ £·¥²¤²­m´ £´ ©m´ ´¥Â¥·¤

³©Ã ¥¶ £º£ ´ ¬Ï´­¥³ ¥²¤²Ã ¥É 35 (track pitch) ·Ê m´ ³ ¸ ¬m §Å­n ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É § § ¥» ·Ê 6.6 ì §³ « ² ´¥Â¥·¤ ³© ¯ Ưç q ¶ ãm­§É à ¥¶ £º£ ´ ç²Ã ¥¶ ° ²Ä ³ §

¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ (media noise) Å ¥² ´¥ ³ ¸ à BPMR ²Ã m´

´ ¥² ´¥ ³ ¸ à ·ÊÅ n ³ ³©Ê Æ §m´© ¹¯¥² BPMR ²Æ£m£· ³ ­´Â¥¹Ê¯ ¬³ ´ ¥ ©

´¥Â §·Ê¤ ¬ ´ ² (transition noise) ­¥¹¯ ´¥Â§¹Ê¯ ¶ à ƣm ¶ ¬n (nonlinear bit shift)

 ¥´²©m´ ¶ n¯£»§ » ³ Â É Å §mº£Æ¯Ã§ q ¶ ãm­§É Ã Ä Â£  ·Ê¤© ç² ϴí m ¯ §mº£

BPMR ²Â ¶ ´ ©´£Æ£m¬£ »¥ qÅ ´¥ §¶ ¥¥£ (fabrication imperfection) ¸Ê £· § Ï´Å­n ¶ ©´£ ³ © ¯ ϴí m ´ ©´£¬» ç²¥» ¥m´ ¯ à m§²Æ¯Ã§ q Ä ¤¬³ ´ ¥ ©

¬¹Ê¯ ³ ¸ ·Ë ¹¯Â É ¬³ ´ ¥ © ­§³ ·Ê Å ¥² BPMR ¸Ê ² Ï´Å­n¬£¥¥ ² ¯ ¥² n¯¤§ ¯¤m´ £´ [102, 110, 111]

เทคโนโลยี BPMR

Ưç q ¶ ãm­§É É » Ï´­ Æ©n¯¤m´ à m ¯ ¯¤m´ Æ¥ É ´£¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ Å ¥²

´ ©¶ ³¤ m´ È ·Ê §m´©£´ n´ n ²¯¤m» ¬££º ¶ ´ ·Ê©m´­³©Ã£m­§É (­³©¯m´ ç²­³©Â ·¤ )

£· ´ ·Ê­£´²¬£ ³ ´ ¯ Ưç q ¶ ãm­§É Å ¥² BPMR ¯¤m´ Æ¥ É ´£­³©Ã£m­§É ·ÊÅ n

Å ³ º ³ ²£· ´ Å­ m ©m´ ´ ¯ Ưç q m¯ n´ £´ 36 ´ ©¶ ³¤Å [112] Æ n ϴ¬ ¯ ´¥

Å n­³©Ã£m­§É ·Ê£· ´ Å­ m ©m´Æ¯Ã§ q ¶ ãm­§É ¬Ï´­¥³ ¥² BPMR Å ¤º Â¥¶Ê£ n ´£ ·Êì 35 36

¥²¤²Ã ¥É (track pitch) ¹¯¥²¤²­m´ ¥²­©m´ à ¥É

6

บทที่

2

¥² BPMR ·Ê£· ©´£­ ´Ã m  ¶ ¹Ë ·Ê£´ ©m´­¥¹¯Â m´ ³ 1 Tb/in ² n¯ £·¥²¤²­m´ ¥²­©m´ Ưç q ¶ ãm­§É n ¯¤ ©m´ 25 ´Ä £ ¥ (Ä ¤ ³©Ê Æ Ã m§²Æ¯Ã§ q ²£· ´ n ¯¤ ©m´¥²¤²­m´ ¥²­©m´ Ưç q¬£¯)

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¥» ·Ê 6.7 ¥² BPMR ·ÊÅ n­³©¯m´ à MR ´ Å­ m

Å ¥» ·Ê 6.7 ¯ ´ ·Ë ¤³ Æ n¬ ¯Ã Ï´§¯ m¯ ¬³ ´ ¯m´ ¬Ï´­¥³ “­§´¤Æ¯Ã§ q m¯­ ¸Ê

­³©¯m´ (multiple islands per read head)” Ä ¤¬³ ´ ¯m´ §³ ²Â É ¡³ q ³ ¯ ¬¢´ ©´£

Â É Ã£m­§É ¯ ¶ n¯£»§Å à ¥É ·Ê ¶ ³ ¬´£Ã ¥É (à ¥É à ¥É ­§³ ç²Ã ¥É §m´ ) ³Ê ¹¯ à ¥É ç²Ã ¥É §m´ Â É ¬´Â­ º ¯ ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É (ITI) ¯¤m´ Æ¥ É ´£© ¥¢´ ¥³

² Ï´­ n ´ ·ÊÅ ´¥ ¯ ¥­³¬ n¯£»§ ¯ à ¥É ­§³  m´ ³ Ë (Æ£m¬´£´¥ ¯ ¥­³¬ n¯£»§Å à ¥É

ç²Ã ¥É §m´ Æ n  ¥´²Ã n¯£»§­§´¤Ã ·Ê ¶ ´ à ¥É ³ Ë ¬´£Ã ¥É ¯´ Ï´Å­nÆ nÂ É ¬³ ´ ¯m´ §³ à  ·¤© ³ Æ n [108] ¸ Ï´Å­n¤´ m¯ ´¥ ¯ ¥­³¬ n¯£»§ ³ Ë ¬´£Ã ¥É Æ n¯¤m´ » n¯ )

6.3 § ¯ ¬ ¯ ¬³ ´ ³§¬q ¯ ¥² BPMR ¥² ´¥ ³ ¸ à à © ³ Ë ·ÊÅ nÅ ³ º ³ ¥²¤²Ã ¥É (track pitch) £· m´£´ ©m´ ´ ©§´ ¯ ¶

(bit period) m¯ n´ £´ ¸ Ï´Å­nÆ£m£· ³ ­´Â¥¹Ê¯ ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É (ITI) ¯¤m´ Æ¥ É ´£ n´ n¯ ´¥Å­n¥² BPMR £· ©´£­ ´Ã m  ¶ ¹Ë ·Ê£´ ©m´­¥¹¯Â m´ ³ 1 Tb/in2 à m§²Æ¯Ã§ q

 ¶ ãm­§É n¯ £·¥²¤²­m´ ¥²­©m´ ³ Æ£m ¶ 25 ´Ä £ ¥ (nm) ³ ³ Ë ¥² BPMR ² n¯

£·¥²¤²Ã ¥É Å §n ·¤ ³ ´ ©§´ ¯ ¶ ¸ Ï´Å­n n¯  ¶ ³ ³ ­´Â¥¹Ê¯ ´¥Ã ¥ ¬¯ ¥²­©m´

¬³ §³ « q (ISI) ç² ITI ¸Ê Â¥·¤ ¥©£ ³ ©m´ “ ´¥Ã ¥ ¬¯ à ¬¯ £¶ ¶ (2D interference)”

¯ ´ ·Ë ´¥Â ¶ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ Å ¥² BPMR ²Ã m´ ´ Å ¥²

´¥ ³ ¸ à à © ³ Ë [113] §m´© ¹¯¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ Å ¥² BPMR Â É §£´ ´

©´£ ³ © ¯ ´ ç² ϴí m ¯ Ưç q ¶ ãm­§É Å ¬¯ ¶ª ´ ¹¯ à © ´£Ã ¥É

ç²Ã © ©´ à ¥É ¸Ê £· § Ï´Å­n “¬³ ´ ³§¬q ´£Ã ¥É (along-track pulse)” ç² “Ä ¥Æ¡§q

©´ à ¥É (cross-track profile)”  §·Ê¤ à § Æ Å ´ ¶ ³ ¶ ´¥Ã ¥ ¬¯ à ¬¯ £¶ ¶Ã§²

¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ²£· § ¥² ¯¤m´ £´ m¯¬£¥¥ ² ¯ ¥² BPMR Å ¥» ¯ ¯³ ¥´ n¯ ¶ §´ ¯ ¶ [110, 114]

204

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

Å ­³© n¯ ·Ë ²¯ ¶ ´¤ ´¥¬¥n´ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ¯ m¯ ¬³ ´

BPMR  ¹Ê¯ Ï ´£´Å nÅ ´¥ Ï´§¯ ´¥Ã ¥ ¬¯ à ¬¯ £¶ ¶Ã§²¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ·Ê

­£¹¯ ¥¶ ³ ·Ê Å ¥² BPMR Ä ¤Å ´¥¬¥n´ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ·Ë ²

¯´ª³¤ ´¥ Ï´ © ¯¶ ¶ ¥³§ ´¥ ¯ ¬ ¯ à ¬´££¶ ¶ (3D reciprocity integral)  ·¤ ³ ª³ ¤q (potential) ¯ ­³©¯m´ à MR [108] ´ ³ Ë ² Ï´ ´¥ª¸ «´ § ¥² ¯ ¥» ¥ ¯ ­³©¯m´

ç²Æ¯Ã§ q Ê£ · · m¯ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ·Ë

6.3.1 ´¥ Ï´§¯ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ´¥ Ï´§¯ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶Å ­³© n¯ ·Ë ²¯¤m» ¬££º ¶ ´ ¯ ¬¹Ê¯ ³ ¸  ¶ ãm­§É à à © ³ Ë (perpendicular magnetic media) ç²­³©¯m´ à MR  m´ ³ Ë

¬Ï´­¥³ ­³©¯m´ à MR Ã¥ ³ Æ¡¡n ´¯m´ §³ (readback voltage) ²Â É ¬³ ¬m© ³

¡§³ q¬³ ´ (signal flux) ·ÊŬm n´Æ Å ¶ Ë ¬m© MR (MR element) ¥¶Â© ¹Ë ¶© ¯

ABS (air-bearing surface) ¸Ê  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯

(6.2)

VMR x , z CG x , z

£¹Ê¯ C ¹¯ m´ ³©, VMR ¹¯Ã¥ ³ Æ¡¡n ´¯m´ §³ , G ¹¯¡§³ q¬³ ´ , x ¹¯ ¶ª ´ Å Ã © ´£Ã ¥É , ç² z ¹¯ ¶ª ´ Å Ã © ©´ à ¥É ¥» ·Ê 6.8 ì ¥» ¥ ¯ ­³©¯m´ à MR ç² Ưç q ¶ ãm­§É à ³ º¥³¬ (square island) £¹Ê¯ a ¹¯ ©´£¤´© ¯ Ưç q, G ¹¯ ©´£¬» Ë ¬m© MR, ç² t ¹¯ ©´£­ ´ ¯ © (shield) ç² ¶ Ë ¬m© MR, W ¹¯ ©´£ ©n´ ¯ ¶

¶ Ë ¬m© MR

¯´ª³¤­§³ ´¥ ¯ ¬ ¯ (reciprocity principle) ¡§³ q¬³ ´ ·ÊŬm n´Æ Å ¶ Ë ¬m©

MR ¥¶Â© ¹Ë ¶© ¯ ABS ¬´£´¥  ·¤ Æ nÂ É [108] d d E d

G x , z N0 ¨

¨¨

d d d

H y x a, y a, z a

i

M y x a x , y a, z a z dx ady adz a

(6.3)

เทคโนโลยี BPMR

¯ Ưç q, d ¹¯¥²¤² ¶ ¯ ­³©¯m´ (fly height), g ¹¯ ©´£ ©n´ ¯ m¯ ©m´ (gap) ¥²­©m´

6

บทที่

£¹Ê¯ N0 ¹¯¬¢´ Å­n ¸£ m´ Æ n (permeability) ¯ ¥¶¢»£¶Â¬¥· (free space), i ¹¯ ¥²Ã¬Å §© ¶ ¢´ (imaginary coil), Hy ¹¯¬ ´£ ¯ ­³©¯m´ ·Ê ¶ ´ §© ¶ ¢´ , My(x, y, z) ¹¯

¬¢´ ©´£Â É Ã£m­§É ¯ ¬¹Ê¯ ³ ¸ (medium magnetization), ç² y ¹¯ ¶ª ´ Å Ã © ³ Ë ´

³ ¬¹Ê¯ ³ ¸ ´£¥» ·Ê 6.8  ¹Ê ¯ ´ ¬ ´£Ã£m­§É (magnetic field) ¹¯Â ¥Â ·¤ q ¯ ª³ ¤qãm­§É

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205

t

W

g

d z

E

x

My y

a ¥» ·Ê 6.8 ¥» ¥ ¯ ­³©¯m´ à MR ç²Æ¯Ã§ q ¶ ãm­§É

(magnetic potential) ³ ³ Ë ¬Ï´­¥³ ¬¢´ ©´£Â É Ã£m­§É à à © ³ Ë ¯¶ ¶ ¥³§ ´¥ ¯ ¬ ¯ ¬´£´¥ ì Å­n¯¤m»Å ¥» ¯ ª³ ¤q¬ ´£Ã£m­§É (magnetic field potential) ³Ê ¹¯ : x , y , z

¯ ­³©¯m´ à MR Æ n ³ ·Ë N G x , z 0 i

d d E d

s: x a, y a, z a

M y x a x , y a, z a z dx ady adz a

(6.4)

sM x a x , y a, z a z ¯ y ¡ ° a a a : x , y , z

¡ ° dx ady adz a ¨ a s y ¡ ° d ¢ ±

(6.5)

¨¨¨

d d d

sy a

­¥¹¯ G x , z

N0 i

d d E d

¨¨

d d

­§³ ´¥ ¯ ¬ ¯ ¯ Å­n ¥´ ©m´¡§³ q¬³ ´ ¬´£´¥ ì Å­n¯¤m»Å ¥» ¯ ´¥ Ï´ ¯ Ä©§» ³

¥²­©m´ ª³ ¤q¬ ´£Ã£m­§É ¯ ­³©¯m´ à MR ç² ¥² ºÃ£m­§É ¯ ¬¹Ê¯ ³ ¸ (medium mag-

netic charge) [43]

´ ©¶ ³¤Å [43, 114, 115] ì Å­nÂ­É ©m´ª³ ¤qãm­§É ·Ê ¶ ³ (x, y, z) Å È Â­ ¹ ¯

¹Ë ¶© ¯ ­³©¯m´ £· m´Â m´ ³

: x , y , z

206

d d : s x a, y a

y dx ady a 3/ 2 ¨ ¨ 2 2¯ 2Q d d 2 a a ¡ x x y z z ° ¢ ±

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(6.6)

¥» ·Ê 6.9 ª³ ¤qãm­§É ¹Ë ¶© ¯ ­³©¯m´ à MR ·Ê£· t = 4 nm, W = 20 nm, ç² g = 10 nm

£¹Ê¯ : s ¹¯ª³ ¤qãm­§É ¹Ë ¶© (SMP: surface magnetic potential) ¯ ­³©¯m´ Ä ¤ ·Êª³ ¤q ãm­§É ¹Ë ¶©¬Ï´­¥³ ¥¸Ê ­ ¸Ê ¯ ©´£ ©n´ ¯ ¶ Ë ¬m© MR ­´Æ n ´ [115]

(6.7)

£¹Ê¯

เทคโนโลยี BPMR

: shalf

2Qz ¬­ 2Qx ¬­ ¬­­ ­ cos ­­ 2 K 1 exp 1 ¬­ g ®­­ g ®­­ ­­­ ­­ 1 ­­ arctan Q ® 1 K ­­ ­­­ ®­

2Qz ¬­ 2Qx ¬­ 4Qz ¬­ ­ cos ­ exp ­ K 1 2 exp g ®­­ g ®­­ g ®­­ ç² g ¹¯¥²¤²­m´ ¥²­©m´ © ³ Ë ¬¯ (shield-to-shield spacing) ¸Ê ´ Å ¥ · ·Ë ²Æ n©m´

g x 2g ( »¥» ·Ê 6.8) ¥» ·Ê 6.9 ì ª³ ¤qãm­§É ¹Ë ¶© (SMP) ¯ ­³©¯m´ à MR ·Ê£·

6

บทที่

t = 4 nm, W = 20 nm, ç² g = 10 nm ç²¥» ·Ê 6.10 ì ¥» ¯ ³©¥q ¯ SMP ·Ë

­£´¤Â­ º ª³ ¤qãm­§É ¹Ë ¶© : s ¯ ­³©¯m´ Å ¥» ·Ê 6.9 ­´Æ n ³ ·Ë Â¥¶Ê£ n Å­n­´ m´ : shalf ´ ¬£ ´¥ (6.7) ¬Ï´­¥³ g / 2 b x b g / 2 ç² W / 2 b z bW / 2 Ä ¤ m´ : shalf ·ÊÆ n ·Ë É

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207

0.1

10

0.4

0.3

0.2

0.6

5

Along-track (x)

0.8 1 0

-5

-10 -20

-15

-10

-5

0

5

10

15

20

Cross-track (z)

¥» ·Ê 6.10 ¥» ¯ ³©¥q ¯ ª³ ¤qãm­§É ¹Ë ¶© (SMP) ¯ ­³©¯m´ à MR Å ¥» ·Ê 6.9

 ·¤ ¥¸Ê ¬m© ¯ : s  m´ ³ Ë ³ ³ Ë n´¬££º ¶©m´ : s £· ©´£¬££´ ¥ ¯· ¥¸Ê ¬m© ¯ : s É ¹¯ ¬m© ·ÊÂ É ¢´ ¬² n¯ ¯ : shalf ¸Ê £¹Ê¯ Ï ´Â¯´ : shalf 粬m© ·ÊÂ É ¢´ ¬² n¯ ¯ : shalf £´ · ·¬£´ ¶ ¬m© Å­ mÅ Ã © §´ Â É m´­ ¸Ê ¥² ³ É ²Æ nÂ É m´ : s ¸Ê £·§³ « ²Â É Â£ ¥¶ q Ê£ ( ¸Ê ì ¸ m´ª³ ¤qãm­§É ­³©¯m´ )  ¹Ê ¯ ´ ª³ ¤qãm­§É ­³©¯m´ £· m´Â m´ ³ ­ ¸Ê ¬£¯

³ ³ Ë Å­n Ï´¬Ï´Â ´ n¯£»§Å à © §´ ·Ë çn©Ã ¥  ¶Ê£Â n´Æ Š£ ¥¶ q¥¯ à © §´  ¶£­§´¤È

à © ´£ Ï´ © ·Ê¬¯ §n¯ ³ ©´£­ ´ ¯ ¶ Ë ¬m© MR

ª³ ¤qãm­§É Å ¬£ ´¥ (6.6) ¬´£´¥ ­´Æ n ´ m´ SMP Å ¬£ ´¥ (6.7) Ä ¤Å n¯¶ ¶ ¥³§

 ¶ ³©Â§ (numerical integral) ¯ ´ ·Ë Å ´¥ Ï´§¯ ³ Ë SUL (soft magnetic underlayer)

¯ ¬¹Ê¯ ³ ¸ à à © ³ Ë ²¬££º ¶©m´ ³ Ë SUL Â É Ã ¬£ »¥ q Ê£ · · ©´£­ ´Â É m´¯ ³ q n´Å­n

­³©¯m´ £·¢´ ¬£ »¥ q (perfect image) ²Æ n©m´¡³ q ³ ©´£Æ©¥©£ (total sensitivity function)

¥² ¯ n©¤¡³ q ³ ©´£Æ© ¯ ­³©¯m´ 粡³ q ³ ©´£Æ© ¯ ¢´ ­³©¯m´ (read-head’s image)

£¹Ê¯Â ·¤ ³ ¯ ¯ ³ Ë SUL [116] ³ ³ Ë ¡§³ qãm­§É ¥©£ ·ÊŬm n´Æ Å ¶ Ë ¬m© MR ·Ê ˹ ¶© ¯ ABS ¬´£´¥  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯ N G x , z 0 i

208

£ ¯ ¦² ¦ a a a ¦ ¡ sM y x x , y , z z ° ¦ ¦ ¦ a a a : q x , y , z

¤ » dx ady adz a total ¡ ° ¨ ¦¦ ¦ a s y ¡ ° d ¥ ¢ ±¦ ¦ ¦ ¼

d d E d

¨¨

d d

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(6.8)

z

x

y

d

E

M d E

¥» ·Ê 6.11 ¥² BPMR ·Ê£· ³ Ë SUL

£¹Ê¯ : total : x a, y a, z a : image x a, y a, z a ¯ ´ ·Ë n´¬££º ¶©m´Æ£m£· m¯ ©m´ ¥²­©m´ ³ Ë SUL 粬¹Ê¯ ³ ¸ É ²Æ n©m´ : image x a, y a, z a : x a, y d 2E , z a ´£ ·Êì Å ¥» ·Ê 6.11 ©´£­ ´ ¯ Ưç q ³ ì Å ¥» ·Ê 6.12 ( ³Ê ¹¯¯ º ³ q ¯ My £¹Ê¯Â ·¤ ³ y É ¹¯¡³ q ³ ¯¶£ ³§¬q¬¯ ¡³ q ³ ) ³ ³ Ë § ¯ ¬ ¯ ¬³ ´ ³§¬q­¥¹¯¬³ ´ ¯m´ §³ ·ÊÆ n ´ ­³©¯m´ ·Ê£·

º ª» ¤q §´ ¯¤m» Ê · ¶ ³ (0, 0) ·ÊÂ É §£´ ´ Ưç q Ê·£· º ª» ¤q §´ ¯¤m» Ê· ¶ ³ (x, y) ¬´£´¥

 ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯ d

\

^

V x , z C ¨ M x a x , y a, z a z ¡ : x a, y a d , z a : x a, y a d 2E , z a ¯° dx a (6.9) ¢ ± d

เทคโนโลยี BPMR

ç² n´¬££º ¶¯· ©m´¬¢´ ©´£Â É Ã£m­§É à à © ³ Ë My Â É Ã Â¯ ¥» (uniform) ´£Ã ©

6

บทที่

£¹Ê¯ £¦M (media magnetization), x , z island M x , z ¦¤ ¦¦¥0, else

(6.10)

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209

My M

d

d E

y

¥» ·Ê 6.12 ¬¢´ ©´£Â É Ã£m­§É ¯ Ưç q ¶ ãm­§É Å ¥² BPMR

¬£ ´¥ (6.10) ¯ Å­n ¥´ ©m´¬¢´ ©´£Â É Ã£m­§É à à © ³ Ë My £· m´Â m´ ³ m´ ³© M

 ´² ¥¶Â© ·ÊÂ É Æ¯Ã§ q ( ¯ ³ Ë £· m´Â m´ ³ ª» ¤q)  ¥´² ² ³ Ë ¬£ ´¥ (6.9) ¬´£´¥ ³ ¥»

Å­£mÆ n ¹¯

V x , z C

x a / 2 z a / 2

¨ ¨ \: x a,d , z a : x a,d 2E, z a ^dx adz a

(6.11)

x a / 2 z a / 2

£¹Ê¯ C CM ¹¯ m´ ³© ¬£ ´¥ (6.11) Ï´Å­n¬´£´¥ ¬¥n´ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ (2D pulse response) ¬Ï´­¥³ ¥» ¥ ¯ ­³©¯m´ ç²Æ¯Ã§ q ¶ ãm­§É §³ « ²Å È

Æ nÄ ¤ m´¤ ¥» ·Ê 6.13 ì § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶¬Ï´­¥³ Ưç q Ê·£· ©´£¤´©

11 ´Ä £ ¥ (a = 11 nm), ©´£¬» 10 ´Ä £ ¥ (G = 10 nm), ç²¥²¤² ¶ 10 ´Ä £ ¥

(d = 10 nm) Ä ¤Å n­³©¯m´ à MR ·Ê£· ´¥´£¶Â ¯¥q ´£¥» ·Ê 6.9 ç²¥» ·Ê 6.14 ì ¥» ¯ ³©¥q ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶Å ¥» ·Ê 6.13

¢´ ³ ©´ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶Å à © ´£Ã ¥É (z = 0) Â¥·¤ ©m´ “ § ¯

¬ ¯ ¬³ ´ ³§¬q ´£Ã ¥É (along-track pulse response)” ç²¢´ ³ ©´ ¯ ¬³ ´ ³§¬q

à ¬¯ £¶ ¶Å à © ©´ à ¥É (x = 0) ²Â¥·¤ ©m´ “Ä ¥Æ¡§q ©´ à ¥É (cross-track profile)”

¥» ·Ê 6.15 ì § ¯ ¬ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ç²Ä ¥Æ¡§q ©´ à ¥É ¯ ¬³ ´ ³§¬q

à ¬¯ £¶ ¶Å ¥» ·Ê 6.13 ´ ¥» ²Â­É Æ n©m´Ä ¥Æ¡§q ©´ à ¥É £· ©´£ ©n´ £´ ©m´ § ¯ ¬ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ¸Ê ­£´¤ ©´£©m´¥² BPMR37 ²Â ¶ ³ ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É

(ITI) ·Ê£· ©´£¥º Ã¥ £´ ©m´ ´¥Ã ¥ ¬¯ ¥²­©m´ ¬³ §³ « q (ISI) n´ Ï´­ Å­n PW50 ¹¯

©´£ ©n´ ¯ ¬³ ´ ³§¬q©³ ϴí m ·Ê¬³ ´ ³§¬q£· ©´£¬» Â É ¥¸Ê ­ ¸Ê ¯ ©´£¬» ¬» ¬º ³ ³ Ë ¥» ·Ê 6.15 ¯ Å­n ¥´ ©m´ PW50 Å Ã © ´£Ã ¥É £· m´Â m´ ³ 22.1 ´Ä £ ¥

ç² PW50 Å Ã © ©´ à ¥É £· m´Â m´ ³ 30 ´Ä £ ¥ 37

Å ´ ¶ ³ ¶Ä ¥Æ¡§q ©´ à ¥É ²Â É ³© ¯ Å­n ¥´ ¸ ©´£¥º Ã¥ ¯ ITI Å ² ·Ê § ¯ ¬ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ²Â É ³© ¯ Å­n ¥´ ¸ ©´£¥º Ã¥ ¯ ISI

210

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 6.13 § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ¬Ï´­¥³ Ưç q Ê£ · · a = 11 nm, G = 10 nm, ç²

d = 10 nm

40 0 30 0.1 0.2

10 0.9

0

เทคโนโลยี BPMR

Cross-track (z)

20

-10 -20 -30 -40 -40

-20

0

20

40

Along-track (x)

¥» ·Ê 6.14 ¥» ¯ ³©¥q ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶Å ¥» ·Ê 6.13

­£´¤Â­ º

6

บทที่

§ ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ¯ ¥² BPMR ·Ê ϴ¬ ¯Å ­³© n¯ ·Ë [108]

²Â­£¹¯ ³ § ¯ ¬ ¯ ¬³ ´ ³§¬q Ê · » Ï ´Â¬ ¯Å [110]

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211

1.2

Along-track pulse Cross-track profile

1

Normalized amplitude

0.8

0.6

0.4

0.2

0

-0.2 -40

-30

-20

-10

0

10

20

30

40

nm

¥» ·Ê 6.15 § ¯ ¬ ¯ ¬³ ´ ³§¬q ´£Ã ¥É (¬n ¸ ) ç²Ä ¥Æ¡§q ©´ à ¥É (¬n ²) ¯ ¬³ ´

³§¬qà ¬¯ £¶ ¶Å ¥» ·Ê 6.13

6.3.2 § ¥² ·Ê ¶ ´ Ưç qç²¥» ¥ ¯ ­³©¯m´ ´ ·Ê §m´©£´Å ¯ n ©m´ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶Å ¥² BPMR ² ¸Ë ¯¤m» ³ §³ « ² ¯ Ưç q ¶ ãm­§É ( m ¥» ¥m´ ç² ´ ¯ Ưç q) ç²¥» ¥ ¯ ­³©¯m´

( m ©´£ ©n´ W ç² m¯ ©m´ g) ³ ³ Ë ­³© n¯ ·Ë ²ª¸ «´ § ¥² ¯ §³ « ² ¯ Ưç q

ç²¥» ¥ ¯ ­³©¯m´ ·Ê£· m¯ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ·Ë Ä ¤ ² ¶ ´¥ ´Â ´²

Ưç qà ¬·Ê­§·Ê¤£ ³ º¥³¬Ã§²­³©¯m´ à MR  m´ ³ Ë ¸Ê ´¥ª¸ «´ ·Ë m©¤ Ï´Å­n n»¯m´  n´Å ¸ ´¥Â§¹¯ m´ ´¥´£¶Â ¯¥q m´ È ·ÊÅ nÅ ¥² ´¥ ³ ¸ n¯£»§Ã BPMR

¥» ·Ê 6.16 ì ï£ §¶ » ·Ê » Ï´Å­nÂ É ¥¥ ³ ´ (normalized amplitude) ¯

¬³ ´ ³§¬q ´£Ã ¥É ( ¯ à ¥É ­§³ ) ·ÊÂ É ¡³ q ³ ¯ ©´£¤´© ¯ Ưç q (£¹Ê¯Â ·¤ ³

ï£ §¶ » ¯ ¬³ ´ ³§¬q£¹Ê¯ ©´£¤´© ¯ Ưç q m´ ³ 13 nm) ç²¥» ·Ê 6.17 ì m´

PW50 Å Ã © ´£Ã ¥É (along-track) ç²Å à © ©´ à ¥É (cross-track) £·­ m ©¤Â É ´Ä

£ ¥ ·ÊÂ É ¡³ q ³ ¯ ©´£¤´© ¯ Ưç q Ä ¤¬³ ´ ³§¬qà ¬¯ £¶ ¶ ·ÊÅ nÅ ¥» ·Ê 6.16

ç² 6.17 Æ n£´ ´ Ưç qà ¬·Ê­§·Ê¤£ ³ º¥³¬ ·Ê£· ©´£¬» ¯ Ưç q G = 10 nm ç²¥²¤²

¶ ¯ ­³©¯m´ d = 10 nm ç²Å n­³©¯m´ à MR ·Ê£· ©´£­ ´ t = 4 nm, ©´£ ©n´ W =

20 nm, ç² ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR  m´ ³ g = 10 nm

212

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

2.5

Normalized amplitude

2

1.5

1

0.5

0

5

7

9

11

13

15

17

19

21

Island length, a (nm)

¥» ·Ê 6.16 ï£ §¶ » ·Ê » Ï´Å­nÂ É ¥¥ ³ ´ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ·ÊÂ É ¡³ q ³ ¯ ©´£¤´© ¯ Ưç q (£¹Ê¯Â ·¤ ³ ï£ §¶ » ¯ ¬³ ´ ³§¬q£¹Ê¯ a = 13 nm)

32

30

PW50 (nm)

28

Along-track PW 50 26

Cross-track PW 50

เทคโนโลยี BPMR

24

22

20

5

7

9

11

13

15

17

19

21

Island length, a (nm)

¥» ·Ê 6.17 PW50 ·ÊÂ É ¡³ q ³ ¯ ©´£¤´© ¯ Ưç q ( ´¥´£¶Â ¯¥q a)

´ ¥» ·Ê 6.16 ©m´Ã¯£ §¶ » ¯ ¬³ ´ ³§¬qà ¬¯ £¶ £ ¶ · m´£´ ¸Ë £¹Ê¯ ©´£¤´©

6

บทที่

¯ Ưç q ¶Ê£ ¸Ë ¸Ê ­£´¤ ©´£©m´¥² BPMR ·ÊÅ nƯç q ´ Å­ m ²£· § Ï´Å­n Ï´§³ ¯

¬³ ´ ¯m´ §³ £· m´¬» ¸ Ë ( ¸Ê m©¤ Ï´Å­n m´¤ m¯ ´¥ ¯ ¥­³¬ n¯£»§) ¯¤m´ Æ¥ É ´£¥» ·Ê 6.17 ¯

Å­n ¥´ ©m´Â£¹Ê¯Æ¯Ã§ q£· ´ Å­ m ¸Ë m´ PW50 Å Ã © ´£Ã ¥É ç²Å à © ©´ à ¥É É ²£·

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38

Along-track PW 50

36

Cross-track PW 50

34

PW50 (nm)

32 30 28 26 24 22 20 10

12

14

16

18

20

22

24

26

28

30

MR width, W (nm)

¥» ·Ê 6.18 PW50 ·ÊÂ É ¡³ q ³ ¯ ©´£ ©n´ ¯ ¶ Ë ¬m© MR ( ´¥´£¶Â ¯¥q W)

m´£´ ¸Ë ¸Ê ­£´¤ ©´£©m´¥² ²Â ¶ ³ ³ ­´Â¥¹Ê¯ ´¥Ã ¥ ¬¯ ¥²­©m´ ¬³ §³ « q (ISI)

ç² ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É (ITI) £´ ¸Ë n©¤ ³ ³ Ë ³ ¯¯ à ¥² ² n¯ ¥² · ¥² ¯£ ¥²­©m´ Ï´§³ ¯ ¬³ ´ ¯m´ §³ ·Ê n¯ ´¥Ã§²¥² ³ ©´£¥º Ã¥ ¯ ISI ç² ITI ·Ê¤¯£¥³ Æ n

³©¯¤m´  m n´ n¯ ´¥Å­n¥² BPMR £· ©´£­ ´Ã m  ¶ ¹Ë ·Ê m´ ³ 1 Tb/in2 É ©¥£· ´

©§´ ¯ ¶ ç²¥²¤²Ã ¥É n ¯¤ ©m´ 25 nm [108] ç² ©¥Å n ©´£¤´© ¯ Ưç q m´ ³ 11 nm

­¥¹¯ 13 nm  ¹Ê¯Å­n£·¥²¤²­m´ ¥²­©m´ Ưç q ·¤ ¯ (£· ISI ç² ITI n ¯¤) ç²Æ n Ï´§³ ¯ ¬³ ´ ¯m´ §³ ·Ê ·¤ ¯¬Ï´­¥³ ´¥ ¯ ¥­³¬ n¯£»§

¥» ·Ê 6.18 ì m´ PW50 Å Ã © ´£Ã ¥É ç²Å à © ©´ à ¥É ·ÊÂ É ¡³ q ³ ¯

©´£ ©n´ ¯ ¶ Ë ¬m© MR ( ³Ê ¹¯ ´¥´£¶Â ¯¥q W) ç²¥» ·Ê 6.19 ì ï£ §¶ » ·Ê » Ï´Å­n

Â É ¥¥ ³ ´ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ·ÊÂ É ¡³ q ³ ¯ ©´£ ©n´ ¯ ¶ Ë ¬m© MR ( ·¤ ³ ï£ §¶ » ¯ ¬³ ´ ³§¬q£¹Ê¯ ©´£ ©n´ ¯ ¶ Ë ¬m© MR  m´ ³ 20 nm) Ä ¤¬³ ´

³§¬qà ¬¯ £¶ ¶ Ê·Å nÅ ¥» ·Ê 6.18 ç² 6.19 Æ n£´ ´ Ưç qà ¬·Ê­§·Ê¤£ ³ º¥³¬ ·Ê£· ©´£¤´©

¯ Ưç q a = 13 nm, ©´£¬» ¯ Ưç q G = 10 nm, ç²¥²¤² ¶ ¯ ­³©¯m´ d = 10

nm ç²Å n­³©¯m´ à MR ·Ê£· ©´£­ ´ t = 4 nm ç² ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR  m´ ³ g = 10 nm

¥» ·Ê 6.18 ì Å­nÂ­É ©m´Â£¹Ê¯ ©´£ ©n´ ¯ ¶ Ë ¬m© MR £· m´Â ¶Ê£ ¸Ë m´ PW50 Å Ã ©

´£Ã ¥É ²£· ´¥Â §·Ê¤ à § ¯¤m´ n´È Å ² ·Ê m´ PW50 Å Ã © ©´ à ¥É ²£· ´¥Â §·Ê¤ à §

¯¤m´ ¥© ¥ɩ ¸Ê ­£´¤ ©´£©m´ ©´£ ©n´ ¯ ¶ Ë ¬m© MR £· § ¥² m¯ ©´£¥º Ã¥ ¯ ITI

214

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1.1

Normalized amplitude

1.05 1 0.95 0.9 0.85 0.8 0.75 0.7 10

12

14

16

18

20

22

24

26

28

30

MR width, W (nm)

¥» ·Ê 6.19 ï£ §¶ » ·Ê » Ï´Å­nÂ É ¥¥ ³ ´ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ·ÊÂ É ¡³ q ³ ¯ ©´£ ©n´ ¯ ¶ Ë ¬m© MR (£¹Ê¯Â ·¤ ³ ï£ §¶ » ¯ ¬³ ´ ³§¬q£¹Ê¯ W = 20 nm)

£´ ©m´ ISI ¯ ´ ·Ë ¥» ·Ê 6.19 ¯ Å­n ¥´ ©m´Â£¹Ê¯ ©´£ ©n´ ¯ ¶ Ë ¬m© MR £· m´Â ¶Ê£ ¸Ë

ï£ §¶ » ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ²£· m´Â ¶Ê£ ¸Ë ¯¤m´ n´È ç²Â¥¶Ê£§m»Â n´¬m» m´ ³© ³ ³ Ë n´ n¯ ´¥Å­n¥² £· ITI n ¯¤ É ©¥Å n­³©¯m´ à MR ·Ê£· ©´£ ©n´ W n ¯¤ ¯¤m´ Æ¥ É ´£ ´¥

¬¥n´ ­³©¯m´ ·Ê£· ©´£ ©n´ n ¯¤¤³ Â É ¬¶Ê ·Ê n´ ´¤ (¬¥n´ ¤´ ç²£·¥´ ´Ã ) ³ ³ Ë Å ¤º Ã¥ ¥² BPMR ²Å n ©´£ ©n´ ¯ ¶ Ë ¬m© MR ¥²£´ 15 – 20 nm [108]

Â É ¡³ q ³ ¯ ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR ( ´¥´£¶Â ¯¥q g) ç²¥» ·Ê

6.21 ì ï£ §¶ » ·Ê » Ï´Å­nÂ É ¥¥ ³ ´ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ·ÊÂ É ¡³ q ³ ¯

©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR ( ·¤ ³ ï£ §¶ » ¯ ¬³ ´ ³§¬q£¹Ê¯

g = 10 nm) Ä ¤¬³ ´ ³§¬qà ¬¯ £¶ ¶ Ê·Å nÅ ¥» ·Ê 6.20 ç² 6.21 Æ n£´ ´ Ưç qÃ

เทคโนโลยี BPMR

Å Ï´ ¯  ·¤© ³ ¥» ·Ê 6.20 ì m´ PW50 Å Ã © ´£Ã ¥É ç²Å à © ©´ à ¥É ·Ê

¬·Ê­§·Ê¤£ ³ º¥³¬ ·Ê£· ©´£¤´© a = 13 nm, ©´£¬» G = 10 nm, ç²¥²¤² ¶ ¯ ­³©¯m´ d = 10

Ë ¬m© MR  m´ ³ nm ç²Å n­³©¯m´ à MR ·Ê£· ©´£­ ´ t = 4 nm ç² ©´£ ©n´ ¯ ¶

W = 20 nm

´ ¥» ·Ê 6.20 ©m´Â£¹Ê¯ ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶Ë ¬m© MR £· m´

6

บทที่

 ¶Ê£ ¸Ë m´ PW50 Å Ã © ´£Ã ¥É ç²Å à © ©´ à ¥É É ²£· m´£´ ¸Ë n©¤ ¸Ê ­£´¤ ©´£©m´

m´ ITI ç² ISI ¬´£´¥ » © º£Æ n Ä ¤ ´¥Â §·Ê¤ à § ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR ¯ ´ ·Ë¥ » ·Ê 6.21 ¯ Å­n ¥´ ©m´Ã¯£ §¶ » ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶

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34

32

PW50 (nm)

30

28

Along-track PW 50 Cross-track PW 50

26

24

22

20 6

8

10

12

14

16

18

20

Gap length, g (nm)

¥» ·Ê 6.20 PW50 ·ÊÂ É ¡³ q ³ ¯ ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR ( ´¥´£¶Â ¯¥q g)

1.4

Normalized amplitude

1.3

1.2

1.1

1

0.9

0.8

0.7

6

8

10

12

14

16

18

20

Gap length, g (nm)

¥» ·Ê 6.21 ï£ §¶ » ·Ê » Ï´Å­nÂ É ¥¥ ³ ´ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ·ÊÂ É ¡³ q ³ ¯ ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR (£¹Ê¯Â ·¤ ³ ï£ §¶ » ¯ ¬³ ´ ³§¬q£¹Ê¯ g = 10 nm)

²£· m´Â ¶Ê£ ¸Ë £¹Ê ¯ ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR £· m´£´ ¸Ë (à mÆ£m

¥© ¥ɩ­£¹¯ ´¥Â §·Ê¤ à § ¯ m´ PW50 Å ¥» ·Ê 6.20) ¯¤m´ Æ¥ É ´£Å ´ ¶ ³ ¶­³©¯m´

à MR ·ÊÅ nÅ ¥² BPMR ²£· ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç² ¶ Ë ¬m© MR ¥²£´ 6 – 10 nm [108]

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6.4 à ϴ§¯ ¯ ¬³ ´ ¯m´ §³ Å ¥² BPMR Ä ¤ ³Ê©Æ ¬³ ´ ¯m´ §³ Å ¥² ´¥ ³ ¸ n¯£»§Â ¶ ãm­§É ²Æ n£´ ´ ´¥ n¯ ³  ¶ ¬n

(linear superposition) ¯ § ¯ ¬ ¯ ¬³ ´ ³§¬qÅ Ã © ´£Ã ¥É ¯¤m´ Æ¥ É ´£¬Ï´­¥³

¥² BPMR ·Ê£· ©´£ º n¯£»§¬» ¥²¤²­m´ ¥²­©m´ Ưç q ²£· m´ n ¯¤£´ ³ ³ Ë § ¥² ·Ê

 ¶ ´ à ¥É n´  ·¤ (adjacent track) ¸ Â É ¬¶Ê ·Ê­§· §·Ê¤ Æ£mÆ n ´ ¥» ·Ê 6.14 ç² 6.15 ²

Â­É Æ n©m´Ä ¥Æ¡§q ©´ à ¥É (cross-track profile) £· ©´£ ©n´ £´ ©m´ § ¯ ¬ ¯ ¬³ ´ ³§¬q ´£Ã ¥É (along-track pulse)  ¥´² ² ³ Ë ¬³ ´ ¯m´ §³ ¯ ¥² BPMR ·Ê¥©£

§ ¥² ·Ê ¶ ´ à ¥É n´  ·¤ ²Æ n£´ ´ ´¥ n¯ ³  ¶ ¬n ¯ § ¯ ¬ ¯ ¬³ ´ ³§¬q à ¬¯ £¶ ¶ ( ·¤ ³ n¯£»§¯¶ º Ã Æ ´¥·Ã ¬¯ £¶ ¶)

 ¹Ê ¯ ´ ϴí m ¯ Ưç q (­¥¹¯ ¶ n¯£»§) Å ¥² BPMR Æ n » Ï´­ Æ©nçn©

³ ³ Ë ¬³ ´ ¯m´ §³ ¸ ¬´£´¥ » à n©¤ ϴí m ¯ ¶ n¯£»§ (à ·Ê ²Â É ¥¥ · ©§´) Å­n ¶ ´¥ ´Æ¯Ã§ q ¶ ãm­§É à ³ º¥³¬ ´£¥» ·Ê 6.6 ( ) ²Æ n©m´¬³ ´ ¯m´ §³ ·Ê m¯Â ¹Ê ¯

´ ©§´¬´£´¥  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯

s x

M

N

a

m ,n

P mTz , x nTx

m M n N

(6.12)

£¹Ê¯ P(z, x) ¹¯ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ( »¥» ·Ê 6.13), x ¹¯¥²¤² ´ Å Ã © ´£ à ¥É , z ¹¯¥²¤² ´ Å Ã © ©´ à ¥É , Tx ¹¯ ´ ©§´ ¯ ¶ Å Ã © ´£Ã ¥É , Tz ¹¯¥²¤² ¯ m¯ ¬³ ´ Å Ã © ´£Ã ¥É , ç² am,n ¹¯ n¯£»§Æ ´¥·Ã ¬¯ £¶ ¶ ´ ¬£ ´¥ (6.12)

m = 0 ¬¯ §n¯ ³ à ¥É ­§³ ·ÊÆ n ´ ­³©¯m´ ·Ê£· º ª» ¤q §´ ¯¤m» Ê · Ê ¸ §´ à ¥É

¥» ·Ê 6.22 ì ´ ©§´ ¯ ¶ Tx ç²¥²¤²Ã ¥É Tz Å ¥² BPMR Ä ¤ n´ Tx

ç² Tz £· m´ n ¯¤ É ² Ï´Å­n¥² £· ©´£ º n¯£»§£´ ¸Ë à m ²¬m §Å­n ISI ç² ITI ¥º Ã¥ £´

เทคโนโลยี BPMR

à ¥É , (2M + 1)Tz ¹¯ ©´£ ©n´ ¯ m¯ ¬³ ´ Å Ã © ©´ à ¥É , (2N + 1)Tx ¹¯ ©´£¤´©

¸Ë ´£Æ n©¤ Ä ¤ ³©Ê Æ ©´£­ ´Ã m  ¶ ¹Ë ·Ê38 ¯ ¥² BPMR Ï´ © Æ n ´ 39 [107] ©´£­ ´Ã m  ¶ ¹Ë ·Ê |

38

(6.13)

6

บทที่

 n ´­£´¤ ¯ ¬ ´ ³ ©¶ ³¤ ·Ê ·Ê¤© n¯ ³ ¯º ¬´­ ¥¥£°´¥q ¶¬ qÆ ¥q¡ ¹¯ [117] n¯ ´¥Å­n£· ©´£­ ´Ã m  ¶ ¹Ë ·Ê 2

39

106 1550 TxTz

2

2

 m´ ³ 2 Tb/in Å · .ª. 2010, 5 Tb/in Å · .ª. 2013, ç² 10 Tbit/in Å · .ª. 2015 ¯´ª³¤£´ ¥´¬m© : 1 ´¥´ ¶Ë © = 0.00064516 ´¥´ £ ¥

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217

Tz

Tx

Tx Tz ¥» ·Ê 6.22 ´ ©§´ ¯ ¶ (bit period) ç²¥²¤²Ã ¥É (track pitch)

£·­ m ©¤Â É Â ¥² ¶ m¯ ´¥´ ¶Ë© (Tb/in2) £¹Ê¯ Tx ç² Tz £·­ m ©¤Â É ´Ä £ ¥ (nm) ³©¯¤m´  m n´ Ï´­ Å­n Tx = Tz ¥² BPMR ·Ê£· ©´£­ ´Ã m  ¶ ¹Ë ·Ê m´ ³ 1 Tb/in2 ²£· Tx =

Tz | 25.4 nm, ©´£­ ´Ã m  ¶ ¹Ë ·Ê m´ ³ 5 Tb/in2 ²£· Tx = Tz | 11.4 nm, ç² ©´£

­ ´Ã m  ¶ ¹Ë ·Ê m´ ³ 10 Tb/in2 ²£· Tx = Tz | 8 nm

6.4.1 m´ ¥²£´ ¯ ¬³ ´ ³§¬q BPMR  ¹Ê ¯ ´ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ P(z, x) ­¥¹¯Â¥·¤ ¬³ Ë È ©m´¬³ ´ ³§¬q BPMR ·Ê£· ©´£§²Â¯·¤ ¬» ( ¹Ê¯Å­n¬³ ´ ¯m´ §³ £· ©´£ » n¯ ç²Â­£¹¯ ³ ¬³ ´ ¥¶ ·ÊÆ n ´

­³©¯m´ Å­n£´ ¬º ) ¬¥n´ Æ n m¯ n´ ¤´ ³ ³ Ë Â ¹Ê¯Å­n m´¤ m¯ ´¥©¶Â ¥´²­q¥² BPMR ´ ©¶ ³¤

Å [108] ¸ Æ n ¥²£´ m´ (approximation) ¬³ ´ ³§¬q BPMR Å­nÂ É ¬³ ´ ³§¬q ´¬q  ·¤ à ¬¯ £¶ ¶ Ê ¸  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯

£ 1 x2 ² ¦ z 2 ¬¦ P z , x A exp ¦¤ 2 2 ­­­¦» ¦ ¦ 2 Wx Wz ®­¦ ¦ ¥ ¼

(6.14)

£¹Ê¯ A ¹¯Ã¯£ §¶ » ¬» ¬º £· m´Â m´ ³ 1, Wx PW50along / 2.3548 ç² Wz PW50cross / 2.3548 Ä ¤ PW50along ¹¯ m´ PW50 ¯ ¬³ ´ ³§¬q ´£Ã ¥É , PW50cross ¹¯ m´ PW50 ¯ Ä ¥Æ¡§q ©´ à ¥É , ç² m´ 2.3548 ¹¯ m´ ³© ¯ ©´£¬³£ ³ q¥²­©m´ m´ PW50 粬m©  ·Ê¤  £´ ¥ ´ ¯ ¡³ q ³  ´¬q ·¤ [108] ·Ê£· PW

¥» ·Ê 6.23 ì § ¯ ¬ ¯ ¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶ ´£¬£ ´¥ (6.14)

along 50

218

= 22.1 nm ç² PW50cross = 30 nm ¸Ê £·¥» ¥m´ §n´¤ ³ ¬³ ´ ³§¬q BPMR Å

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

1 0.8 0.6 0.4 0.2 0 40 20

40 20

0

0

-20

-20

Along-track (x)

-40

-40

Cross-track (z)

¥» ·Ê 6.23 § ¯ ¬ ¯ ¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶ ´£¬£ ´¥ (6.14) ·Ê£· PW50along = 22.1 nm cross ç² PW50 = 30 nm

1.2

2D BPMR pulse 2D Gaussian pulse

1

0.6

Cross-track profile

0.4

เทคโนโลยี BPMR

Normalized amplitude

0.8

0.2

0

Along-track pulse -0.2 -40

-30

-20

-10

0

10

20

30

40

nm

¥» ·Ê 6.24  ¥·¤  ·¤ ¬³ ´ ³§¬q ´£Ã ¥É ç²Ä ¥Æ¡§q ©´ à ¥É ¯ ¬³ ´ ³§¬q BPMR Å ¥» ·Ê 6.13 (¬n ¸ ) ç² ¯ ¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶ ´£¬£ ´¥ (6.14) (¬n ²)

6

บทที่

¥» ·Ê 6.13 ( ¸Ê £· PW50along = 22.1 nm ç² PW50cross = 30 nm) ¯ ´ ·Ë¥» ·Ê 6.24  ¥·¤  ·¤ ¬³ ´ ³§¬q ´£Ã ¥É ç²Ä ¥Æ¡§q ©´ à ¥É ¯ ¬³ ´ ³§¬q BPMR Å ¥» ·Ê 6.13 ç² ¯

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

219

¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶ ´£¬£ ´¥ (6.14) (ì n©¤Â¬n ²) ´ ¥» ·Ê 6.24 ©m´

¬³ ´ ³§¬q ´£Ã ¥É ç²Ä ¥Æ¡§q ©´ à ¥É ¯ ¬³ ´ ³§¬q BPMR ç² ¯ ¬³ ´ ³§¬q

 ´¬q ·¤ à ¬¯ £¶ ¶£· m´Å §n ·¤ ³ ³ ³ Ë ¬¥º Æ n©m´¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶Å ¬£ ´¥ (6.14) ¬´£´¥ Ï ´£´Å n ¥²£´ m´¬³ ´ ³§¬q BPMR Å ¥» ·Ê 6.13 Æ n  ¹Ê¯Å­n m´¤

m¯ ´¥©¶Â ¥´²­q¥² BPMR

6.4.2 m´ ¥²£´ ¯ ¬³ ´ ³§¬q BPMR ·Ê£·¬ ³ ´ ¥ © ¬¹Ê¯ ³ ¸ ´ ·Ê §m´©£´Å ¯ n m¯ ¬³ ´ BPMR ¬´£´¥ § ³ ­´Â¥¹Ê¯ ¬³ ´ ¥ © ´¥Â §·Ê¤

¬ ´ ² (transition noise) ç² ´¥Â§¹Ê¯ ¶ à ƣmÂ É Â ¶ ¬n (nonlinear bit shift) ¯¤m´ Æ¥ É ´£ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ (media noise) Â É ¬¶Ê ·Ê­§· §·Ê¤ Æ£mÆ nÅ m¯ ¬³ ´ BPMR ¸Ê £·

§Å­n¬£¥¥ ²¥©£ ¯ ¥² § § £´ Ä ¤ n Ï´Â ¶ ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ £´ ´ 5

¬´Â­ º­§³ ³ ·Ë [108]

1) ©´£ ³ © ¯ ϴí m (location fluctuation) ¯ à m§²Æ¯Ã§ q §m´© ¹¯Â ¹Ê ¯ ´ à m§² Ưç q£·¥²¤²­m´ n ¯¤ ©m´ 25 ´Ä £ ¥ ¸ Â É ´¥¤´ ·Ê Ï´Å­n º Ưç q£·¥²¤²­m´  m´ ³

¯¤m´ ¬£Ïʴ¬£¯

2) ©´£ ³ © ¯ ´ (size fluctuation) ¯ à m§²Æ¯Ã§ q 3) ©´£ ³ © ¯ ©´£¬» (height fluctuation) ¯ à m§²Æ¯Ã§ q

4) ©´£ ³ © ¯ ¥» ¥m´ (shape fluctuation) ¯ à m§²Æ¯Ã§ q

5) ©´£ ³ © ¯ ¬¢´ ©´£Â É Ã£m­§É ¯¶Ê£ ³© (saturation magnetization)  ¹Ê ¯ ´ à m§² Ưç q£· ´ Æ£mà m ¯ ¸ Ï´Å­n¬¢´ ©´£Â É Ã£m­§É ¯ à m§²Æ¯Ã§ q£· ©´£¯¶Ê£ ³© ¯ ãm­§É ·ÊÆ£m m´ ³

¯¤m´ Æ¥ É ´£¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ·Ê £´ Å ¥² BPMR [108]  ¶ ´ ©´£

³ © ¯ ϴí m ç² ´ ¯ à m§²Æ¯Ã§ q ³ ì Å ¥» ·Ê 6.25 ³ ³ Ë m´ ¥²£´ ¯

¬³ ´ ³§¬q BPMR ·Ê£·¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ·Ê ¶ ´ ©´£ ³ © ¯ ϴí m ç² ´

¯ Ưç q¬´£´¥  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯ [108]

£ ¦ ¦ ¬­2 ¬­2 ¯° ² ¦ ¦ z %z ¦ 1 ¡¡ x %x ¦ ­ ­­ ° ¦ ¦ ­­ P z , x A %A exp ¤ ¡ » ­ ° ­ ­ ¦ ¦ 2 ¡ c Wx %Wx ®­ c Wz %Wz ®­ ° ¦¦ ¦¦ ¢ ±¼ ¦ ¦ ¥

220

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(6.15)

¥» ·Ê 6.25 §³ « ² ¯ ©´£ ³ © ¯ ϴí m ç² ´ ¯ à m§²Æ¯Ã§ q

-1

10

-2

-3

10

No media noise 2% media noise 4% media noise 6% media noise 8% media noise 10% media noise

-4

10

12

13

14

15

16

17

18

19

20

21

22

SNR (dB)

¥» ·Ê 6.26 ³©¯¤m´ ¬£¥¥ ² ¯ ¥² BPMR ¥² ³ ©´£¥º Ã¥ m´ È ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸

Ä ¤ ·Ê %A ¹¯ ©´£ ³ © ¯ ï£ §¶ » , %x ¹¯ ©´£ ³ © ¯ ϴí m Å Ã © ´£Ã ¥É , %z ¹¯ ©´£ ³ © ¯ ϴí m Å Ã © ©´ à ¥É , %Wx ¹¯ ©´£ ³ © ¯ PW50 Å Ã ©

´£Ã ¥É , ç² %Wz ¹¯ ©´£ ³ © ¯ PW50 Å Ã © ©´ à ¥É ¥» ·Ê 6.26 ì ³©¯¤m´

เทคโนโลยี BPMR

BER

10

6

บทที่

¬£¥¥ ² ¯ ¥² BPMR ·Ê ¶ ³ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ·Ê£·¥² ³ ©´£¥º Ã¥ m´ È Ä ¤

· ´¥Â §·Ê¤ à § à ¬mº£ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ x % ­£´¤ ¸ ϴí m ç² ´ ¯ Ưç q£

( ³Ê ¹¯ m´ %A , %x , %z , %Wx ç² %Wz ) ´ m´ ¶Â É ¥¶£´ x % ´ ¥» ²Â­É Æ n©m´

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221

m¯ ¬³ ´

a M ,k

nk

H(m, n)

a 0,k

rk

aM ,k ¥» ·Ê 6.27 à ϴ§¯ m¯ ¬³ ´ BPMR ·ÊÆ£m ¯ m  ¹Ê ¯ ´ ©§´Ã ¬££»§

¬£¥¥ ² ¯ ¥² n¯¤§ ¯¤m´ £´ £¹Ê¯¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ £· ©´£¥º Ã¥ £´ ¸Ë ³ ³ Ë © ¥¢´ ¥³ ·Ê · ² n¯ £· ©´£¬´£´¥ Å ´¥ ³ ´¥ ³ ³ ­´Â¥¹Ê¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸

6.4.3 à ϴ§¯ m¯ ¬³ ´ BPMR ·ÊÆ£m m¯Â ¹Ê¯ ´ ©§´Ã ¬££»§ £¹Ê¯¬³ ´ ¯m´ §³ s(x) Å ¬£ ´¥ (6.12) » Ï´ ´¥ ³ ³©¯¤m´ ©§´ ·ÊÂ É ¥²¤²­m´ ¥²­©m´ Ưç q É ²Æ n¬³ ´ ¯m´ §³ ·ÊÆ£m m¯Â ¹Ê ¯ ´ ©§´ ¸Ê  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯ rk s x

M

x kTx

N

a

m ,n

H m , k n nk

m M n N

(6.16)

£¹Ê¯ nk ¹¯¬³ ´ ¥ ©  ´¬q¬· ´©Ã © (AWGN: additive white Gaussian noise) ç²

H(m, n) ¹¯ m¯ ¬³ ´ à ¬¯ £¶ ¶ ÊÆ· £m m¯Â ¹Ê ¯ ´ ©§´ ¸Ê Æ n ´ ´¥ ³ ³©¯¤m´ ¬³ ´ ³§¬q P(z, x ) ©§´ ·ÊÂ É Ï´ ©  m´ ¯ ´ ©§´ ¯ ¶ ç²¥²¤²Ã ¥É ³Ê ¹¯ H m , n P mTz , nTx

(6.17)

¬Ï´­¥³ –M d m < M ç² –N d n < N ¥» ·Ê 6.27 ì à ¢´ §É¯ ¯ m¯ ¬³ ´

BPMR ·ÊÆ£m m¯Â ¹Ê ¯ ´ ©§´Ã ¬££»§ Ä ¤ ·Ê a0,k ¬¯ §n¯ ³ §Ï´ ³ n¯£»§¯¶ º ¯ à ¥É ­§³ ·Ê ² » ¯m´ ç² » ¯ ¥­³¬ n¯£»§ n©¤© ¥¢´ ¥³ ¯ ´ ·Ë ´¥ Ï´ © ­´ m´¬³ ´ ¯m´ §³

rk Å ¬£ ´¥ (6.16) ² n¯ ¯´ª³¤ ´¥ Ï´ ¯ Ä©§» ³ à ¬¯ £¶ ¶ (2D convolution) ¸Ê m¯ n´ ³ n¯ [118]

 ¹Ê ¯ ´ m¯ ¬³ ´ H(m, n) Å ¬£ ´¥ (6.17) ¬´£´¥  ·¤ Å­n¯¤mÅ» ¥» £ ¥¶ q H

Æ n ¯ ´ ·Ë ´¥ Ï´§¯ ¬³ ´ ¯m´ §³ ·Ê£· § ¥² ¯ ISI ç² ITI Å ­§´¤È ´ ©¶ ³¤

[108, 109] ² ¶ ´¥ ´Å n n¯£»§Â ·¤ 3 ´ ©§´ ¯ ¶ ç² 3 à ¥É ´£§Ï´ ³  ¥´²¥² BPMR ·Ê ©´£ º n¯£»§¬» È (£´ ©m´ 1 Tb/in2) § ¥² ·Ê ¶ ´ ¶ ç²Ã ¥É n´  ·¤ ¯¹Ê È

222

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223

a 1,k

H 1 D

a 0,k

H 0 D

a1,k

H 1 D

nk rk

zk

aˆ0,k

¥» ·Ê 6.28 à ϴ§¯ m¯ ¬³ ´ BPMR ·ÊÆ£m ¯ m  ¹Ê ¯ ´ ©§´

²£· m´ n ¯¤£´ (¬´£´¥ §² ¶ Ë Æ n) ¯ ´ ·Ë  ¹Ê¯Å­n m´¤ m¯ ´¥ Ï´§¯ ¥² ç² ´¥¬¥n´ ¬³ ´

¯m´ §³ ·ÊÆ£m m¯Â ¹Ê ¯ ´ ©§´ ¯ ¥² BPMR Karakulak et al. [112] Æ n ϴ¬ ¯Ã Ï´§¯

m¯ ¬³ ´ BPMR ·ÊÆ£m m¯Â ¹Ê ¯ ´ ©§´ ´£¥» ·Ê 6.28 Ä ¤ ·Ê m¯ ¬³ ´ BPMR ¸Ê à n©¤

£ ¥¶ q H £· m´Â m´ ³

H 1 D ¯ ¡h 1, 1D 1 h 1,0 h 1,1D ¯° ¡ ° ¡ ° H ¡¡ H 0 D °° ¡ h0, 1D 1 h0,0 h0,1D ° ¡ H D ° ¡¡ h D 1 h h D °° 1,0 1,1 ¡¢ 1 °± ¢ 1, 1 ±

h 1,1 ¯° h0,1 °° h1,1 °±°

(6.18)

粬³ ´ ¯m´ §³ rk ¬´£´¥  ·¤ Å­n¯¤mÅ» ¥» ´¥ Ï´ ¯ Ä©§» ³ à ­ ¸Ê £¶ ¶Æ n ¹¯

rk a 0,k h0,k a 1,k h 1,k a1,k h1,k nk

(6.19)

£¹Ê¯ ¹¯ ³© Ï´Â ¶ ´¥ ¯ Ä©§» ³ (convolution operator) ´ ³ Ë ¬³ ´ ¯m´ §³ rk É ² » ¬m  n´Æ Å © ¥ ¥© ­´ PRML (partial-response maximum-likelihood) [10, 27]  ¹Ê¯­´ m´ ¥²£´ ¯ §Ï´ ³ n¯£»§ ¯ à ¥É ­§³ ( aˆ0,k )  m´ ³ Ë

เทคโนโลยี BPMR

h 1, 1 h 1,0 ¡ ¡¡h0, 1 h0,0 ¡h ¢¡ 1, 1 h1,0

6

บทที ่

© ¥ ¥© ­´ PRML Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ ¯· ©¯Æ§Â ¯¥q粩 ¥ ¥© ­´©·Â ¯¥q ¶

[10, 13] Ä ¤¯· ©¯Æ§Â ¯¥q ² Ï´­ n ´ ·Ê ¥³ ¥» ¥m´ ¯ ¬³ ´ Å­nÂ É Æ ´£ “ ´¥qÂ É (target)”

·Ê ¯ n ´¥ 粩 ¥ ¥© ­´©·Â ¯¥q ¶ ² Ï´­ n ´ ·Ê ¯ ¥­³¬ n¯£»§Ä ¤Å n© ¥ ¥© ­´©·Â ¯¥q ¶ ʬ · ¥n´

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%T Tz

Tx ¥» ·Ê 6.29 §³ « ² ¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³ (TMR) Å ¥² BPMR

´ ´¥qÂ É 40 ·Ê Ï´­ Æ©n  ¥´² ² ³ Ë ²Â­É Æ n©m´© ¥ ¥© ­´ PRML ·ÊÅ nÅ ´¥ ¯ ¥­³¬ n¯£»§

¯ ¥² ´¥ ³ ¸ n¯£»§Â ¶ ãm­§É à à © ¯ ç²Ã à © ³ Ë [10] ¤³ ¬´£´¥ Ï ´£´Å n ¯ ¥­³¬ n¯£»§ ¯ ¥² BPMR Æ n¯¤m´ £· ¥²¬¶ ¶¢´  m ³ [108, 109]

6.4.4 à ¥É £¶¬Â¥ ¶¬Â ¥ ³ ¥» ·Ê 6.7 ì ϴí m ·Ê­£´²¬º ¯ ­³©¯m´ à MR ·Ê¯¤m» ¬¹Ê¯ ³ ¸ §m´© ¹¯ º ª» ¤q §´ ¯ ­³©¯m´ ©¥¯¤m» º ¸Ê §´ ¯ à ¥É ­§³ ç²Â §¹Ê¯ ·Ê ´ Æ ³ à © ´£Ã ¥É  ¹Ê¯Å­n ¬³ ´ ¯m´ §³ ·Ê n´ ´¯¯ ¯ ­³©¯m´ £· º ¢´ ·¬º ¯¤m´ Æ¥ É ´£Å ´ ¶ ³ ¶­³©¯m´ £·

į ´¬Â §¹Ê¯ ·Ê§¹Ê¯ ¯¯ Æ ´ ϴí m ·Ê ©¥ ²Â É Ä ¤ n´ º ª» ¤q §´ ¯ ­³©¯m´ ²Â §¹Ê¯ ·Ê

Æ Å Ã © ©´ à ¥É ´ n´ (­¥¹¯ n´ §m´ ) ´£ ·Êì Å ¥» ·Ê 6.29 ²Â¥·¤ ¥´ ´¥ q ·Ë

©m´ “à ¥É £¶¬Â¥ ¶¬Â ¥ ³ ” (TMR: track mis-registration) ­¥¹¯¯¯¡Â É ¯ ­³©¯m´ (read head

offset) ¸Ê » Ï´­ Ä ¤ [119]

TMR

%T q100 Tz

(6.20)

£·­ m ©¤Â É Â ¯¥qÂ É q £¹Ê¯ 'T (track offset) ¹¯¥²¤² ·Ê­³©¯m´  §¹Ê¯ ·Ê¯¯ Æ ´ à ¥É ­§³

Å Ã © ©´ à ¥É ç² Tz ¹¯¥²¤²Ã ¥É (track pitch) ³ ³ Ë ¬³ ´ ³§¬q BPMR à ·ÊÆ£m m¯Â ¹Ê ¯ ´ ©§´ ·Ê£· § ¥² ¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³ £· m´Â m´ ³

40

´¥qÂ É ·Ê · ² n¯ £· § ¯ ¬ ¯  ¶ ©´£ ·Ê (frequency response) ­£¹¯ ³ § ¯ ¬ ¯  ¶ ©´£ ·Ê ¯ m¯ ¬³ ´ Å­n£´ ·Ê¬º [10]  ¹Ê¯Å­n© ¥ ¥© ­´©·Â ¯¥q ¶ Ï´ ´ Æ n¯¤m´ £· ¥²¬¶ ¶¢´ ¬» ¬º

224

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

On track (TMR = 0%) 20% off track (TMR = 20%) 40% off track (TMR = 40%)

Normalized amplitude

1

0.8

0.6

0.4

Along-track pulse (main track)

Cross-track pulse (adjacent track)

0.2

0 -40

-30

-20

-10

0

10

20

30

40

nm

¥» ·Ê 6.30 ¬³ ´ ³§¬q ´£Ã ¥É 粬³ ´ ³§¬q n´£Ã ¥É ·Ê£· § ¥² ¯ TMR

H m , n P mTz %T , nTx

(6.21)

Å ´ ¶ ³ ¶ TMR £· § ¥² m¯¬£¥¥ ² ¯ ¥² BPMR m¯ n´ £´  ¥´²£· §Å­n

¬³ ´ ¯m´ §³ ·ÊÆ n£·¥» ¥m´ ¶  ·¤ Ë Æ ´ ·Ê ©¥ ²Â É ¥» ·Ê 6.30 ì ¬³ ´ ³§¬q ´£

à ¥É 41 (along-track pulse) 粬³ ´ ³§¬q n´£Ã ¥É 42 (cross-track pulse) ·Ê£· § ¥²

©m´ Tx = Tz = 22 nm ´ ¥» ©m´Â£¹Ê¯£· TMR  ¶ ¸Ë Å ¥² ²¬m §Å­n¬³ ´ ³§¬q ´£

à ¥É ç²¬³ ´ ³§¬q n´£Ã ¥É £·Ã¯£ §¶ »  §·Ê¤ à § Æ ´  ¶£ ¸Ê Ï´Å­n¤´ m¯ ´¥ ¯ ¥­³¬ n¯£»§ ·Ê© ¥¢´ ¥³ ¥» ·Ê 6.31 ì ³©¯¤m´ ¬£¥¥ ² ¯ ¥² BPMR ·Ê ¶ ³ à ¥É £¶¬

เทคโนโลยี BPMR

¯ TMR Ä ¤¯´ª³¤¬£ ´¥ (6.14) £¹Ê¯ PW50along = 22.1 nm ç² PW50cross = 30 nm 粬££º ¶

Â¥ ¶¬Â ¥ ³ ·Ê£·¥² ³ ©´£¥º Ã¥ m´ È ´ ¥» ©m´Â£¹Ê¯Ã ¥É £¶¬Â¥ ¶¬Â ¥ ³ £· ©´£¥º Ã¥ £´ ¸Ë

É ² Ï´Å­n¥² £·¬£¥¥ ²§ § ³ ³ Ë ¥² BPMR ©¥£· ¥² © ´¥ n ¯ ³ ç²Ã nÆ ³ ­´

Â¥¹Ê¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³  ¹Ê¯Å­n¥² BPMR £·¬£¥¥ ²¬» ¬º

6

บทที่ 41 42

¬³ ´ ³§¬q ´£Ã ¥É (along-track pulse) É ¹¯ § ¯ ¬ ¯ ¯ ¬³ ´ ³§¬q ÊÆ· n ´ ­³©¯m´ ¯ à ¥É ­§³ Å ´ ¯º £ ¶ £¹Ê¯¥² BPMR Æ£m£·¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ç² § ¥² ¯ TMR ¬³ ´ ³§¬q n´£Ã ¥É (cross-track pulse) ¯ à ¥É ç²Ã ¥É §m´ ²£· m´Â m´ ³  ¹Ê ¯ ´ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ÊÆ· n ´ ­³©¯m´ ²£·§³ « ²¬££´ ¥ (symmetry) ´£ ·Êì Å ¥» ·Ê 6.13 ­¥¹¯ 6.23

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225

-1

10

-2

BER

10

-3

10

-4

On track (TMR = 0%) 10% off track (TMR = 10%) 15% off track (TMR = 15%) 20% off track (TMR = 20%)

10

10

11

12

13

14

15

16

17

18

SNR (dB)

¥» ·Ê 6.31 ³©¯¤m´ ¬£¥¥ ² ¯ ¥² BPMR ¥² ³ ©´£¥º Ã¥ m´ È ¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³ (TMR)

6.5 ¬¥º n´¤ Â Ä Ä§¤· ´¥ ³ ¸ n¯£»§Â ¶ ãm­§É à à © ³ Ë (perpendicular magnetic recording) ¸Ê Å n Å °´¥q ¶¬ qÆ ¥¡q ³ º ³ 43 Ï´§³  n´Å §n · Ï´ ³ »Â ¯¥q ´¥´Ã£  ¶ ³ ì Å ¥» ·Ê 6.32

³ ³ Ë Â Ä Ä§¤·¯Ê ¹ È ·Ê¬´£´¥  ¶Ê£ ©´£­ ´Ã m  ¶ ¹Ë ·Ê (areal density) Æ n£´ ©m´ 1 Tb/in2

¸ Â É ¬¶Ê Ï´Â É ¯¤m´ ¤¶Ê ¸Ê Æ nà m Â Ä Ä§¤· BPMR, Â Ä Ä§¤· HAMR, Â Ä Ä§¤· MAMR

(microwave assisted magnetic recording), Â Ä Ä§¤· SWR (shingled write recording), ç² Â Ä Ä§¤· TDMR Ä ¤Ã m§²Ã £· ©´£ n´ ´¤Å ´¥¯¯ à  ¹Ê¯Å n ´ ¥¶ ³ ·Ë [117]

1) Â Ä Ä§¤· BPMR ¤³ £· ³ ­´Â ·Ê¤© ³ ´¥¬¥n´ ¬¹Ê¯ ³ ¸ ·Ê£· ©´£Â¥·¤ (planarization) Å ¥² ³ ´Ä £ ¥, ´¥¯¯ à m¯ ¬³ ´ ¯m´ Å­£m (new read channel), ç² ´¥Â n´

³ ­©² ´¥Â ·¤ (write synchronization)

2) Â Ä Ä§¤· HAMR ¤³ £· ³ ­´Â ·Ê¤© ³ ´¥¬¥n´ ­³©Â ·¤ ·Ê£·Â§Â ¯¥q (laser)  ¹Ê¯Å­n ©´£¥n¯ ³ ¬¹Ê¯ ³ ¸ , ¥² © ´¥ Ï´Å­n¬Ê ¯ ¹ ³ ¸ Â¤É ³©§ ¯¤m´ ¥© ¥ɩ, ç² ϴí m ¯ ´¥ ¶ ³ Ë Â§Â ¯¥q Ê£ · · § ¥² m¯ ´¥Â ·¤

3) Â Ä Ä§¤· MAMR ¤³ £· ³ ­´Â ·Ê¤© ³  ¥¹Ê¯ Ï´Â ¶ ©´£ ·Ê ¯ ¬³ ´ Æ£Ä ¥Â©¡ 43

226

2

°´¥q ¶¬ qÆ ¥¡q Å ³ º ³ ( .ª. 2011) £· ©´£ º n¯£»§ ¥²£´ 400 – 600 Gb/in

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

Areal density

¥» ·Ê 6.32 à ©Ä n £ ©´£ º n¯£»§ ¯ °´¥q ¶¬ qÆ ¥¡q [117]

4) Â Ä Ä§¤· SWR ¸Ê Å n¥m©£ ´ ³ Â Ä Ä§¤· TDMR ¤³ £· ³ ­´Â ·Ê¤© ³ ´¥ ¥²£©§ § ¬³ ´ à ¬¯ £¶ ¶ (2D signal processing) ³ Ë ¬» Å m¯ ¬³ ´ ¯m´

¯¤m´ Æ¥ É ´£ ·Ë Æ n n Æ ·ÊÂ Ä Ä§¤· BPMR ¸Ê ¹¯©m´Â É ´ §¹¯ ­ ¸Ê ·Ê m©¤Â ¶Ê£

©´£ º n¯£»§ ¯ °´¥q ¶¬ qÆ ¥¡q Æ n£´ ©m´Â Ä Ä§¤· ´¥ ³ ¸ à à © ³ Ë ·ÊÅ n¯¤m»Å ³ º ³

Ä ¤ ·Ë ²Â¥¶Ê£ n ´¥ §m´© ¸ ´ ©¶ ³¤ n´ m´ È ·Ê£· § m¯ ´¥ ³ ´Â Ä Ä§¤· BPMR ´ ³ Ë

¯ ¶ ´¤©¶ · ´¥¬¥n´ § ¯ ¬ ¯ ¬³ ´ ³§¬q ¯ ¥² BPMR Ä ¤¯´ª³¤ ´¥ Ï´ © ¯¶ ¶ ¥³§

¯ ¥» ¥ ¯ ­³©¯m´ ç²Æ¯Ã§ q Ê£ · · m¯ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ·Ë

Å ¥² ´¥ ³ ¸ à BPMR ¬³ ´ ¯m´ §³ ¬¥n´ Æ n ´ ´¥ n¯ ³  ¶ ¬n ¯

§ ¯ ¬ ¯ ¬³ ´ ³§¬q ¯ à ¥É ­§³ ç²Ã ¥É n´  ·¤ ¸ Ï´Å­n ¶ ³ ­´Â¥¹Ê¯ ´¥Ã ¥

¬¯ ¥²­©m´ ¬³ §³ « q (ISI) ç² ´¥Ã ¥ ¬¯ ¥²­©m´ à ¥É (ITI) Ä ¤ ·Ê ITI ²£· ©´£¥º Ã¥

เทคโนโลยี BPMR

´¥ ¯ ¬ ¯ à ¬´££¶ ¶Â ·¤ ³ ª³ ¤q ¯ ­³©¯m´ à MR [108] ¥n¯£ ³ Ë ª¸ «´ § ¥²

£´ ¸Ë £¹Ê¯ ©´£ º n¯£»§¬» ¸Ë ¯ ´ ·Ë ¬³ ´ ¥ © ­§³ ·Ê £´ Å ¥² BPMR É ¹¯

¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ¸Ê  ¶ ´ ©´£Æ£m¬£ »¥ qÅ ´¥ §¶ ¬¹Ê¯ ³ ¸ ( Ï´Å­n ¶ ©´£ ³ ©

¯ ϴí m ´ ©´£¬» ç²¥» ¥m´ ¯ à m§²Æ¯Ã§ q)

³ ³ Ë ·Ë ¸ Æ n¯ ¶ ´¤Ã Ï ´ §¯ ¯ ¬³ ´ ¯m´ §³ Å ¥² BPMR ¸Ê Å n ­ ´

6

บทที่

m´ ¥²£´ ¯ ¬³ ´ ³§¬q BPMR ( ·Ê£·Ã§²Æ£m£·¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ )  ¹Ê¯Å­n¬´£´¥ ©¶Â ¥´²­q¥² BPMR Æ n m´¤ ¸Ë ¬º n´¤Æ n §m´© ¸ ¥´ ´¥ qà ¥É £¶¬Â¥ ¶¬Â ¥ ³ (TMR) ¥n¯£ ³ Ë ¯ ¶ ´¤ ´¥¬¥n´ ¬³ ´ ¯m´ §³ ·Ê£· § ¥² ¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³ n©¤

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227

6.6 Ã ¸ ­³ n´¤ 1.

¯ ¶ ´¤Ã © ¶ ¯ Â Ä Ä§¤· BPMR

2.

¯ ¶ ´¤ ©´£­£´¤ ¯ ¬£ ´¥ (6.1)

3.

¯ ¶ ´¤¬´Â­ ºÃ§² § ¥² ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ·Ê Å ¥² BPMR

4.

¯ ¶ ´¤¬´Â­ ºÃ§² § ¥² ¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³ (TMR)

5.

Å nÄ ¥Ã ¥£ SCILAB ©´ ¥» 5.1) § ¯ ¬ ¯ ¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶ ´£¬£ ´¥ (6.14) ç² (6.15) Ä ¤

Å­n Ï´­ m´ ´¥´£¶Â ¯¥q m´ È n©¤ ¯ ¥n¯£ ³ Ë §¯ ¥³ m´ ´¥´£¶Â ¯¥q m´ È Ã§n© ¬³  ¥» ¥m´ ¯ § ¯ ¬ ¯ ¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶ ÊÆ· n

5.2) ¬³ ´ ³§¬q ´£Ã ¥É 粬³ ´ ³§¬q n´£Ã ¥É ·Ê£· § ¥² ¯ TMR ´£¥» ·Ê 6.30

6.

Ï´­ Å­n t = 4 nm, W = 20 nm, g = 10 nm, a = 11 nm, G = 10 nm, ç² d = 10 nm Å nÄ ¥Ã ¥£ SCILAB ©´ ¥»

6.1) ª³ ¤qãm­§É ¹Ë ¶© ¯ ­³©¯m´ à MR ( ´£¥» ·Ê 6.9) 6.2) § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ( ´£¥» ·Ê 6.13) 6.3) § ¯ ¬ ¯ ¬³ ´ ³§¬q ´£Ã ¥É ç²Ä ¥Æ¡§q ©´ à ¥É ( ´£¥» ·Ê 6.15) 7.

228

¥³ m´ ´¥´£¶Â ¯¥q m´ È ·ÊÅ nÅ Ã ¸ ­³ n´¤ ·Ê n¯ 6 n©¤ ¯ çn© Ï´ Ï´Ë n¯ 6.1 – 6.3 ¥n¯£ ³ Ë ¬³  ç²¯ ¶ ´¤ §§³ q ÊÆ· n

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

·Ê 7 ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q ¬Ï´­¥³ ¥² BPMR

 ¶ § ¯ ¬ ¯ ´ ¬m© ©¥ ²Â É ¬» ¬º (PRML: partial-response maximum-likelihood) [10, 27] Â É Â ¶ ­§³ ·ÊÅ nÅ ´¥ ¥© ­´ n¯£»§ ¯ ¥² ´¥ ³ ¸ n¯£»§Â ¶ ãm­§É à ´¥ ¤´¤¬³ ´ ¥ © (noise enhancement) ç² ©´£ ³ n¯ ¯ ¥² ÉÆ£m£´  m´Å

© ¥ ¥© ­´ PRML Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ ¯· ©¯Æ§Â ¯¥q粩 ¥ ¥© ­´

©·Â ¯¥q ¶ [10, 13] ¸Ê ¬£¥¥ ² ¯ © ¥ ¥© ­´ PRML ² ¸Ë ¯¤m» ³ ©´£Â­£´²¬£ ¯ ´¥q É

粯· ©¯Æ§Â ¯¥q Ê·Å nÅ ¥² Ä ¤¯· ©¯Æ§Â ¯¥q ² Ï´­ n ´ ·Ê ¥³ ¥» ¥m´ ¯ ¬³ ´ Å­nÂ É Æ ´£ ´¥qÂ É ·Ê n¯ ´¥ ´ ³ Ë © ¥ ¥© ­´©·Â ¯¥q ¶ ʸ ¬¥n´ ´ ´¥qÂ É ·Ë ² Ï´­ n ´ ·Ê ¯ ¥­³¬ n¯£»§

¯ ´ ·Ë ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q Ê · ·Å ¥² BPMR ¤³ ¬´£´¥ m©¤§ § ¥² ·Ê ¶ ´ ISI ç² ITI Æ n¯· n©¤

 ¹Ê ¯ ´ m¯ ¬³ ´ BPMR £· § ¥² ´ ITI ³ ³ Ë © ¥¢´ ¥³ ©¥Å n© ¥

¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ (2D Viterbi detector) [108, 109]  ¹Ê¯Å­n¥² £·¬£¥¥ ²¬» ¬º ¯¤m´ Æ¥ É ´£© ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶£· ©´£ ³ n¯ ¬» £´ ³ ³ Ë Nabavi [108] ç² Karakulak

[109] ¸ Æ n ϴ¬ ¯©¶ · ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥qà m´ È Â m ´¥qÂ É ­ ¸Ê £¶ ¶ ³

¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶, ´¥qÂ É ¬¯ £¶ ¶ ³ ¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶, ç² ´¥qÂ É ¬¯ £¶ ¶ ³ ¯· ©¯Æ§Â ¯¥q

¬¯ £¶ ¶ Â É n  ¹Ê¯Å­n¬´£´¥ Å n© ¥ ¥© ­´©·Â ¯¥q ¶Ã ³Ê©Æ Æ n ( ³Ê ¹¯© ¥ ¥© ­´©·Â ¯¥q ¶

­ ¸Ê £¶ ¶ ´£ ·Ê¯ ¶ ´¤Å ·Ê 4 ¯ [10])  ¥´² ² ³ Ë Å ·Ë ²¯ ¶ ´¤©¶ · ´¥¯¯ à ´¥q É

เทคโนโลยี การออกแบบทาร BPMR เก็ตและอีควอไลเซอรสำหรับระบบ BPMR

m´ È Â m à à © ¯ à à © ³ Ë Ã§²Ã BPMR  ¥´²£· n¯ · ¹¯¥² ²Æ£m£· ³ ­´Â¥¹Ê¯

76

บทที่ บทที่

粯· ©¯Æ§Â ¯¥qà m´ È ¬Ï´­¥³ ¥² BPMR ¥n¯£ ³ Ë Ã¬ ¬£¥¥ ² ¯ ´¥qÂ É ³ Ë ­£ ³ m¯Æ ·Ë

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229

nk

a 1,k a 0,k a1,k

zk

rk

a 0,k

dk

aˆ0,k

wk

¥» ·Ê 7.1 à ϴ§¯ m¯ ¬³ ´ ¬Ï´­¥³ ´¥¯¯ à ´¥qÂ É ­ ¸Ê £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ [10]

­£´¤Â­ º Å ·Ë x m¯ ¬³ ´ BPMR ·ÊÆ£m m¯Â ¹Ê ¯ ´ ©§´ ² » Ï´­ n©¤Â£ ¥¶ q H ¸Ê Æ n£´ ´ ´¥ ³

³©¯¤m´ (sampling) § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ ©§´ ·ÊÂ É Ï´ ©  m´ ¯ ´ ©§´ ¯ ¶ (Tx) ç²¥²¤²Ã ¥É (Tz)

x ¬³ ´ ¯m´ §³ ·ÊÆ n ´ ­³©¯m´ ²£· § ¥² ¯ ISI ·Ê£´ ´ n¯£»§Â ·¤ 3 ´ ©§´ ¯

¶ ç²£· § ¥² ¯ ITI ·Ê£´ ´ n¯£»§Â ·¤ 3 à ¥É  m´ ³ Ë ³Ê ¹¯Â£ ¥¶ q H ²£· ´ 3u3 ( ³Ê ¹¯ 3 à ©Ã§² 3 à © ³ Ë ) ´£¬£ ´¥ (6.18)

x ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q º à ²Å n©¶ · ´¥ “ n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤ n ¯¤¬º

(MMSE: minimum mean-squared error)” [14] ¸Ê Â É ´¥ Ï´Å­n n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤ (MSE) ¥²­©m´ ¬³ ´ ·Ê n´ ´¯¯ ¯ ¯· ©¯Æ§Â ¯¥q {zk} 粬³ ´ n´ ´¯¯ ¯

´¥qÂ É {dk} £· m´ n ¯¤¬º ( »¥» ·Ê 7.1) ¸Ê ©¶ · ´¥ MMSE ·Ë Â É ©¶ · Ê· m´¤Ã§²Â­£´²¬Ï´­¥³ ´¥ Ï ´£´Å n ´ ¥¶ Å ´ ¶ ³ ¶

7.1 ´¥qÂ É ­ ¸Ê £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ BPMR ·ÊÆ£m m¯Â ¹Ê ¯ ´ ©§´¬Ï´­¥³ ´¥¯¯ à ´¥qÂ É ­ ¸Ê

£¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶Å ¥» ·Ê 7.1 Ä ¤ ·Ê \a 1,k ,a 0,k , a1,k ^ \o1^ ¹¯§Ï´ ³ n¯£»§¯¶ º

¯ à ¥É à ¥É §´ ç²Ã ¥É §m´ ´£§Ï´ ³ ² » ¬m  n´Æ ¤³ m¯ ¬³ ´ H Ï´Å­nÆ n ¬³ ´ ¯m´ §³ rk ¸Ê  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯ 1

rk

1

h

230

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

a

m ,n m ,k n

m 1 n 1

nk

(7.1)

£¹Ê¯ hm,n ¹¯ m´¬³£ ¥²¬¶ ¶ Î ¯ £ ¥¶ q H ( »¬£ ´¥ (6.18)) ç² nk ¹¯¬³ ´ ¥ ©  ´¬q  ·¤ ¬· ´©Ã © (AWGN) ·Ê£· m´Â §·Ê¤Â m´ ³ ª» ¤qç² ©´£Ã ¥ ¥©  m´ ³ ı2 ³Ê ¹¯

nk N 0, T 2 ´ ³ Ë © ¥¢´ ¥³ ¬³ ´ ¯m´ §³ rk ² » ¬m  n´Æ ¤³ ¯· ©¯Æ§Â ¯¥q

­ ¸Ê £¶ ¶ F(D)  ¹Ê¯ ¥³ ¥» ¥m´ ¯ ¬³ ´ ¯m´ §³ Å­n£· º ¬£ ³ ¶Â É Æ ´£ ´¥qÂ É G(D) çn©

¸ ¬m n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q {zk}  n´Æ Å © ¥© ¥ ¥© ­´©·Â ¯¥q ¶Ã ³Ê©Æ  ¹Ê¯­´ m´ ¥²£´ ¯ §Ï´ ³ n¯£»§ ¯ à ¥É §´ ³Ê ¹¯­´ m´ aˆ0,k

n´¬££º ¶©m´ § ¥² ·Ê ¶ ´ ITI ¹¯Â É ¬³ ´ ¥ © ¥²Â¢ ­ ¸Ê ·Ê­£¹¯ ³

¬³ ´ ¥ © nk ³ ³ Ë ´¥¯¯ à ´¥qÂ É ­ ¸Ê £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶Å ­³© n¯ ·Ë ²

­£¹¯ ³ ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q Ê·Å nÅ ¥² ´¥ ³ ¸ n¯£»§Ã à © ³ Ë ´£ ·Ê

¯ ¶ ´¤Å ·Ê 3 ¯ [10] ¸Ê ¬¥º Æ n ³ ·Ë n´ Ï´­ Å­n¯· ©¯Æ§Â ¯¥q ´ N = 2K + 1 à É

(£¹Ê¯ K ¹¯Â§ Ï´ ©  ɣ © ) ¬´£´¥  ·¤ Å­n¯¤m»Å ¥» ¬£ ´¥ ¶ ª´¬ ¥qÅ Ä Â£ D Æ n ¹¯ K

fD

(7.2)

k

k

k K

£¹Ê¯ D ¹¯ ³© Ï´Â ¶ ´¥­ m © ©§´ Tx ­ m ©¤ Å Ï´ ¯  ·¤© ³ ´¥qÂ É ´ L = 3 Ã É 44 ɬ´£´¥  ·¤ Å­n¯¤m»Å ¥» ¯ ¬£ ´¥ ¶ ª´¬ ¥qÅ Ä Â£ D Æ n ¹¯ 2

G D gk D k

(7.3)

k 0

Ä ¤ ·Ê fk ç² gk ¹¯ m´¬³£ ¥²¬¶ ¶§Î Ï´ ³ ·Ê k ¯ ¯· ©¯Æ§Â ¯¥qç² ´¥qÂ É ´£§Ï´ ³

º ¥²¬ qÅ ´¥¯¯ à ´¥qÂ É n©¤©¶ · ´¥ MMSE É ¹¯ ² Ï´ ´¥ Ï´ © ­´ m´

¬³£ ¥²¬¶ ¶ Î ¯ F(D) ç² H(D) Æ ¥n¯£ ³ Š©§´Â ·¤© ³ Ä ¤ ´¥ Ï´Å­n m´ MSE ¥²­©m´

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

F D

n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q zk ç² n¯£»§Â¯´ q º ¯ ´¥qÂ É dk £· m´ n ¯¤¬º ­¥¹¯ §m´©¯· ³ ¤­ ¸Ê ¹¯ m´¬³£ ¥²¬¶ ¶ Î fk ç² gk ² » §¹¯  ¹Ê¯ Ï´Å­n m´

2¯ E ¡wk2 ¯° E ¡ rk fk a 0,k gk ° ¢ ± ¢¡ ±°

\

^

(7.4)

7

บทที่

£· m´ n ¯¤¬º £¹Ê¯ wk = zk – dk ¹¯ n¯ ¶ §´ ·Ê ¶ ´ ´¥¯¯ à ´¥qÂ É , ¹¯ ³© Ï´Â ¶ ´¥ ¯ Ä©§» ³ , ç² E[ ] ¹¯ ³© Ï´Â ¶ ´¥ m´ ´ ­£´¤ (expectation operator)

44

2

´¥qÂ É ´ 3 Ã É É ·¤ ¯ ·Ê ² Ï ´£´Å nÅ ¥² BPMR [108, 109]  ¹Ê ¯ ´ £¹Ê¯ ©´£ º n¯£»§£´ ©m´ 1 Tb/in § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶Å à © ´£Ã ¥É ² ¥¯ §º£ n¯£»§Â ·¤ 3 ´ ©§´ ¯ ¶ (Tx)

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231

n´ Ï´­ Å­n g = [g 0 g1 g2]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ´¥qÂ É G(D) ç² f = [f–K …

f0 … fK]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ¯· ©¯Æ§Â ¯¥q F(D), rk = [rk +K … rk … rk – K]T ¹¯Â©  ¯¥q à © ³ Ë ¯ ¬³ ´ ¯m´ §³ , ak = [a0,k a0,k – 1 a0,k – 2]T ¹¯Â©  ¯¥qà © ³ Ë ¯ n¯£»§¯¶ º Å

à ¥É §´ {a0,k}, ç² [ ]T ¹¯Â ¥¹Ê¯ £ ¥¶ q¬§³  §·Ê¤ (transpose matrix) ³ ³ Ë ¬£ ´¥ (7.4) ¬´£´¥  ·¤ Å­n¯¤m»Å ¥» £ ¥¶ qÆ n ³ ·Ë

T¯ E ¡w 2 ¯° E ¡ f T rk g T ak f T rk g T ak ° ¢ ± ¢ ±

f T Rf g T Ag 2f T Pg

(7.5)

£¹Ê¯ R E ¡rk rkT ¯° ¹¯Â£ ¥¶ q¯³ ¬­¬³£ ³ q (auto-correlation matrix) ´ NuN ¯ n¯£»§ ¢ ± {rk}, A E ¡ak akT ¯° ¹¯Â£ ¥¶ q¯³ ¬­¬³£ ³ q ´ L u L ¯ n¯£»§ {a0,k}, P E ¡rk akT ¯° ¹¯ ¢ ± ¢ ± £ ¥¶ q¬­¬³£ ³ q n´£ (cross-correlation matrix) ´ N u L ¥²­©m´ n¯£»§ {rk} ç² {a0,k},

N = 2K + 1 ¹¯ Ï´ © Ã É ¯ ¯· ©¯Æ§Â ¯¥q, ç² L = 3 ¹¯ Ï´ © Ã É ¯ ´¥qÂ É Ä ¤ ·Ê ¬£´ ¶ (i, j) (à © ·Ê i ç²Ã © ³ Ë ·Ê j) ¯ £ ¥¶ q ³ Ë ¬´£ ·Ë ¹¯

S 1 ¯ R i , j E ¡ rk K i rk K j ° , 0 b i , j b 2K ¡ ° ¢ k 0 ±

(7.6)

S 1 ¯ A i , j E ¡ a 0,k ia 0,k j ° , 0 b i , j b L 1 ¡ ° ¢ k 0 ±

(7.7)

S 1 ¯ P i , j E ¡ rk K ia 0,k j ° , 0 b i b 2K , 0 b j b L 1 ¡ ° ¢ k 0 ±

(7.8)

£¹Ê¯ S ¹¯ ©´£¤´© (­¥¹¯ Ï´ © ¶ ) ¯ §Ï´ ³ n¯£»§¯¶ º {a0,k}

´¥ Ï´Å­n m´ E[w2] Å ¬£ ´¥ (7.5) £· m´ n ¯¤¬º £¹Ê¯Â ·¤ ³ f ç² g ² n¯ £· ´¥

Ï´­  ¹Ê¯ Æ ³ ³ (constraint)  n´Æ Å ¥²­©m´ ¥² © ´¥ Ï´Å­n£· m´ n ¯¤¬º (minimization process)  ¹Ê¯­§· §·Ê¤ ³ ­´ ·Ê ²Æ n §§³ qÂ É f = g = 0 ³ ³ Ë Å ·Ê ·Ë ² Ï´ ´¥ ¥²¤º qÅ n

 ¹Ê¯ Æ ³ ³ à ģ ¶ (monic constraint) [10, 14] Å ´¥¯¯ à ´¥qÂ É ¸Ê ² Ï´­ Å­n m´¬³£ ¥²¬¶ ¶ Î ¯ Ã É §´ ¯ ´¥qÂ É £· m´Â m´ ³ ­ ¸Ê ( ³Ê ¹¯ g1 = 1) [108] ³ ³ Ë n´Å­n

©  ¯¥qà © ³ Ë I = [0 1 0]T  ¹Ê¯ Æ ³ ³ à ģ ¶ ·Ë¬´£´¥  ·¤ Å­n¯¤m»Å ¥» ¯ £ ¥¶ qÆ n ¹¯ ITg = 1  ¥´² ² ³ Ë ¥² © ´¥Å ´¥¯¯ à ´¥qÂ É ·ÊÅ n ¹Ê¯ Æ ³ ³ à ģ ¶ ² Ï´Å­n

232

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

m´ MSE Å ¬£ ´¥ (7.5) £· m´ n ¯¤¬º Ä ¤ ¤´¤´£¥³ «´Å­n m´ ITg = 1 §¯ ©§´ ³Ê ¹¯ ¥² © ´¥ ·Ë ² Ï´Å­n m´

E ¡w 2 ¯° f T Rf g T Ag 2f T Pg 2M I T g 1

¢ ±

(7.9)

£· m´ n ¯¤¬º £¹Ê¯ O ¹¯ ³© » §´ ¥´ q (Lagrange multiplier) ·ÊÂ É m´¬Â §´¥q ´¥ Ï´Å­n¬£ ´¥

(7.9) £· m´ n ¯¤¬º Ï´Æ nÄ ¤ ´¥­´¯ º ³ q ¯ ¬£ ´¥ (7.9)  ·¤ ³ f, g ç² O ´£§Ï´ ³ çn© Å­n §§³ q m´ ³ ª» ¤q É ²Æ n Ï´ ¯ ¹¯

1

(7.10)

1

I T A P T R 1 P I 1

g M A P T R 1 P I

(7.11)

f R 1Pg

(7.12)

Ä ¤ m´ O É ¹¯ m´ MMSE ·ÊÆ n ´ ´¥¯¯ à ´¥qÂ É ¢´¤Å n ¹Ê¯ Æ ³ ³ ·Ë ­£´¤Â­ º ¬£ ´¥ (7.10) – (7.12) ²Â­£¹¯ ³ ¬£ ´¥ (3.19) – (3.21) ¯ ´¥¯¯ à ´¥qÂ É Ã§²

¯· ©¯Æ§Â ¯¥q ÊÅ· nÅ ¥² ´¥ ³ ¸  ¶ ãm­§É à à © ³ Ë ´£ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 3.2.1 ¯ [10]

7.2 ´¥qÂ É ¬¯ £¶ ¶ Ê·£·£º£Â É ª» ¤q粯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ Ä ¤ ³©Ê Æ ´¥qÂ É ­ ¸Ê £¶ ¶ ʯ · ¶ ´¤Å ­³© n¯ ·Ê 7.1 ­£´²¬Ï´­¥³ Ï ´£´Å n ´ Å ¥² BPMR ·Ê£·

§ ¥² ¯ ITI n ¯¤ ( m ©´£ º n¯£»§ < 2 Tb/in2) à m£¹Ê¯¥² BPMR £· § ¥² ¯

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

M

ITI ´ §´ ( m ©´£ º n¯£»§ 2 ¸ 2.5 Tb/in2) É ©¥Â §·Ê¤ £´Å n ´¥qÂ É ¬¯ £¶ ¶ Å ­³© n¯ ·Ë

²¯ ¶ ´¤©¶ · ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤q (zero-corner target) 粯· ©¯Æ§Â ¯¥q ­ ¸Ê £¶ ¶ ´£ ·Ê ϴ¬ ¯Å [109] ¸Ê ¬´£´¥ à m ¯¯ Â É 2 ¥ · ³ ·Ë

7

บทที่

7.2.1 £¹Ê¯ ¥´ m¯ ¬³ ´ H ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ ¬Ï´­¥³ ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶Å

¥» ·Ê 7.2 [109] £¹Ê¯ \a 1,k ,a 0,k , a1,k ^ \o1^ ¹¯§Ï´ ³ n¯£»§¯¶ º ¯ à ¥É à ¥É §´ ç²Ã ¥É §m´ ´£§Ï´ ³ ² » ¬m  n´Æ ¤³ m¯ ¬³ ´ H ¸Ê » Ï´­ n©¤¬£ ´¥ (6.18) ³Ê ¹¯

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233

m¯ ¬³ ´ H

a 1,k

nk

H 1 D

a 0,k

H 0 D

a1,k

H 1 D

rk

¯· ©¯Æ§Â ¯¥q

F(D)

zk

Viterbi detector

aˆ0,k

´¥qÂ É G

G 1 D

G0 D

dk

wk

G1 D

¥» ·Ê 7.2 à ϴ§¯ m¯ ¬³ ´ ¬Ï´­¥³ ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ [109]

H 1 D ¯ h 1, 1 h 1,0 ¡ ° ¡ H ¡¡ H 0 D °° ¡¡h0, 1 h0,0 ¡ H D ° ¡h ¡¢ 1 °± ¡¢ 1, 1 h1,0

h 1,1 ¯° h0,1 °° h1,1 °°±

(7.13)

£¹Ê¯ H –1 (D), H0(D) ç² H1(D) ¹¯ § ¯ ¬ ¯ ¯ m¯ ¬³ ´ Å Ã ¥É à ¥É §´ ç²Ã ¥É §m´ ´£§Ï´ ³ Ï´Å­nÆ n¬³ ´ ¯m´ §³ rk ´£¬£ ´¥ (6.19) ³Ê ¹¯

rk a 0,k h0,k a 1,k h 1,k a1,k h1,k nk

(7.14)

Ä ¤ ·Ê hm,k ¹¯ m´¬³£ ¥²¬¶ ¶ Î ¯ £ ¥¶ q H ¬Ï´­¥³ m {–1, 0, 1} ç² nk N 0, T 2 ¹¯ ¬³ ´ ¥ © AWGN ·Ê£· m´Â §·Ê¤Â m´ ³ ª» ¤qç² ©´£Ã ¥ ¥©  m´ ³ ı2 ´ ³ Ë © ¥ ¢´ ¥³ ¬³ ´ ¯m´ §³ rk ² » ¬m  n´Æ ¤³ ¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ F(D)  ¹Ê¯ ¥³ ¥» ¥m´ ¯ ¬³ ´ ¯m´ §³ Å­n£· º ¬£ ³ ¶Â É Æ ´£ ´¥qÂ É Gm(D) çn© ¸ ¬m n¯£»§Â¯´ q º ¯ ¯· ©¯

Ƨ ¯¥q {zk}  n´Æ Å © ¥ ¥© ­´©·Â ¯¥q ¶Ã ·Ê » ¥³ ¥º 45 (modified Viterbi detector) [108]

 ¹Ê¯­´ m´ ¥²£´ ¯ §Ï´ ³ n¯£»§ ¯ à ¥É §´ { aˆ0,k } 45

© ¥ ¥© ­´©·Â ¯¥q ¶Ã ·Ê » ¥³ ¥º [108] » ¯¯ à £´Â ¹Ê¯Å n ³ ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤qç²Ã ¥É n´  ·¤ £· m´¬³£ ¥²¬¶ ¶ÂÎ m´ ³ ³Ê ¹¯ g–1,0 = g1,0 = g–1,2 = g1,2 = 0 ç² g–1,1 = g1,1 ( »¬£ ´¥ (7.15))

234

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q ²Å n©¶ · ´¥ MMSE Ä ¤ n´ Ï´­ Å­n¯· ©¯Æ§Â ¯¥q

­ ¸Ê £¶ ¶ F(D) £· Ï´ © N = 2K + 1 Ã É ´£¬£ ´¥ (7.2) ç² ´¥qÂ É ¬¯ £¶ ¶ ´ 3 u 3 £· m´

 m´ ³

G 1 D ¯ g 1,0 ¡ ° ¡ G ¡¡ G0 D °° ¡¡g 0,0 ¡ G D ° ¡g ¢¡ 1 ±° ¢¡ 1,0

g 1,1 g 1,2 ¯° g 0,1 g 0,2 °° g1,1 g1,2 °±°

(7.15)

£¹Ê¯ G –1 (D), G0(D) ç² G1(D) ¹¯ § ¯ ¬ ¯ ¯ ´¥qÂ É Å Ã ¥É à ¥É §´ ç² · ·£º£Â É ª» ¤q46 à ¥É §m´ ´£§Ï´ ³ , ç² g–1,0 = g1,0 = g–1,2 = g1,2 = 0 ¬Ï´­¥³ ´¥qÂ É ¬¯ £¶ ¶ Ê£

Å Ï´ ¯  ·¤© ³ n´Å­n f = [f–K, …, f0, …, fK]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ¯· ©¯Æ§Â ¯¥q,

ak = [a –1,k +K a0,k +K a1,k +K … a –1,k a0,k a1,k … a –1,k –K – 2 a0,k –K – 2 a1,k –K – 2]T ¹¯Â©  ¯¥q

m¯ ¬³ ´ ´ N u (6K + 9) ¸Ê £· m´Â m´ ³

h 1, 1 h0, 1 h1, 1 h 1,0 h0,0 h1,0 h 1,1 h0,1 h1,1 0 0 0 0 "¯ ¡ ° H ¡ 0 0 0 h 1, 1 h0, 1 h1, 1 h 1,0 h0,0 h1,0 h 1,1 h0,1 h1,1 0 "°° ¡ ¡ # # # # # # # # # # # # # %°± ¢

(7.16)

³ ³ Ë §Ï´ ³ n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q¬´£´¥  ·¤ Å­n¯¤m»Å ¥» £ ¥¶ qÆ n ¹¯ n f T r z k f T Ha k k k

(7.17)

n ¹¯Â©  ¯¥qà © ³ Ë ·Ê£·¬£´ ¶ N ³© ¯ ¬³ ´ ¯m´ §³ £¹Ê¯ rk Ha k k

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

à © ³ Ë ·Ê£·¬£´ ¶ 6K + 9 ³© ¯ §Ï´ ³ n¯£»§¯¶ º ³ Ë ¬´£Ã ¥É , nk = [nk+K … nk … nk–K]T ¹¯Â£ ¥¶ q ¹¯Â©  ¯¥qà © ³ Ë ·Ê£·¬£´ ¶ N = 2K + 1 ³© ¯ ¬³ ´ ¥ © nk, ç²Å­n H

¯ ´ ·Ë n´ Ï´­ Å­n uk = [a0,k a –1,k –1 a0,k –1 a1,k –1 a0,k – 2]T ¹¯Â©  ¯¥qà © ³ Ë

¯ §Ï´ ³ n¯£»§¯¶ º ³ Ë ¬´£Ã ¥É ·Ê¬¯ §n¯ ³ ©  ¯¥qà © ³ Ë ¯ ´¥qÂ É ·Ê£·£º£Â É ª» ¤q

( ´²¬£´ ¶ ·Ê£· m´Æ£m m´ ³ m´ª» ¤q) g = [g0, 0 g –1,1 g0,1 g1,1 g0,2]T ¸Ê Ï´Å­n§Ï´ ³ n¯£»§ ¯

´¥qÂ É G £· m´Â m´ ³

dk = gTuk

46

7

บทที่

(7.18)

Ä ¤ ³©Ê Æ ´¥qÂ É ·Ë ² » Ï ´£´Å n£¹Ê¯ {h–1,–1, h1,–1, h–1,1, h1,1} ¯ m¯ ¬³ ´ H Å ¬£ ´¥ (7.13) £· m´ n ¯¤£´

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235

³ ³ Ë § m´ ¥²­©m´ n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q zk ç² n¯£»§Â¯´ q º ¯ ´¥qÂ É dk ¹¯ wk z k dk f T rk g T uk

(7.19)

´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q n©¤©¶ · ´¥ MMSE ²Â§¹¯ m´¬³£ ¥²¬¶ ¶ Î fk

ç² gk ·Ê Ï´Å­n m´ n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤ (MSE) ³Ê ¹¯

T¯ 2 E ¡w 2 ¯° E ¡ z k dk ¯° E ¡ f T rk g T uk f T rk g T uk ° ¢ ± ¢ ± ¢ ±

(7.20)

g T Ug 2f T Pg f T Rf

E r r T ¯ ¹¯Â£ ¥¶ q¯³ ¬­¬³£ ³ q ´ N uN, U E u u T ¯ ¹¯Â£ ¥¶ q £· m´ n ¯¤¬º £¹Ê¯ R ¡¢ k k ±° ¢¡ k k ±° T ¯³ ¬­¬³£ ³ q ´ 5 u 5, ç² P E ¡ rk uk ¯° ¹¯Â£ ¥¶ q¬­¬³£ ³ q n´£ ´ N u 5 ¢ ±

´¥¯¯ à ´¥qÂ É n©¤©¶ · ´¥ MMSE ²Å n ¹Ê¯ Æ ³ ³ à ģ ¶ ¸Ê ² Ï´­ Å­n

m´¬³£ ¥²¬¶ ¶ Î ¯ Ã É ª» ¤q §´ ¯ ´¥qÂ É £· m´Â m´ ³ ­ ¸Ê ( ³Ê ¹¯ g0,1 = 1) [109] ç² n´Å­n

©  ¯¥qà © ³ Ë I = [0 0 1 0 0]T  ¹Ê¯ Æ ³ ³ à ģ ¶ ·Ë ²Â ·¤ Å­n¯¤m»Å ¥» ¯ £ ¥¶ qÆ n

¹¯ ITg = 1 ³ ³ Ë ¥² © ´¥Å ´¥¯¯ à ´¥qÂ É ·ÊÅ n ¹Ê¯ Æ ³ ³ à ģ ¶ ·Ë ² Ï´Å­n m´

MSE Å ¬£ ´¥ (7.20) £· m´ n ¯¤¬º Ä ¤ ¤´¤´£¥³ «´Å­n m´ ITg = 1 §¯ ©§´ §m´© ¹¯ ´¥

¯¯ à ´¥qÂ É n©¤©¶ · ´¥ MMSE ² Ï´Å­n m´

g T Ug 2f T Pg 2M I T g 1

E ¡w 2 ¯° f T Rf ¢ ±

(7.21)

£· m´ n ¯¤¬º £¹Ê¯ O ¹¯ ³© » §´ ¥´ q ´ ³ Ë Å­n­´¯ º ³ q ¯ ¬£ ´¥ (7.21)  ·¤ ³ f, g ç² O ´£§Ï´ ³ çn©Å­n §§³ q m´ ³ ª» ¤q É ²Æ n Ï´ ¯ ¹¯ 1

M

I

T

U P

T

1 P 1 I R 1

(7.22)

TR 1 P I g M U P

(7.23)

1Pg f R

(7.24)

Ä ¤ m´ O É ¹¯ m´ MMSE ·ÊÆ n ´ ´¥¯¯ à ´¥qÂ É ¢´¤Å n ¹Ê¯ Æ ³ ³ Ä£ ¶ ¬³  ² ©m´ ¬£ ´¥ (7.22) – (7.24) ² §n´¤ ³ ¬£ ´¥ (7.10) – (7.12)

236

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7.2.2 £¹Ê¯Æ£m ¥´ m¯ ¬³ ´ H ©¶ · ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q Ê·Æ n¯ ¶ ´¤Å ­³© n¯ ·Ê 7.2.1 n¯ Å n m¯ ¬³ ´ H  ¹Ê¯

­´ m´ rk ¯¤m´ Æ¥ É ´£¥² ·ÊÅ n ´ ¥¶ Å ´ ¶ ³ ¶ ²Æ£m ¥´ ©m´ m¯ ¬³ ´ H £· m´Â m´Å

à m¤³ ¬´£´¥ ­´ m´¬³ ´ ¯m´ §³ rk Æ n ( »¥» ·Ê 7.2) ³ ³ Ë Å ·Ê ·Ë ²¯ ¶ ´¤ ´¥¯¯ Ã

´¥qÂ É ¬¯ £¶ ¶ Ê·£·£º£Â É ª» ¤q粯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ Ä ¤¯´ª³¤¬³ ´ ¯m´ §³ rk ¸Ê £·

¬£¥¥ ²Å §n ·¤ ³ ´¥¯¯ à ´¥qÂ É Å ­³© n¯ ·Ê 7.2.1

´ à ϴ§¯ m¯ ¬³ ´ BPMR Å ¥» ·Ê 7.2 n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q£· m´

 m´ ³ zk = rk fk = fTrk £¹Ê¯ f = [f–K … f0 … fK]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ¯· ©¯Æ§Â ¯¥q Ê·

£·¬£´ ¶ N = 2K + 1 ³© ç² rk = [rk +K … rk … rk – K]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ¬³ ´

¯m´ §³ Å Ï´ ¯  ·¤© ³ n´Å­n g = [g0,0 g–1,1 g0,1 g1,1 g0,2]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ´¥q É

·Ê£·£º£Â É ª» ¤q ç² uk = [a0,k a –1,k –1 a0,k –1 a1,k –1 a0,k – 2]T ¹¯Â©  ¯¥qà © ³ Ë ¯ §Ï´ ³ n¯£»§ ¯¶ º ³ Ë ¬´£Ã ¥É ·Ê¬¯ §n¯ ³ ©  ¯¥q g  ¥´² ² ³ Ë n¯£»§Â¯´ q º ¯ ´¥qÂ É £· m´Â m´ ³

(7.25)

wk z k dk f T rk g T uk

ç² m´ n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤ (MSE) £· m´Â m´ ³ 2 E ¡w 2 ¯° E ¡ z k dk ¯° f T Rf g T Ug 2f T Pg ¢ ± ¢ ±

(7.26)

£¹Ê¯ R E ¡rk rkT ¯° ¹¯Â£ ¥¶ q¯³ ¬­¬³£ ³ q ´ N uN, P E ¡rk ukT ¯° ¹¯Â£ ¥¶ q¬­¬³£ ³ q ¢ ± ¢ ± T n´£ ´ N u 5, ç² U E ¡uk uk ¯° ¹¯Â£ ¥¶ q¯ ³ ¬­¬³£ ³ q ´ 5 u 5 ¢ ± ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q n©¤©¶ · ´¥ MMSE ·ÊÅ n ¹Ê¯ Æ ³ ³ à ģ ¶

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

dk = gTuk ¸Ê Ï´Å­nÆ n©m´ § m´ ¥²­©m´ §Ï´ ³ n¯£»§ zk 粧ϴ ³ n¯£»§ dk ¹¯

² ¤´¤´£ Ï´Å­n m´ MSE Å ¬£ ´¥ (7.26) £· m´ n ¯¤¬º Ä ¤¥³ «´Å­n m´ ITg = 1 §¯ ©§´ £¹Ê¯

I = [0 0 1 0 0]T ( ³Ê ¹¯ g0,1 = 1) §m´© ¹¯ ´¥¯¯ à ´¥qÂ É ©¶ · ·Ë ² Ï´Å­n m´ E ¡w 2 ¯° f T Rf g T Ug 2f T Pg 2M I T g 1

¢ ±

7

(7.27)

บทที่

£· m´ n ¯¤¬º £¹Ê¯ O ¹¯ ³© » §´ ¥´ q ´ ³ Ë Å­n­´¯ º ³ q ¯ ¬£ ´¥ (7.27)  ·¤ ³ f, g ç² O ´£§Ï´ ³ çn©Å­n §§³ q m´ ³ ª» ¤q É ²Æ n Ï´ ¯ Â É Æ ´£¬£ ´¥ (7.22) – (7.24) Â É R ç²Â §·Ê¤ P Â É P  m´ ³ Ë Â ·¤ à m §·Ê¤ m´ R

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

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7.3 ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ Å ´ ¯º £ ¶Ã§n© (£¹Ê¯¥² BPMR Æ£m£·¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ç²Æ£m£· ³ ­´Â¥¹Ê¯ ©´£ Æ£mÂ É Â ¶ ¬n m´ È Â m à ¥É £¶¬Â¥ ¶¬Â ¥ ³ ) § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ Ê·Æ n ´

­³©¯m´ ²£·§³ « ²¬££´ ¥ (symmetry) ´£ ·Êì Å ¥» ·Ê 6.13 ç² 6.23 §m´© ¹¯¬³ ´ ³§¬q n´£Ã ¥É (across-track pulse) ¯ à ¥É ç² ¯ à ¥É §m´ ²£· m´Â m´ ³ 47 Å ´ ¶ ³ ¶

£¹Ê¯¥² BPMR £· ©´£ º n¯£»§¬» È ­¥¹¯£· § ¥² ¯ ITI £´ ( m ©´£ º n¯£»§ t 3 Tb/in2) ´¥qÂ É ¬¯ £¶ ¶ Ê· ©¥ Ï ´£´Å n ² n¯ £· m´¬³£ ¥²¬¶ ¶ Î ¯ ´¥qÂ É ¯ à ¥É ç²Ã ¥É

§m´ Æ£m m´ ³ m´ª» ¤q  ¹Ê¯Å­n£· § ¯ ¬ ¯  ¶ ©´£ ·Ê­£¹¯ ³ § ¯ ¬ ¯ ¯ m¯ ¬³ ´ H Å­n£´ ·Ê¬º ³ ³ Ë Å ­³© n¯ ·Ë ²¯ ¶ ´¤ ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥ [120]  ¹Ê¯Å n

´ ³ ¥² BPMR £· ©´£ º n¯£»§¬» ç²Æ£m£· § ¥² ¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³ (TMR)

Ï´­ Å­n ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥ ³Ê ¹¯ G–1(D) = G1(D) ¬´£´¥  ·¤ Å­n¯¤m»Å

¥» £ ¥¶ qÆ n ³ ·Ë

G 1 (D )¯ g 1,0 ¡ ° ¡ G = ¡¡ G0 (D ) °° = ¡¡ g 0,0 ¡ G (D ) ° ¡g ¢ 1 ± ¡¢ 1,0

g 1,1 g 1,2 ¯° g 0,1 g 0,2 °° g 1,1 g 1,2 °°±

(7.28)

´ à ϴ§¯ m¯ ¬³ ´ BPMR Å ¥» ·Ê 7.2 n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q£· m´Â m´ ³ zk

= rk fk = fTrk £¹Ê¯ f = [f–K … f0 … fK]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ¯· ©¯Æ§Â ¯¥q Ê·£·¬£´ ¶ N = 2K + 1 ³© ç² rk = [rk +K … rk … rk – K]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ¬³ ´ ¯m´ §³ Å

Ï´ ¯  ·¤© ³ n´Å­n g = [g–1,0 g0,0 g–1,1 g0,1 g–1,2 g0,2]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ´¥qÂ É Ã

¬££´ ¥ ç² uk = [(a –1,k + a 1,k) a0,k (a –1,k – 1 + a 1,k – 1) a0,k – 1 (a –1,k – 2 + a 1,k – 2) a0,k – 2]T

¹¯Â©  ¯¥qà © ³ Ë ¯ §Ï´ ³ n¯£»§¯¶ º ·Ê¬¯ §n¯ ³ ©  ¯¥q g ³ ³ Ë n¯£»§Â¯´ q º ¯ ´¥qÂ É £· m´Â m´ ³ dk = gTuk ¸Ê Ï´Å­nÆ n©m´ § m´ ¥²­©m´ zk ç² dk ¹¯ wk z k dk f T rk g T uk

(7.29)

ç² m´ n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤ (MSE) £· m´Â m´ ³

47

¬³  ´ § ¯ ¬ ¯ ¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶ P(z, x) Å ¬£ ´¥ (6.14) ² ©m´ P(Tz, x) = P(–Tz, x) Ä ¤ ·Ê P(Tz, x) ç² P(–Tz, x) ¹¯¬³ ´ ³§¬q n´£Ã ¥É ¯ à ¥É ç² ¯ à ¥É §m´ ´£§Ï´ ³ £¹Ê¯ Tz ¹¯ ¥²¤²Ã ¥É (track pitch) Å ² ·Ê P(0, x) ¹¯¬³ ´ ³§¬q ´£Ã ¥É (along-track pulse) ¯ à ¥É §´

238

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

2 E ¡w 2 ¯° E ¡ z k dk ¯° f T Rf g T Ug 2f T Pg ¢ ± ¢ ±

(7.30)

£¹Ê¯ R E ¡rk rkT ¯° ¹¯Â£ ¥¶ q¯³ ¬­¬³£ ³ q ´ N uN, P E ¡rk ukT ¯° ¹¯Â£ ¥¶ q¬­¬³£ ³ q ¢ ± ¢ ± T n´£ ´ N u 6, ç² U E ¡uk uk ¯° ¹¯Â£ ¥¶ q¯ ³ ¬­¬³£ ³ q ´ 6 u 6 ¢ ± ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q n©¤©¶ · ´¥ MMSE ·ÊÅ n ¹Ê¯ Æ ³ ³ à ģ ¶

² ¤´¤´£ Ï´Å­n m´ MSE Å ¬£ ´¥ (7.30) £· m´ n ¯¤¬º Ä ¤¥³ «´Å­n m´ ITg = 1 §¯ ©§´ £¹Ê¯ I = [0 0 0 1 0 0]T ( ³Ê ¹¯ g0,1 = 1) §m´© ¹¯ ´¥¯¯ à ´¥qÂ É ©¶ · ·Ë ² Ï´Å­n m´ E ¡w 2 ¯° f T Rf g T Ug 2f T Pg 2M I T g 1

¢ ±

(7.31)

£· m´ n ¯¤¬º £¹Ê¯ O ¹¯ ³© » §´ ¥´ q ´ ³ Ë Å­n­´¯ º ³ q ¯ ¬£ ´¥ (7.31)  ·¤ ³ f, g

1

M

I

T

U P

T

(7.32)

1

R 1 P I 1

g M U P T R 1 P I

(7.33)

f R 1Pg

(7.34)

£¹Ê¯ O Å ¬£ ´¥ (7.32) É ¹¯ m´ MMSE ·ÊÆ n ´ ´¥¯¯ à ´¥qÂ É ¢´¤Å n ¹Ê¯ Æ ³ ³ Ä£ ¶

7.4 ´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

ç² O ´£§Ï´ ³ çn©Å­n §§³ q m´ ³ ª» ¤q É ²Æ n Ï´ ¯ ¹¯

´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥Æ£m ©¥ Ï ´£´Å n ´ ³ ¥² BPMR ·Ê£· ³ ­´Â¥¹Ê¯ ©´£Æ£mÂ É Â ¶

¬n ( m à ¥É £¶¬Â¥ ¶¬Â ¥ ³ )  ¹Ê ¯ ´ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ Ê·Æ n ´ ­³©¯m´ ²£·§³ « ²Æ£m¬££´ ¥ ³ ³ Ë Å ·Ê ·Ë ²¯ ¶ ´¤ ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥ [120,

121] ³ ·Ë

7

บทที่

Å Ï´ ¯  ·¤© ³ ´ à ϴ§¯ m¯ ¬³ ´ BPMR Å ¥» ·Ê 7.2 n¯£»§Â¯´ q º ¯

¯· ©¯Æ§Â ¯¥q£· m´Â m´ ³ zk = rk fk = fTrk £¹Ê¯ f = [f–K … f0 … fK]T ¹¯Â©  ¯¥qà © ³ Ë ¯

¯· ©¯Æ§Â ¯¥q Ê·£·¬£´ ¶ N = 2K + 1 ³© ç² rk = [rk +K … rk … rk – K]T ¹¯Â©  ¯¥qà © ³ Ë

¯ ¬³ ´ ¯m´ §³ ¶ ´¥ ´ ´¥qÂ É ¬¯ £¶ ¶ ´ 3 u 3 Å ¬£ ´¥ (7.15) n´Å­n g = [g–1,0

g0,0 g1,0 g–1,1 g0,1 g1,1 g–1,2 g0,2 g1,2]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ´¥qÂ É Ã ¯¬££´ ¥ ç² uk = เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

239

[a –1,k a0,k a 1,k a –1,k – 1 a0,k – 1 a 1,k – 1 a –1,k – 2 a0,k – 2 a 1,k – 2]T ¹¯Â©  ¯¥qà © ³ Ë ¯ §Ï´ ³

n¯£»§¯¶ º ·Ê¬¯ §n¯ ³ ©  ¯¥q g ³ ³ Ë n¯£»§Â¯´ q º ¯ ´¥qÂ É £· m´Â m´ ³ dk = gTuk ¸Ê Ï´Å­nÆ n©m´ § m´ ¥²­©m´ zk ç² dk ¹¯

wk z k dk f T rk g T uk

(7.35)

ç² m´ n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤ (MSE) £· m´Â m´ ³ 2 E ¡w 2 ¯° E ¡ z k dk ¯° f T Rf g T Ug 2f T Pg ¢ ± ¢ ±

(7.36)

£¹Ê¯ R E ¡rk rkT ¯° ¹¯Â£ ¥¶ q¯³ ¬­¬³£ ³ q ´ N uN, P E ¡rk ukT ¯° ¹¯Â£ ¥¶ q¬­¬³£ ³ q ¢ ± ¢ ± T n´£ ´ N u 9, ç² U E ¡uk uk ¯° ¹¯Â£ ¥¶ q¯ ³ ¬­¬³£ ³ q ´ 9 u 9 ¢ ± ´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q n©¤©¶ · ´¥ MMSE ·ÊÅ n ¹Ê¯ Æ ³ ³ à ģ ¶

² ¤´¤´£ Ï´Å­n m´ MSE Å ¬£ ´¥ (7.36) £· m´ n ¯¤¬º Ä ¤¥³ «´Å­n m´ ITg = 1 §¯ ©§´ £¹Ê¯ I = [0 0 0 0 1 0 0 0 0]T ( ³Ê ¹¯ g0,1 = 1) §m´© ¹¯ ´¥¯¯ à ´¥qÂ É ©¶ · ·Ë ² Ï´Å­n m´ E ¡w 2 ¯° f T Rf g T Ug 2f T Pg 2M I T g 1

¢ ±

(7.37)

£· m´ n ¯¤¬º £¹Ê¯ O ¹¯ ³© » §´ ¥´ q ´ ³ Ë Å­n­´¯ º ³ q ¯ ¬£ ´¥ (7.37)  ·¤ ³ f, g ç² O ´£§Ï´ ³ çn©Å­n §§³ q m´ ³ ª» ¤q É ²Æ n Ï´ ¯ ¹¯ 1

M

I

T

U P

T

1

R 1 P I 1

(7.38)

g M U P T R 1 P I

(7.39)

f R 1Pg

(7.40)

£¹Ê¯ O Å ¬£ ´¥ (7.32) É ¹¯ m´ MMSE ·ÊÆ n ´ ´¥¯¯ à ´¥qÂ É ¢´¤Å n ¹Ê¯ Æ ³ ³ Ä£ ¶

7.5 ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ ­³© n¯ ·Ë ²¯ ¶ ´¤©¶ · ´¥§ § ¥² ¯ ISI ç² ITI Ä ¤Å n ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q ¬¯ £¶ ¶ Ê ¸ £·¬£¥¥ ² · ©m´ ´¥Å n¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ [108] ¯ ´ ·Ë¤³ ¬´£´¥ Ï ´£´ ¥²¤º q

240

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

n j ,k rj ,k

a j ,k

z j ,k

F Dz , Dx

d j ,k

G Dz , Dx

aˆ0,k

w j ,k

¥» ·Ê 7.3 à ϴ§¯ m¯ ¬³ ´ ¬Ï´­¥³ ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ [108]

Å n ³ ¥² ³ Â É n¯£»§¬¯ £¶ ¶Ã ¯¹Ê È Æ n n©¤  m ¥² ³ Â É n¯£»§°¯Ä§ ¥´¡· (holographic

data storage system) [122], ¥² ³ Â É Â ¶ ì à ¬¯ £¶ ¶ (TwoDOS: 2D optical storage

system) [123], ­¥¹¯¥² ³ Â É n¯£»§Ã à © ¯ /à © ³ Ë Ã ·ÊÅ n­³©¯m´ ­§´¤­³© (multiread-head) [124, 125] Â É n

¬Ï´­¥³ ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶  ¹Ê ¯ ´ ϴí m ¯ Ưç q (­¥¹¯ ¶ n¯£»§) Æ n » Ï´­ Æ©n¯¤m´ à m ¯ çn©Å ¬¹Ê¯ ³ ¸ ³ ³ Ë ¬³ ´ ¯m´ §³ ¸ » Ï´­

n©¤ ϴí m ¯ ¶ n¯£»§ (à ·Ê ²Â É ¥¥ · ©§´) n´Å­n ´¥´£¶Â ¯¥q j ç² k à ϴí m

¯ Ưç qÅ Ã © ©´ à ¥É ç²Å à © ´£Ã ¥É ´£§Ï´ ³ Ä ¤ ·Ê j = 0 ²¬¯ §n¯ ³

à ¥É §´ ´ ¥» ·Ê 7.3 §Ï´ ³ n¯£»§¯¶ º aj,k {r1} ² » n ¯  n´ m¯ ¬³ ´ BPMR ·Ê

£· § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ H(m,n) Ï´Å­nÆ nÂ É ¬³ ´ ¯m´ §³ rj,k ¸Ê  ·¤

Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯

rj ,k hm ,na j m ,k n n j ,k m

(7.41)

n

£¹Ê¯ hm,n ¹¯ m´¬³£ ¥²¬¶ ¶ Î ¯ m¯ ¬³ ´ H(m,n) ç² nj,k ¹¯¬³ ´ ¥ © AWGN

Å Ï´ ¯  ·¤© ³ © ¥¢´ ¥³ ¬³ ´ ¯m´ §³ rj,k ² » ¬m  n´Æ ¤³ ¯· ©¯Æ§Â ¯¥q

¬¯ £¶ ¶ F Dz , Dx ·Ê£·¥» ¬£ ´¥ ¹¯

F Dz , Dx

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

¥» ·Ê 7.3 ì à ϴ§¯ m¯ ¬³ ´ BPMR ·ÊÅ n­³©¯m´ ­§´¤­³©Å ´¥¯m´ n¯£»§

7

บทที่ M

K

f

m ,n

m M n K

Dzm Dxn

(7.42)

£¹Ê¯ fm,n ¹¯ m´¬³£ ¥²¬¶ ¶ Î ¯ F Dz , Dx , {M, K} ¹¯Â§ Ï´ ©  ɣ © , ç² Dz ç² Dx ¹¯ ³©Â§¹Ê¯ ­ ¸Ê ­ m ©¤ (unit shift) Å Ã © ©´ à ¥É ç²Å à © ´£Ã ¥É ´£§Ï´ ³  ¹Ê¯ ¥³

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

241

º ¬£ ³ ¶ ¯ ¬³ ´ ¯m´ §³ Å­nÂ É Æ ´£ ´¥qÂ É ¬¯ £¶ ¶ G Dz , Dx ·Ê n¯ ´¥ ¸Ê £·¥» ¬£ ´¥ ¹¯ G Dz , Dx

2L

L

g

m ,n

Dzm Dxn

m L n 0

(7.43)

£¹Ê¯ gm,n ¹¯ m´¬³£ ¥²¬¶ ¶ Î ¯ G Dz , Dx ´£§Ï´ ³ ç² L ¹¯Â§ Ï´ ©  ɣ © m¯ ²¬m §§³ q ÊÆ· nÆ ¤³ © ¥ ¥© ­´©·Â ¯¥q ¶Â ¹Ê¯­´ m´ ¥²£´ ¯ §Ï´ ³ n¯£»§ a0,k ( ³Ê ¹¯ aˆ0,k ) º ¥²¬ q ¯ © ¥¢´ ¥³ ¹¯ ² Ï´ ´¥ ¥© ­´§Ï´ ³ n¯£»§Â ´² ¯ à ¥É §´ ( ³Ê ¹¯

j = 0) ³ ³ Ë Å ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ ·Ë ²Å n ´² n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q ¯ à ¥É §´ ç² n¯£»§Â¯´ q º ¯ ´¥qÂ É ¯ à ¥É §´  m´ ³ Ë ¸Ê  ·¤

à n©¤ z0,k ç² d0,k ´£§Ï´ ³  ¥´² ² ³ Ë n´Å­n F Dz , Dx Å ¬£ ´¥ (7.42) £·¥» £ ¥¶ q

´ (2M+1) × (2K+1) ¹¯ f M , K ¡ ¡ # ¡ F ¡¡ f0, K ¡ # ¡ ¡ ¢¡ fM , K

" f M ,0 " f M ,K ¯ ° # # # # °° " f0,0 " f0,K °° # # # # °° ° " fM ,0 " fM ,K ±°

(7.44)

ç²Å­n G Dz , Dx Å ¬£ ´¥ (7.43) £·¥» £ ¥¶ q ´ (2L+1) × (2L+1) ¹¯ g L ,0 " g L ,L " g L ,2 L ¯ ¡ ° ¡ # # # # # °° ¡ G ¡¡ g 0,0 " g 0,L " g 0,2 L °° ¡ # # # # # °° ¡ ¡ ° ¡¢ g L ,0 " gL ,L " gL ,2 L °±

(7.45)

£¹Ê¯ 2M+1 ¹¯ Ï´ © ­³©¯m´ , N = 2K+1 ¹¯ Ï´ © Ã É ¯ ¯· ©¯Æ§Â ¯¥qÅ Ã m§²Ã ©, ç² 2L+1 ¹¯ Ï´ © Ã É ¯ ´¥qÂ É Å Ã m§²Ã © ³ ³ Ë ´ à ϴ§¯ m¯ ¬³ ´ BPMR Å ¥» ·Ê 7.3 n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q ¯ à ¥É §´ £· m´Â m´ ³ M

z k z 0,k

K

f

242

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

r

m ,n m ,k n

m M n K

f T rk

(7.46)

¸Ê Â É ´¥ Ï´ ¯ Ä©§» ³ à ¬¯ £¶ ¶ (2D convolution) ¥²­©m´ n¯£»§ rj,k ç² fm,n £¹Ê¯ f =

[f–M,–K f–M,–K+1 … f–M,K f–M+1,–K … f0 … fM,K – 1 fM,K ]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ¯· ©¯Æ§Â ¯¥q

( ³Ê ¹¯ Ï ´¬£´ ¶ Å Ã m§²Ã © ¯ £ ¥¶ q F £´Â¥·¤ m¯ ³ Â É Â©  ¯¥q f) ·Ê£·¬£´ ¶ N(2M+1)

³© ç² rk = [rM,k +K rM,k +K – 1 … rM,k –K rM – 1,k +K … r0,k … r–M,k – K+1 r–M,k – K]T ¹¯Â©  ¯¥q

à © ³ Ë ¯ ¬³ ´ ¯m´ §³ ·Ê£·¬¯ §n¯ ³ ©  ¯¥q f Å Ï´ ¯  ·¤© ³ n¯£»§Â¯´ q º ¯ ´¥qÂ É ¯ à ¥É §´ £· m´Â m´ ³

L

dk d0,k

2L

g

a

m ,n m ,k n

(7.47)

g T ak

m L n 0

£¹Ê¯ g = [g–L,0 g–L,1 … g–L,2L g–L+1,0 … g0,L … gL,2L – 1 gL,2L ]T ¹¯Â©  ¯¥qà © ³ Ë ¯ ´¥q É

( ³Ê ¹¯ Ï ´¬£´ ¶ Å Ã m§²Ã © ¯ £ ¥¶ q G £´Â¥·¤ m¯ ³ Â É Â©  ¯¥q g) ·Ê£·¬£´ ¶ (2L+1)2

³© ç² ak = [aL,k aL,k –1 … aL,k –2L aL – 1,k … a0,k – L … a–L,k – 2L+1 a–L,k – 2L]T ¹¯Â©  ¯¥q §Ï´ ³ n¯£»§ dk £· m´Â m´ ³

(7.48)

wk z k dk f T rk g T ak

ç² m´ n¯ ¶ §´ Ï´§³ ¬¯  §·Ê¤ (MSE) £· m´Â m´ ³ 2 E ¡w 2 ¯° E ¡ z k dk ¯° f T Rf g T Ag 2f T Pg ¢ ± ¢ ±

(7.49)

£¹Ê¯ R E ¡rk rkT ¯° ¹¯Â£ ¥¶ q¯³ ¬­¬³£ ³ q ¯ n¯£»§ rk, P E ¡rk akT ¯° ¹¯Â£ ¥¶ q¬­¬³£ ³ q ¢ ± ¢ ± T¯ n´£ ¯ n¯£»§ rk ç² ak, ç² A E ¡ak ak ° ¹¯Â£ ¥¶ q¯ ³ ¬­¬³£ ³ q ¯ n¯£»§ ak ¢ ±

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

à © ³ Ë ¯ §Ï´ ³ n¯£»§¯¶ º ·Ê¬¯ §n¯ ³ ©  ¯¥q g ³ ³ Ë § m´ ¥²­©m´ §Ï´ ³ n¯£»§ zk ç²

´¥¯¯ à ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q n©¤©¶ · ´¥ MMSE ²Å n ¹Ê¯ Æ ³ ³ à ģ ¶

³Ê ¹¯ g0,0 = 1 ( ¹Ê¯­§· §·Ê¤ ´¥Æ n Ï´ ¯ Â É f = g = 0) ¯ ´ ·Ë  ¹Ê¯­§· §·Ê¤ ´¥Å n ´ © ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ Ê·£· ©´£ ³ n¯ ¬» £´ [108] ² Ï´ ´¥Å¬m ¹Ê¯ Æ ³ ³ ¯· n¯­ ¸Ê

Å­n ³ g Ä ¤ ´¥ Ï´Å­n m´¬³£ ¥²¬¶ ¶ Î ¯ ´¥qÂ É ¯ à ¥É n´  ·¤ ³ Ë ­£ £· m´Â m´ ³ ª» ¤q (zero-

7

บทที่

ITI forcing constraint)  ¹Ê¯ Ï´ ³ § ¥² ¯ ITI ç² Ï´Å­n¬´£´¥ Å n© ¥ ¥© ­´©·Â ¯¥q ¶

à ³Ê©Æ 48 (­¥¹¯© ¥ ¥© ­´©·Â ¯¥q ¶­ ¸Ê £¶ ¶) Æ n ³©¯¤m´ ¯ ´¥qÂ É G ´ 3u3 ( ©´£¤´©

¯ ISI ç² ITI  m´ ³ 3 ­ m ©¤) ·Ê¬¯ §n¯ ³  ¹Ê¯ Æ ³ ³ ³ Ë ¬¯ n¯ ·Ë  m 48

ª¸ «´¥´¤§²Â¯·¤ ­§³ ´¥ Ï´ ´ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶Ã ³©Ê Æ Æ nÅ ·Ê 4 ¯ [10]

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243

0 ¡ G ¡¡g 0,0 ¡ 0 ¢

0 0 ¯ ° 1 g 0,2 °° 0 0 °±

(7.50)

¸Ê  ·¤ Å­n¯¤m»Å ¥» ¯ ©  ¯¥qÆ n ¹¯ T g ¢¡ 0 0 0 g 0,0 1 g0,2 0 0 0¯°±

(7.51)

 ¥´² ² ³ Ë Â ¹Ê¯ Æ ³ ³ ³ Ë ¬¯ à ¬´£´¥  ·¤ Â É ¬£ ´¥ ¶ ª´¬ ¥qÆ n ¹¯ (7.52)

ET g I

Ä ¤ ·Ê (7.53)

T

I <1 0 0 0 0 0 0>

ç² 0 ¡ ¡1 ¡ ¡0 ¡ ET ¡ 0 ¡ ¡0 ¡ ¡0 ¡ ¡¢ 0

0 0 1 0 0 0 0

0 0 0 1 0 0 0

0 0 0 0 0 0 0

1 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 1 0 0

0¯ ° 0° ° 0° ° 0° ° 0° ° 0° ° 1°±

0 0 0 0 0 1 0

(7.54)

©¶ · ´¥ MMSE ·ÊÅ n ¹Ê¯ Æ ³ ³ ³ Ë ¬¯ à ² ¤´¤´£ Ï´Å­n m´ MSE Å ¬£ ´¥ (7.49)

£· m´ n ¯¤¬º Ä ¤¥³ «´Å­n ETg = I §¯ ©§´ §m´© ¹¯ ´¥¯¯ à ´¥qÂ É ©¶ · ·Ë ² Ï´Å­n m´ E ¡w 2 ¯° f T Rf g T Ag 2f T Pg 2Ȝ T ET g I

¢ ±

(7.55)

£· m´ n ¯¤¬º £¹Ê¯ O ¹¯Â©  ¯¥qà © ³ Ë ·Ê£·¬£´ ¶ Â É ³© » §´ ¥´ q Ï´ © 7 ³© (¬¯ §n¯

³ Ï´ © à © ¯ £ ¥¶ q ET) ´ ³ Ë Å­n­´¯ º ³ q ¯ ¬£ ´¥ (7.55)  ·¤ ³ f, g ç² O

´£§Ï´ ³ çn©Å­n §§³ q m´ ³ ©  ¯¥qª» ¤q É ²Æ n Ï´ ¯ ¹¯

1

Ȝ E T A P T R 1 P E

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1

I

(7.56)

wk N 0, T 2

a 0,k

dk

rk

aˆ0,k

¥» ·Ê 7.4 à ϴ§¯ m¯ ¬³ ´ à ¬££»§

1

g A P T R 1P EȜ

(7.57)

f R 1Pg

(7.58)

­³© n¯ ·Ë ²¬¥º ­§³ ´¥ Ï´ ´ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶Ã ³Ê©Æ (­¥¹¯© ¥ ¥© ­´©·Â ¯¥q ¶­ ¸Ê £¶ ¶) ç²Ã ¬¯ £¶ ¶§³ « ² m´ È ·ÊÅ nÅ ¥² BPMR ¥n¯£ ³ Ë Ã¬ ©´£ ³ n¯ ¯ © ¥

¥© ­´©·Â ¯¥q ¶Ã m´ È

7.6.1 © ¥ ¥© ­´©·Â ¯¥q ¶­ ¸Ê £¶ ¶ Å ·Ê 4 ¯ [10] Æ n¯ ¶ ´¤­§³ ´¥ Ï´ ´ Ä ¤§²Â¯·¤ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶Ã ³©Ê Æ (­¥¹¯

© ¥ ¥© ­´©·Â ¯¥q ¶­ ¸Ê £¶ ¶) ·ÊÅ n ³ ´¥qÂ É ­ ¸Ê £¶ ¶ ³ ³ Ë Å ·Ê ·Ë ²¬¥º ­§³ ´¥ Ï´ ´ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶­ ¸Ê £¶ ¶  ¹Ê¯Â É Ã © ´ Å­n n»¯m´ ¬´£´¥  n´Å ­§³ ´¥ Ï´ ´ ¯ © ¥ ¥© ­´

©·Â ¯¥q ¶¬¯ £¶ ¶Æ n m´¤ ¸Ë

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

7.6 © ¥ ¥© ­´©·Â ¯¥q ¶ Ê·Å nÅ ¥² BPMR

n´¬££º ¶©m´¯· ©¯Æ§Â ³ à ¬£ »¥ q (perfect equalization) à ϴ§¯ Å ¥» ·Ê 7.1

²§ ¥» Æ nÂ É Ã Ï´§¯ m¯ ¬³ ´ à ¬££»§ ´£¥» ·Ê 7.4 £¹Ê¯ wk N 0, T 2 ¹¯¬³ ´ ¥ © AWGN Å ´ ¶ ³ ¶­§³ ´¥ Ï´ ´ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶ ²¯¤m» ¹Ë ´ ¯ à ¢´  ¥§§¶¬ (trellis diagram) [13] Ä ¤¥» ·Ê 7.5 ² ¶ ¤´£¬³ §³ « q m´ È Å Ã ¢´

7

บทที่

O  ¥§§¶¬ ³ ·Ë : k ¢ak ak 1 ... ak O 1 ¯± ¹¯¬ ´ ² (state) ©§´ k, Q A ¹¯ Ï´ © ¬ ´ ² ³ Ë ­£ ·ÊÂ É Æ Æ n, A ¹¯ Ï´ © m´ ·ÊÂ É Æ Æ n ³ Ë ­£ ¯ n¯£»§¯¶ º , Q ¹¯­ m ©¤ ©´£ Ï´ ¯

m¯ ¬³ ´ (­¥¹¯ ´¥qÂ É ), ç² (u, q) ¹¯¬³ §³ « q ÊÅ· nà ´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² u

Æ ¤³ ¬ ´ ² q

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245

¥» ·Ê 7.5 Ï´¯ ¶ ´¤Ã ¢´  ¥§§¶¬

time k (0)

0

-1 -1

k+1

2 (1)

1 -1

0 2 -2

(2)

-1 1

Mk (1, 2)

'k 1 (2) Qk 1 (2)

0 -2

(3)

1 1

state

0

rk

a 0,k 1 a 0,k 1

¥» ·Ê 7.6 à ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ PR4, H(D) = 1 – D2

¥» ·Ê 7.6 ì ³©¯¤m´ à ¢´  ¥§§¶¬ ¯ m¯ ¬³ ´ PR4 ³Ê ¹¯ G(D) = 1 – D2

¸Ê £· Q = 22 = 4 ¬ ´ ² ·Êì n©¤¬³ §³ « q (0), (1), (2) ç² (3) £¹Ê¯ n¯£»§¯¶ º a0,k {r1} Å ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ¬¶Ê ·Ê n¯ Ï´ © Å º m© ©§´ ¹¯ m´Â£ ¥¶ ¬´ ´

(branch metric) ©§´ k ¯ ´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² u Æ ¤³ ¬ ´ ² q ³Ê ¹¯ Mk (u , q ) ,

m´Â£ ¥¶ ¬n ´ (path metric) ¬Ï´­¥³ ¬ ´ ² q ©§´ k + 1 ³Ê ¹¯ 'k 1 (q ) , ç² ³© Ï ´­ n ´ (predecessor) ¬Ï´­¥³ ¬ ´ ² q ©§´ k + 1 ³Ê ¹¯ Qk 1 (q ) ¸Ê ²Â É m´¬ ´ ²Â¥¶Ê£ n ·ÊÂ É § Ï´Å­n ¶ ¬n ´ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º (best transition)  m ¶ ´¥ ´ ·Ê¬ ´ ² (2)

©§´ k + 1 ²£·Â¬n ´ ´¥Â §·Ê¤ ¬ ´ ² 2 ¬n ´ ¹¯ (1, 2) ç² (3, 2) ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶

§¹¯ ¬n ´ ·Ê ·¬º  ·¤ ¬n ´  ·¤© ·Ê£´ ¸ ¬ ´ ² (2) ©§´ k + 1 n´¬££º ¶©m´Â¬n ´ (1, 2)

¹¯Â¬n ´ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º É ²Æ n©m´ Qk 1 (2) 1

246

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© ¥ ¥© ­´ ·Ê Ï´Å­n ©´£ m ´ ²Â É ¯ n¯ ¶ §´ ¯ §Ï´ ³ n¯£»§£· m´ n ¯¤¬º ¹¯ “© ¥

¥© ­´§Ï´ ³ ·Ê ©¥ ²Â É ¬» ¬º (MLSD: maximum-likelihood sequence detector)” [13] ¸Ê ¬¥n´ Æ nÄ ¤Å n¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ¸ Â¥·¤ ©m´ “© ¥ ¥© ­´©·Â ¯¥q ¶” ´ à ϴ§¯ Å ¥» ·Ê 7.4 © ¥ ¥© ­´©·Â ¯¥q ¶ ²Â§¹¯ §Ï´ ³ n¯£»§¯¶ º a0,k ·Ê Ï´Å­n ©´£ m ´ ²Â É ¯ §Ï´ ³ n¯£»§ rk

(­¥¹¯ r) £¹Ê¯ Ï´­ §Ï´ ³ n¯£»§ a0,k (­¥¹¯ a) £´Å­n ³Ê ¹¯ p r | a

1

2QT2

S O

£ 1 ¦ exp ¦ ¤ 2 ¦ ¦ ¦ 2T ¥

S O

k 0

² 2¦ rk dk ¦ » ¦ ¦ ¦ ¼

(7.59)

£· m´£´ ¬º Ä ¤ ·Ê S ¹¯ Ï´ © ¶ n¯£»§ ³ Ë ­£ ¯ a0,k ´ ³ Ë Å¬m§¯ ´¥¶ ¸£ ¥¥£ ´ ¶ (natural logarithm) ³ Ë ¬¯ n´ ¯ ¬£ ´¥ (7.59) ²Æ n É

² ¦ ¦ S O 1 ¦ 1 ¦ ¦ rk dk » S O ¦ 2T2 k 0 2 ¦ 2QT ¦ ¦ ¦ ¼ 1

2

(7.60)

¬³  ² ©m´ ´¥ Ï´Å­n¬£ ´¥ (7.60) £· m´£´ ¬º £· §Â ·¤  m´ ³ ´¥ Ï´Å­n q Ê·¬¯ ´ n´

©´£¹¯ ¯ ¬£ ´¥ (7.60) £· m´ n ¯¤¬º  ¹Ê ¯ ´ q Ê·­ ¸Ê  ¥·¤ ¬£¹¯ ³ m´ ³© ³ ³ Ë © ¥ ¥© ­´©·Â ¯¥q ¶ ²Â§¹¯ §Ï´ ³ n¯£»§¯¶ º a0,k ·Ê Ï´Å­n£ ¥¶ (metric) S O 1

rk dk

(7.61)

2

k 0

£· m´ n ¯¤¬º ¸Ê Ï´Æ nÄ ¤ ´¥ n ­´Â¬n ´ (path) ·Ê£· m´Â£ ¥¶ n ¯¤¬º ´£Ã ¢´  ¥§§¶¬ £¹Ê¯

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

¦£¦ ¦¦ ln \p r | a ^ ln ¦¤ ¦¦ ¦¦ ¥¦

£ ¥¶ ¬n ´ £· m´Â m´ ³ §¥©£ ¯ £ ¥¶ ¬´ ´ Ä ¤ ·Ê£ ¥¶ ¬´ ´ ¯ ´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² u Æ ¤³ ¬ ´ ² q ¶ ¤´£Ä ¤

Mk u ,q rk dˆk u , q

2

(7.62)

7

บทที่

º ¯ m¯ ¬³ ´ ·Ê¬¯ §n¯ ³ (u, q) ç²Â£ ¥¶ ¬n ´ ¬´£´¥ £¹Ê¯ dˆk u , q ¹¯ n¯£»§Â¯´ q ­´Æ n ´ 'k 1 q

k

M

i

(7.63)

i 0

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247

(A-1)

Ï´­ m´Â¥¶Ê£ n ¯ £ ¥¶ ¬n ´ '0 p 0 ¬Ï´­¥³ º È ¬ ´ ² p

(A-2)

For k 0, 1,..., S O 1

(A-3)

For q 0, 1,..., Q 1 2

(A-4)

Mk p , q rk dˆ p ,q

(A-5)

Qk 1 q arg min p \'k p Mk p ,q ^

(A-6)

'k 1 q 'k Qk 1 q

Mk Qk 1 q ,q

(A-7)

Sk 1 q ¡Sk Qk 1 q

Qk 1 q ¯° ¢ ±

(A-8) (A-9)

for p

End End

(A-10) ¯ ¥­³¬ n¯£»§¯¶ º aˆ0,k ´ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Ê·£· m´ 'S O n ¯¤ ·Ê¬º ¥» ·Ê 7.7 ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶­ ¸Ê £¶ ¶ [10]

¥» ·Ê 7.7 ì ³ Ë ¯ ´¥ Ï´ ´ ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶ ³©¯¤m´  m ¶ ´¥ ´¥²¤² ·Ê k

¯ à ¢´  ¥§§¶¬Å ¥» ·Ê 7.6 ² ©m´£· ´¥Â¬n ´ ´¥Â §·Ê¤ ¬ ´ ² 2 ¬n ´ ·Ê£´ ¸ ¬ ´ ²

(2) ©§´ k + 1 ³Ê ¹¯ (1, 2) ç² (3, 2) ´ ³ Ë Ï´ ´¥ Ï´ © m´Â£ ¥¶ ¬´ ´ ³ Ë 2 ¬n ´ Ë ¯ ·Ê (A-4) Ä ¤¬ ´ ²Â¥¶Ê£ n ·Ê¬¯ §n¯ ³ ¬n ´ ³Ê ¹¯ Mk 1, 2 ç² Mk 3, 2 ´£ ³

Ë ¯ ·Ê (A-5) ¬££º ¶ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º ·Ê£´ ¸ ¬ ´ ² (2) ©§´ k + 1 ² » §¹¯ ´£ ³

©m´ (1, 2) ¹¯Â¬n ´ ´¥Â §·Ê¤ ¬ ´ ² ·Ê ·¬º É ²Æ n©m´ Qk 1 2 1 ´ ³ Ë ¥³ m´Â£ ¥¶ ¬n ´ Ë ¯ ·Ê (A-6) ç² ¥³ m´Â¬n ´ ·Ê ·Ê£´ ¸ ¬ ´ ² (2) ©§´ k + 1 ³Ê ¹¯ 'k 1 (2) ´£ ³ Ë ¯ ·Ê ¤³ £· ·©¶ ¯¤m» (survivor path) ·Ê£´ ¸ ¬ ´ ² (2) ©§´ k + 1 ³Ê ¹¯ Sk 1 2 ´£ ³ (A-7) Å­n Ï´ ´£ ³ Ë ¯ m´ È Â­§m´ ·Ë ´£¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶¬Ï´­¥³ §Ï´ ³ n¯£»§ {rk} ·ÊÆ n¥³ £´

³ Ë ­£ ç² ³ Ë ¯ ¬º n´¤ ¹¯ ´¥ ³ ¬¶ Å ­´ m´§Ï´ ³ n¯£»§ {a0,k} ·Ê ©¥ ²Â É ¬» ¬º Ä ¤Â§¹¯

´ ¬n ´ ·Ê¤³ £· ·©¶ ¯¤m» Ê£ · · m´Â£ ¥¶ ¬n ´ ©§´ S + Q (­¥¹¯ 'S O ) n ¯¤¬º

 ¹Ê ¯ ´ © ¥ ¥© ­´©·Â ¯¥q ¶ ² Ï´ ´¥ ¥²£©§ §§Ï´ ³ n¯£»§ ³ Ë ­£ m¯ ³ ¬¶ Å ©m´

§Ï´ ³ n¯£»§ ·ÊÆ n¥³ ©¥ ²Â É §Ï´ ³ n¯£»§¯¶ º Å £´ ·Ê¬º ³ ³ Ë Å ´ ¶ ³ ¶ ©´£ ³ n¯ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶ ² ¸Ë ¯¤m» ³ ­§´¤ ³ ³¤ Æ nà m Ï´ © m´ ·ÊÂ É Æ Æ n ³ Ë ­£ ¯ n¯£»§¯¶ º

A , ©´£¤´© ¯ §Ï´ ³ n¯£»§¯¶ º S, ç² Ï´ © ­ m ©¤ ©´£ Ï´ ¯ ´¥qÂ É Q ¬Ï´­¥³ ³©¯¤m´

´¥ Ï´ © ¯ ¯³§ ¯¥¶ ¸£©·Â ¯¥q ¶¬´£´¥ ª¸ «´Æ n ´ ·Ê 4 ¯ [10]

248

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

7.6.2 © ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ Å ­³© n¯ ·Ë ²Å nà ϴ§¯ m¯ ¬³ ´ Å ¥» ·Ê 7.2 Å ´¥¯ ¶ ´¤ ¹Ë ´ ´¥ Ï´ ´ ¯ © ¥ ¥© ­´©·Â ¯¥q ¬ ¶ ¯ £¶ ¶ Ä ¤ ·Ê ¯ n £»§¯¶ º ¯ ´¥qÂ É ²£· 3 à ¥É (à ¥É à ¥É §´ ç² à ¥É §m´ ) 粩 ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ ² ¯ ¥­³¬ n¯£»§Â ´² n¯£»§¯¶ º ¯ à ¥É §´  m´ ³ Ë

Ë ¯ ´¥ Ï´ ´ §n´¤ ³ © ¥ ¥© ­´©·Â ¯¥q ¶ Ä ¤ ³©Ê Æ © ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ ²£· ³

49

­ ¸Ê £¶ ¶ ´£ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 7.6.1  ·¤ à mà ¢´  ¥§§¶¬ ·ÊÅ nÅ © ¥ ¥© ­´©·Â ¯¥q ¶¬¯

£¶ ¶¯´ ²£· Ï´ © ¬ ´ ² Q £´ ¸Ë , £·Â¬n ¬´ ´£´ ©m´­ ¸Ê ¬n Å Ã m§² ´¥Â §·Ê¤ ¬ ´ ² ´

¬ ´ ² u Æ ¤³ ¬ ´ ² q, ç²£·Â¬n ¬´ ´£´ ©m´¬¯ ¬n ·Ê©Ê¶ ¯¯ ´ à m§²¬ ´ ² ³ ³ Ë © ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶Ã m§²Ã ²£· ©´£ ³ n¯ à m´ ³ Ä ¤ ¸Ë ¯¤m» ³ Ï´ © ¯ ¬ ´ ² ç² Ï´ © ¬n ¬´ ´ ³ Ë ­£ ·ÊÅ nÅ Ã m§²¥²¤² ·Ê k ¯ à ¢´  ¥§§¶¬ ¸Ê ¯ ¶ ´¤Æ n ³ m¯Æ ·Ë

Ä ¤ ³Ê©Æ ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶ Ê·£·£º£Â É ª» ¤q ´£ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 7.2 £¹Ê¯¥² Æ£m£·

³ ­´Â¥¹Ê¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³ (TMR) §§³ q Ê·Æ n É ¹¯ ´¥qÂ É ¬¯ £¶ ¶ G ´£¬£ ´¥ (7.15) ·Ê£· m´¬³£ ¥²¬¶ ¶ Î g 1,1 g1,1 ç² g 1,0 g1,0 g 1,2 g1,2 0 ³ ³ Ë Å ­³© n¯ ·Ë ²¯ ¶ ´¤

¹Ë ´ ´¥ Ï´ ´ ¯ © ¥ ¥© ­´©·Â ¯¥q ¶ ʬ · ¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤qà ¬££´ ¥

n´ Ï´­ Å­n ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤qà ¬££´ ¥ ´ 3 u 3 £· m´Â m´ ³ G 1 (D )¯ 0 c 0 ¯ ¡ ° ¡ ° G = ¡¡ G0 (D ) °° = ¡¡u p w °° ¡ G (D ) ° ¡ 0 c 0 ° ¢ 1 ± ¢ ±

(7.64)

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

7.6.2.1 ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤qà ¬££´ ¥

³ ³ Ë ´ ¥» ·Ê 7.2 ²Æ n©m´ n¯£»§Â¯´ q º ¯ ´¥qÂ É £· m´Â m´ ³ dk c a 1,k 1 a1,k 1 u a 0,k p a 0,k 1 w a 0,k 2

(7.65)

¥» ·Ê 7.8 ì ¥´¤§²Â¯·¤ ¯ ´¥Â §·Ê¤ ¬ ´ ²Å ­ ¸Ê ¬n ¬´ ´ ¯ à ¢´  ¥§§¶¬ ·Ê

7

บทที่

¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶ G Å ¬£ ´¥ (7.64) Ä ¤ ·Êà m§²¬ ´ ² ©§´ k ² » Ï´­ n©¤

n¯£»§ 2 ³© ¹¯ n¯£»§¯¶ º ¯ à ¥É §´ ©§´ k – 2 ç² k – 1 ( ³Ê ¹¯ a0,k – 2 ç² a0,k – 1) 49

v

à ¢´  ¥§§¶¬ ·ÊÅ nÅ © ¥ ¥© ­´©·Â ¯¥q ¶­ ¸Ê £¶ ¶ ²£· Ï´ © ¬ ´ ²Â m´ ³ Q = | A | , £·Â¬n ¬´ ´Â ·¤ ­ ¸Ê ¬n ¬Ï´­¥³ à m§² ´¥Â §·Ê¤ ¬ ´ ² ´ ¬ ´ ² u Æ ¤³ ¬ ´ ² q, ç²£·Â¬n ¬´ ´Â ·¤ ¬¯ ¬n ·Ê©Ê ¶ ¯¯ ´ à m§²¬ ´ ² u

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

249

¬ ´ ²

©§´

a 0,k 1 a 0,k 2

a 1,k 1 ¯ ¡ ° ¡ a ° /d 0, k ¡ ° k ¡a ° ¢¡ 1,k 1 ±° ¬n ¬´ ´

¬ ´ ²

©§´

+1

a 0,k a 0,k 1

¥» ·Ê 7.8 ´¥Â §·Ê¤ ¬ ´ ²Å ­ ¸Ê ¬n ¬´ ´ ¯ à ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤q à ¬££´ ¥

 ¥´² ² ³ Ë Ã ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶ Ê·£·£º£Â É ª» ¤qà ¬££´ ¥ ²£· Ï´ ©

¬ ´ ² ³ Ë ­£  m´ ³ 2 u 2 = 4 ¬ ´ ²50 ç²Ã m§²Â¬n ¬´ ´ ² » Ï´­ n©¤¬³ §³ « q x /y £¹Ê¯ x = ¡¢a 1,k 1 a 0,k a1,k 1 ¯°± ¹¯ n¯£»§¯¶ º ¯ ´¥qÂ É Â©§´ k ( ¸Ê ¥² ¯ n©¤ n¯£»§ ¯¶ º ¯ à ¥É ©§´ k – 1, n¯£»§¯¶ º ¯ à ¥É §´ ©§´ k, ç² n¯£»§¯¶ º

¯ à ¥É §m´ ©§´ k – 1), ç² y = dk ¹¯ n¯£»§Â¯´ q º ¯ ´¥qÂ É Â©§´ k ·Ê¬¯ §n¯

³ ´¥Â §·Ê¤ ¬ ´ ² ¯ ¬n ¬´ ´ ³ Ë ³ ³ Ë Ã m§²¬ ´ ² ©§´ k ²£· Ï´ © ¬n ¬´ ´ ³ Ë ­£ 2 u 2 u 2 = 8 ¬n ¬´ ´ Ä ¤Ã m ¯¯ Â É 2 §mº£ ( §mº£§² 4 ¬n ¬´ ´) ç²Ã m§² §mº£Â¬n ¬´ ´ ²Â ¶ ´ Æ ¤³ 2 ¬ ´ ² ·Êà m´ ³ ©§´ k + 1

n´ Ï´­ Å­n dk1 ç² dk2 ¹¯ n¯£»§Â¯´ q º ¯ ´¥qÂ É Â©§´ k ·Ê¬¯ §n¯ ³ n¯£»§

¯´ q º \a 1,k 1 1, a1,k 1 1^ ç² \a 1,k 1 1, a1,k 1 1^ ´£§Ï´ ³ ³ ³ Ë ´ ¬£ ´¥ (7.65) ²Æ n©m´ dk1 dk2 ¸Ê ­£´¤ ©´£©m´Å à m§² §mº£Â¬n ¬´ ´ ²£· 2 ¬n ¬´ ´ ( ´ 4

¬n ¬´ ´) ·Ê£· n¯£»§Â¯´ q º ¯ ´¥qÂ É Â m´ ³ ¸ Ï´Å­n¬´£´¥ § Ï´ © ¬n ¬´ ´ ·Ê ¶ ¯¯ ´

¬ ´ ² u ©§´ k Æ ¤³ ¬ ´ ² q ©§´ k + 1 ­§¹¯Â ·¤ 3 ¬n ¬´ ´ Ä ¤ ·Êà m§²Â¬n ¬´ ´

²£· m´ n¯£»§Â¯´ q º ¯ ´¥qÂ É Â m´ ³

£ ¦ g0,k a0,k 2c, if a 1,k 1 a1,k 1 1 ¦ ¦ ¦ dk ¦ if a 1,k 1 v a1,k 1 ¤ g 0,k a 0,k , ¦ ¦ ¦ ¦ g a 2c , if a 1,k 1 a1,k 1 1 ¦ ¥ 0,k 0,k

(7.66)

£¹Ê¯ ¹¯ ³© Ï´Â ¶ ´¥ ¯ Ä©§» ³ , ç² g0,k ¹¯ m´¬³£ ¥²¬¶ ¶ Î ¯ ´¥qÂ É G0(D) ·Ê¬¯ §n¯

³ n¯£»§¯¶ º ¯ à ¥É §´ a0,k ¥» ·Ê 7.9 ì à ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶ G

50

250

 ¹Ê ¯ ´ a0,n {r1} £· m´ ·ÊÂ É Æ Æ n ³ Ë ­£  ·¤ 2 à ¬Ï´­¥³ n = k – 1 ç² k – 2

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

¥» ·Ê 7.9 à ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶ G Å ¬£ ´¥ (7.64)

“© ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶Ã ·Ê » ¥³ ¥º (modified 2D Viterbi detector)” [126] ¸Ê ¹¯©m´ £· ©´£ ³ n¯ n ¯¤¬º £¹Ê¯Â ·¤ ³ © ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶Ã ¯¹Ê È

7.6.2.2 ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥ Å ·Ê ·Ë ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥ ´ 3 u 3 ´£¬£ ´¥ (7.28) ²­£´¤ ¸ ´¥qÂ É ¬¯ £¶ ¶ G

·Ê£· m´¬³£ ¥²¬¶ q ¯ à ¥É ç² ¯ à ¥É §m´  m´ ³ ³Ê ¹¯ g–1,0 = g1,0, g–1,1 = g1,1 ç²

g–1,2 = g1,2  ¹Ê¯Å­n m´¤¬Ï´­¥³ ´¥¯ ¶ ´¤ ² Ï´­ Å­n ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥£· m´Â m´ ³ G 1 (D )¯ b c d ¯ ¡ ° ¡ ° G = ¡¡ G0 (D ) °° = ¡¡u p w °° ¡ G (D ) ° ¡b c d ° ¢ 1 ± ¢ ±

(7.67)

³ ³ Ë ´ ¥» ·Ê 7.2 ²Æ n©m´ n¯£»§Â¯´ q º ¯ ´¥qÂ É £· m´Â m´ ³

7

บทที่

dk b a 1,k a1,k c a 1,k 1 a1,k 1 d a 1,k 2 a1,k 2

u a 0,k p a 0,k 1 w a 0,k 2

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

Å ¬£ ´¥ (7.64) Ä ¤© ¥ ¥© ­´©·Â ¯¥q ¶ Ê·Å nà ¢´  ¥§§¶¬ ·Ë Å ´¥ ¯ ¥­³¬ n¯£»§ ²Â¥·¤ ©m´

(7.68)

 ¹Ê ¯ ´ ¥² BPMR Å n ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥ ¸ Ï´Å­n¬´£´¥ Ï ´ n¯£»§¯¶ º ¯ à ¥É a–1,k ç²Ã ¥É §m´ a1,k £´¥©£ ³ Æ n Ê ¸ £· m´Â m´ ³

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

251

a 1,k 1 a1,k 1

a 1,k 2 a1,k 2

a ¯ ¡ 1,k a1,k ° / d ¡ ° k a 0,k ¢¡ ±°

a 0,k 1 a 0,k 2

a 1,k a1,k

a 1,k 1 a1,k 1

a 0,k a 0,k 1

¥» ·Ê 7.10 ´¥Â §·Ê¤ ¬ ´ ²Å ­ ¸Ê ¬n ¬´ ´ ¯ à ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥

a 1,k

£ 2, ¦ ¦ ¦ ¦ ¦0,

a1,k ¤ ¦ 0, ¦ ¦ ¦ ¦ ¦ ¥ 2,

if a 1,k 1 and a1,k 1 if a 1,k 1 and a1,k 1 if a 1,k 1 and a1,k 1

(7.69)

if a 1,k 1 and a1,k 1

´¥ Ï ´ n¯£»§¯¶ º ¯ ³ Ë ¬¯ à ¥É £´ ¶ ´¥ ´¥©£ ³ ² m©¤§ ©´£ ³ n¯ ¯ © ¥

¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶Æ n §m´© ¹¯¥» ·Ê 7.10 ì ¥´¤§²Â¯·¤ ¯ ´¥Â §·Ê¤ ¬ ´ ²Å ­ ¸Ê

¬n ¬´ ´ ¯ à ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥ Ä ¤ ·Êà m§²¬ ´ ² ©§´

k ² » Ï´­ n©¤ n¯£»§ 4 ³© ¹¯ §¥©£ ¯ n¯£»§¯¶ º ¯ à ¥É ç²Ã ¥É §m´ ©§´

k – 2, §¥©£ ¯ n¯£»§¯¶ º ¯ à ¥É ç²Ã ¥É §m´ ©§´ k – 1, n¯£»§¯¶ º ¯ à ¥É §´ ©§´ k – 2, ç² n¯£»§¯¶ º ¯ à ¥É §´ ©§´ k – 1 ³ ³ Ë Ã ¢´  ¥§§¶¬ ·Ê

¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥ ²£· Ï´ © ¬ ´ ² ³ Ë ­£  m´ ³ 3 u 3 u 2 u 2 = 36 ¬ ´ ²51

ç²Ã m§²¬ ´ ² ©§´ k ²£· Ï´ © ¬n ¬´ ´ ³ Ë ­£ 3 u 2 = 6 ¬n ¬´ ´ ·Ê ¶ ´ Æ ¤³ 6 ¬ ´ ² ·Êà m´ ³ ©§´ k + 1 ¯ ´ ·Ëà m§²Â¬n ¬´ ´ ² » Ï´­ n©¤¬³ §³ « q x /y Ä ¤ ·Ê x ¡ a 1,k a1,k a 0,k ¯° ¹¯ n¯£»§¯¶ º ¯ ´¥qÂ É Â©§´ k, ç² y = dk ¹¯ n¯£»§ ¢ ± ¯´ q º ¯ ´¥qÂ É Â©§´ k ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² ¯ ¬n ¬´ ´ ³ Ë

7.6.2.3 ´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥ Å ·Ê ·Ë ´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥ ´ 3 u 3 ´£¬£ ´¥ (7.15) ²­£´¤ ¸ ´¥qÂ É ¬¯ £¶ ¶

G ·Ê£· m´¬³£ ¥²¬¶ q ¯ à ¥É ç² ¯ à ¥É §m´ Æ£m m´ ³ ³Ê ¹¯ G–1(D) z G1(D) ³ ³ Ë © ¥¢´ ¥³ ¯ ¥² BPMR ² n¯ Å n© ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ ·Ê£· ©´£ ³ n¯ £´ ¬º (full-complexity 2D Viterbi detector) Å ´¥ ¯ ¥­³¬ n¯£»§ ¥» ·Ê 7.11 ì ¥´¤§²Â¯·¤ ¯

51

252

 ¹Ê ¯ ´ (a–1,n + a1,n ) {0, r2} £· m´ ·ÊÂ É Æ Æ n ³ Ë ­£  ·¤ 3 à ¬Ï´­¥³ n = k – 1 ç² k – 2

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

a 1,k ¯ ¡ ° ¡a ° /d 0, k ¡ ° k ¡a ° ¢¡ 1,k ±°

a 1,k 1 a 1,k 2 a 0,k 1 a 0,k 2 a1,k 1 a1,k 2

a 1,k a 1,k 1 a 0,k a 0,k 1 a1,k a1,k 1

¥» ·Ê 7.11 ´¥Â §·Ê¤ ¬ ´ ²Å ­ ¸Ê ¬n ¬´ ´ ¯ à ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥

´¥Â §·Ê¤ ¬ ´ ²Å ­ ¸Ê ¬n ¬´ ´ ¯ à ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ ´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥ Å ·Ê ·Ë ² ¹¯©m´ ´¥qÂ É ¬¯ £¶ ¶ G £·­ m ©¤ ©´£ Ï´Â m´ ³ O 2 ­ m ©¤ ç²¥» à ¯ n¯£»§

¯¶ º ·ÊÂ É Æ Æ n ³ Ë ­£ £· Ï´ © A 2q 2q 2 8 à 52 ³ ³ Ë Ã ¢´  ¥§§¶¬ ·Ê¬¥n´ ´ O

´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥ ²£· Ï´ © ¬ ´ ² ³ Ë ­£ A 82 64 Ä ¤ ·Êà m§²¬ ´ ² ©§´ k ² » Ï´­ n©¤ n¯£»§¯¶ º ¯ º à ¥É ©§´ k – 2 ç² k – 1 ´£§Ï´ ³ ç²

¬ ´ ² ·Êà m´ ³ ©§´ k + 1 ¯ ´ ·Ë à m§²Â¬n ¬´ ´ ² » Ï´­ n©¤¬³ §³ « q x /y £¹Ê¯ x ¡¢a 1,k a 0,k a1,k ¯°± ¹¯ n¯£»§¯¶ º ¯ ´¥qÂ É (£´ ´ à ¥É à ¥É §´ ç²Ã ¥É §m´ ) ©§´ k, ç² y = dk ¹¯ n¯£»§Â¯´ q º ¯ ´¥qÂ É Â©§´ k ·Ê¬¯ §n¯ ³ ´¥Â §·Ê¤ ¬ ´ ² ¯ ¬n ¬´ ´ ³ Ë

7.7 § ´¥ §¯ ¶ ´¥ ´Ã Ï´§¯ m¯ ¬³ ´ BPMR Å ¥» ·Ê 7.2 £¹Ê¯ ¶ ¤´£Å­n¯³ ¥´¬m© Ï´§³ ¯ ¬³ ´ m¯ Ï´§³ ¯ ¬³ ´ ¥ © £· m´Â m´ ³

1¬ SNR 10 log10 2 ­­­ T ®

(7.70)

£·­ m ©¤Â É Â ¶Â § (dB) Ä ¤Å ·Ê ·Ë ²Â ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² 4 à ³ ·Ë

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

à m§²¬ ´ ² ©§´ k ²£· Ï´ © ¬n ¬´ ´ ³ Ë ­£ 2 u 2 u 2 = 8 ¬n ¬´ ´ ·Ê ¶ ´ Æ ¤³ 8

7

บทที่

¥² ·ÊÅ n ´¥qÂ É ­ ¸Ê £¶ ¶ (­³© n¯ ·Ê 7.1) ç²Å n© ¥ ¥© ­´©·Â ¯¥q ­ ¶ ¸Ê £¶ ¶ (­³© n¯ ·Ê 7.6.1) Ä ¤ ²Â¥·¤ ¥² ·Ë©m´ “1D target”

52

n¯£»§¯¶ º ² » n ¯  n´¥² ©§´ k ¥³ Ë §² 3 ¶ ¹¯ [a–1,k a0,k a1,k ] Ä ¤ ·Ê n¯£»§Ã m§² ¶ £· m´ ·ÊÂ É Æ Æ n ·¤ 2 m´ ( n¯£»§Æ ´¥·) ³ ³ Ë ¥» à ¯ n¯£»§¯¶ º ³ Ë ­£ ·ÊÂ É Æ Æ n ¹¯ 2 u 2 u 2 = 8 Ã

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

253

¥² ·ÊÅ n ´¥qÂ É ¬¯ £¶ ¶ Ê·£·£º£Â É ª» ¤q (­³© n¯ ·Ê 7.2) ç²Å n© ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ à ·Ê » ¥³ ¥º (­³© n¯ ·Ê 7.6.2.1) Ä ¤ ²Â¥·¤ ¥² ·Ë©m´ “Zero-corner 2D target”

¥² ·ÊÅ n ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥ (­³© n¯ ·Ê 7.3) ç²Å n© ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ (­³© n¯ ·Ê 7.6.2.2) Ä ¤ ²Â¥·¤ ¥² ·Ë©m´ “Symmetric 2D target”

¥² ·ÊÅ n ´¥qÂ É ¬¯ £¶ ¶Ã ¯¬££´ ¥ (­³© n¯ ·Ê 7.4) ç²Å n© ¥ ¥© ­´©·Â ¯¥q ¶¬¯ £¶ ¶ (­³© n¯ ·Ê 7.6.2.3) Ä ¤ ²Â¥·¤ ¥² ·Ë©m´ “Asymmetric 2D target”

ç²¥² ³ Ë ­£ ²Å n¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ Ê·£· Ï´ © 11 Ã É ( ´¥Â ¶Ê£ Ï´ © Ã É ¯ ¯· ©¯

Ƨ ¯¥qÆ£m Ï´Å­n¬£¥¥ ² ¯ ¥² · ¸Ë ¯¤m´ £· ³¤¬Ï´ ³ [108])

¶ ´¥ ´¥² BPMR ·ÊÅ n¬Ê ¯ ¹ ³ ¸ ·Ê¬¥n´ n©¤Æ¯Ã§ qà ¬·Ê­§·Ê¤£ ³ º¥³¬ ·Ê£· ©´£¤´©

a = 11 nm, ©´£¬» G = 10 nm, ¥²¤² ¶ ¯ ­³©¯m´ d = 10 nm, ç²Å n­³©¯m´ à MR

·Ê£· ©´£­ ´ t = 4 nm, ©´£ ©n´ W = 15 nm, ç² ©´£ ©n´ ¯ m¯ ©m´ ¥²­©m´ © ç²

¶ Ë ¬m© MR g = 6 nm ¸Ê ¬¯ §n¯ ³ § ¯ ¬ ¯ ¬³ ´ ³§¬qà ¬¯ £¶ ¶ Ê·£· PW50along

19.8 nm ç² PW50cross 24.8 nm [108] ( » ©´£­£´¤ ¯ ´¥´£¶Â ¯¥q m´ È Å ¥» ·Ê 6.8) Ä ¤ Å ·Ê ·Ë ²Å n¬³ ´ ³§¬q ´¬q ·¤ à ¬¯ £¶ ¶ ´£¬£ ´¥ (6.14) Å ´¥¬¥n´ £ ¥¶ q m¯ ¬³ ´ H ©´£ º n¯£»§ m´ È ¬Ï´­¥³ PW50along ç² PW50cross ·Ê Ï´­ £´Å­n ³Ê ¹¯ ©´£ ºÂ m´ ³ 2 Tb/in2 ´ ¬£ ´¥ (6.13) ²Æ n Tx = Tz | 18 nm ç²

H 2 Tb/in 2

ª 2.43 u 10 5 0.023 0.232 0.023 2.43 u 10 5 º « » 4 0.101 1 0.101 1u 10 4 » « 1u 10 « 2.43 u 10 5 0.023 0.232 0.023 2.43 u 10 5 » ¬ ¼

(7.71)

©´£ ºÂ m´ ³ 2.5 Tb/in2 ´ ¬£ ´¥ (6.13) ²Æ n Tx = Tz | 16 nm ç²

H 2.5 Tb/in 2

ª 2.26 u10 4 0.052 0.315 0.052 2.26 u10 4 º « » 4 0.164 1 0.164 7.16 u10 4 » « 7.16 u10 « 2.26 u10 4 0.052 0.315 0.052 2.26 u10 4 » ¬ ¼

(7.72)

©´£ ºÂ m´ ³ 3 Tb/in2 ´ ¬£ ´¥ (6.13) ²Æ n Tx = Tz | 14.5 nm ç²

H 3 Tb/in 2

ª 0.0010 0.088 0.388 0.088 0.0010 º « 0.0026 0.226 1 0.226 0.0026 » « » ¬« 0.0010 0.088 0.388 0.088 0.0010 ¼»

©´£ ºÂ m´ ³ 3.5 Tb/in2 ´ ¬£ ´¥ (6.13) ²Æ n Tx = Tz | 13.6 nm ç²

254

การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

(7.73)

-1

10

1D target Zero-corner 2D target Symmetric 2D target Asymmetric 2D target

3 Tb/in2

2.5 Tb/in2

-2

BER

10

3.5 Tb/in2

-3

10

-4

10

10

2 Tb/in2

12

14

16

18

20

22

24

26

28

30

32

SNR (dB)

H 3.5 Tb/in 2

ª0.0023 0.117 0.434 0.117 0.0023º «0.0053 0.270 1 0.270 0.0053» « » ¬«0.0023 0.117 0.434 0.117 0.0023»¼

(7.74)

¥» ·Ê 7.12  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² ·ÊÅ n ´¥qÂ É Ã m´ È ¸Ê ² ©m´ ©´£ º

n¯£»§ n ¯¤ ©m´­¥¹¯Â m´ ³ 2 Tb/in2 º ¥² ²£·¬£¥¥ ² ·ÊÅ §n ·¤ ³ ( ¹Ê ¯ ´ ITI ¹¯©m´

£· ©´£¥º Ã¥ n ¯¤ £¹Ê¯Â ·¤ ³ ©´£¥º Ã¥ ¯ ISI) ³ ³ Ë Å ´ ¶ ³ ¶Â£¹Ê¯¥² BPMR £· ©´£ º n¯£»§Æ£m£´ (d 2 Tb/in2) É ©¥Â§¹¯ Å n ´ “1D target”  ¹Ê¯Å­n¬´£´¥ Å n© ¥ ¥© ­´

©·Â ¯¥q ¶­ ¸Ê £¶ ¶ Ê·£· ©´£ ©´£ ³ n¯ n ¯¤Ã§²¤³ Å­n¬£¥¥ ² ·Ê m¯ n´ · ¯¤m´ Æ¥ É ´£Â£¹Ê¯ ©´£ º n¯£»§Â ¶Ê£ ¸Ë (> 2 Tb/in2) ¥² ·ÊÅ n “1D target” Â¥¶Ê£ ·Ê ²£·¬£¥¥ ² n¯¤§ £¹Ê¯Â ·¤

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

¥» ·Ê 7.12 ¬£¥¥ ² ¯ ¥² ·ÊÅ n ´¥qÂ É Ã m´ È

³ ´¥Å n ´ ´¥qÂ É ¬¯ £¶ ¶ ( ¹Ê ¯ ´ ITI £· ©´£¥º Ã¥ £´ ¸Ë )  ¥´² ² ³ Ë Â£¹Ê¯¥² BPMR £· ©´£ º n¯£»§¬» (t 2.5 Tb/in2) É ©¥Â§¹¯ Å n ´ ´¥qÂ É ¬¯ £¶ ¶  ¥´²¬´£´¥ § § ¥²

·Ê ¶ ´ ITI Æ n£´ ©m´ ´¥Å n ´ ´¥qÂ É ­ ¸Ê £¶ ¶ ´ ¥» ·Ê 7.12 ¤³ ©m´¥² ·ÊÅ n “Symmetric 2D target” ç² “Asymmetric 2D target” ²£·¬£¥¥ ² · ©m´¥² ·ÊÅ n “Zero-corner 2D

7

บทที่

target” Ä ¤Â ´²¯¤m´ ¤¶Ê ·Ê ©´£ º n¯£»§¬» È (t 3 Tb/in2) ³ Ë ·Ë Â É Â ¥´²©m´Â£¹Ê¯ ITI ¯¤m»Å ¥² ³

·Ê£· ©´£¥º Ã¥ £´ (¬³ Â Æ n ´ m´¬³£ ¥²¬¶ ¶ Î ¯ £ ¥¶ q H Å Ã © ·Ê­ ¸Ê ç²Ã © ·Ê¬´£)

´¥Å n ´ “Symmetric 2D target” ­¥¹¯ “Asymmetric 2D target” ¬´£´¥ § § ¥² ¯ ITI Æ n · ©m´ ´¥Å n ´ “Zero-corner 2D target” ¯ ´ ·ËÅ ´¥ §¯ ·Ë¤³ ©m´¥² ·ÊÅ n

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n 1,k

n0,k n1,k r 1,k

a 2,k a 1,k a 0,k a1,k a 2,k

r0,k

F Dz , Dx

r1,k

a 1,k a 0,k a1,k

G Dz , Dx

zk

dk

aˆ0,k

wk

¥» ·Ê 7.13 à ϴ§¯ m¯ ¬³ ´ BPMR ·ÊÅ n 3 ­³©¯m´ ¬Ï´­¥³ ´¥¯¯ à ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯ Ƨ ¯¥q¬¯ £¶ ¶ [108]

“Symmetric 2D target” ç² “Asymmetric 2D target” £·¬£¥¥ ²Â m´ ³  ¹Ê ¯ ´ § ¯ ¬ ¯ ¯ m¯ ¬³ ´ (­¥¹¯Â£ ¥¶ q H) Â É Ã ¬££´ ¥ ç²¥² Æ£m£· § ¥² ¯ à ¥É £¶¬

Â¥ ¶¬Â ¥ ³ ¸ Ï´Å­n m´¬³£ ¥²¬¶ ¶ Î ¯ ´¥qÂ É ¬¯ £¶ ¶Ã ¬££´ ¥Ã§²Ã ¯¬££´ ¥ ·ÊÆ n ´ ´¥¯¯ à £· m´Å §n ·¤ ³ £´ ¸Ê ¬m §Å­n¥² £·¬£¥¥ ²Â m´ ³

7.7.1 ¬£¥¥ ² ¯ ¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ ¥» ·Ê 7.13 ì à ϴ§¯ m¯ ¬³ ´ BPMR ·ÊÅ n 3 ­³©¯m´ ¬Ï´­¥³ ´¥¯¯ à ´¥q É

¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ ´£ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 7.5 ( ³ à § £´ ´ ¥» ·Ê 7.3) Ä ¤ ·Ê

¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ F ç² ´¥qÂ É ¬¯ £¶ ¶ G Â É Æ ´£¬£ ´¥ (7.44) ç² (7.45) ´£§Ï´ ³

£¹Ê¯ M = 1 ç² L = 1  ¹Ê ¯ ´ ¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ F ·Ê£· M = 1 ² Ï´ ´ Ä ¤Å n¬³ ´

¯m´ §³ ¯ 3 à ¥É ·Ê ¶ ³ ( ³Ê ¹¯ r–1,k , r0,k ç² r1,k )  ¥´² ² ³ Ë Å ´¥¬¥n´ ¬³ ´ ¯m´ §³ ³ Ë 3 ¬³ ´ ·Ë Ï´Â É n¯ Å n n¯£»§¯¶ º Ï´ © 5 à ¥É ( ³Ê ¹¯ a–2,k , a–1,k , a0,k ,

a1,k ç² a2,k )  ¹Ê¯Å­n¬³ ´ ¯m´ §³ à m§²¬³ ´ £· § ¥² ¯ ITI

¥» ·Ê 7.14  ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² BPMR ·ÊÅ n¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ (à ·ÊÅ n

“1D target” ç² “Zero-corner 2D target”) ç²¥² BPMR ·ÊÅ n 3 ­³©¯m´ ç²Å n¯· ©¯Æ§Â ¯¥q

¬¯ £¶ ¶ (Å ·Ê ·ËÂ¥·¤ ©m´ “1D target with 2D-EQ”) Ä ¤ ´¥qÂ É ¬¯ £¶ ¶ Ê·Å n£·¥» à ´£¬£ ´¥ (7.50) ¸Ê ¹¯©m´Â É ´¥qÂ É ­ ¸Ê £¶ ¶ (Å n© ¥ ¥© ­´©·Â ¯¥q ¶­ ¸Ê £¶ ¶Æ n) ´ ¥» ©m´Ä ¤ ³Ê©Æ

£¹Ê¯¥² Å n ´¥qÂ É §³ « ²Â ·¤© ³ (Å ·Ê ·Ë ¹¯ ´¥qÂ É ­ ¸Ê £¶ ¶) ¥² ·ÊÅ n¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶

²£·¬£¥¥ ² · ©m´¥² ·ÊÅ n¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶Â¬£¯ Ä ¤Â ´²Â£¹Ê¯ ©´£ º n¯£»§¬» È ³ Ë ·Ë É

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-1

1D target (with 1D-EQ) Zero-corner 2D target (with 1D-EQ) 1D target with 2D-EQ

10

-2

10

BER

3 Tb/in2 -3

10

2 Tb/in2 -4

10

-5

10

8

10

12

14

16

18

20

22

24

26

SNR (dB)

 ¥´²©m´¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶¬´£´¥ ¥³ à m ¬³ ´  ¹Ê¯Å­n § ¥² ¯ ITI § § Æ n · ©m´ ¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶

¸ ãn©m´¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ ²£·¬£¥¥ ² · ©m´¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ à m ´¥Å n ´

¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ Ï´Â É n¯ Å n ³ ¥² ·Ê£· 3 ­³©¯m´ ¸Ê ¬¥n´ Æ n¤´ Å ´ ¶ ³ ¶ (Ä ¤Â ´²

¯¤m´ ¤¶Ê n´ Ï ´£´Å n ³ ¥² ´¥ ³ ¸ à à © ³ Ë ·ÊÅ nÅ ³ º ³ ) ¯¤m´ Æ¥ É ´£ n´ n¯ ´¥Å n¯· ©¯

Ƨ ¯¥q¬¯ £¶ ¶ ³ ¥² BPMR ·Ê£·­³©¯m´  ·¤© ɬ´£´¥ Ï´Æ nÆ£m¤´ Ä ¤ ´¥Å n ³¡Â¡¯¥q (buffer

­¥¹¯ ·Ê ³ n¯£»§)  ¹Ê¯Â É ¬³ ´ ¯m´ §³ 3 ¬³ ´ ( ³Ê ¹¯¥² ²¯m´ n¯£»§ 3 ¥³ Ë ) ´ ³ Ë ¸ Ï ´¬³ ´ ¯m´ §³ ³ Ë 3 ¬³ ´ £´ ¥²£©§ §¥©£ ³ Ä ¤Å n¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶ ³ Ë ·Ë Â É Â ¥´²©m´Æ¯Ã§ qà m§²Æ¯Ã§ qÅ ¥² BPMR £· ϴí m ·Êà m ¯ Å ¬¹Ê¯ ³ ¸ ³ ³ Ë ´¥Â n´ ³ ­©² (synchronization) ¬³ ´ ¯m´ §³ ³ Ë 3 ¬³ ´ ¸ Ï´Æ nÆ£m¤´ [108]

7.7.2 § ¥² ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ç²Ã ¥É £¶¬Â¥ ¶¬Â ¥ ³ Å ¬m© ·Ë ²Ã¬ ¬£¥¥ ² ¯ ´¥qÂ É ¬¯ £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶Å ¥² BPMR ·Ê£·

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

¥» ·Ê 7.14 ¬£¥¥ ² ¯ ¥² ·ÊÅ n¯ · ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶Ã§²¬¯ £¶ ¶

7

บทที่

§ ¥² ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ (media noise) ç²Ã ¥É £¶¬Â¥ ¶¬Â ¥ ³ (TMR) ´£ ·Êì Å ¥» ·Ê 7.15 Ä ¤Å n m¯ ¬³ ´ ·Ê m¯Â ¹Ê ¯ ´ ©§´ P(z,x) Å ¬£ ´¥ (6.15) £¹Ê¯¥©£

§ ¥² ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ç²Å n¬£ ´¥ (6.21) £¹Ê¯¥©£ § ¥² ¯ TMR Å

·Ê ·Ë¬³ ´ ¯m´ §³ ·ÊÆ n ´ ­³©¯m´ £· m´Â m´ ³

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%A %x %z %Wx%Wz a 1,k a 0,k a1,k

n t

y t

P z , x

r t

rk

F D

zk

aˆ0,k

t kTx

%T

G Dz , Dx

dk

wk

¥» ·Ê 7.15 à ϴ§¯ m¯ ¬³ ´ BPMR à ­ ¸Ê ­³©¯m´ ·Ê¥©£ § ¥² ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ ç²Ã ¥É £¶¬Â¥ ¶¬Â ¥ ³

y t

1

1

a

m ,n

P mTz %T , t nTx n t

m 1 n 1

(7.75)

£¹Ê¯ n(t) ¹¯¬³ ´ ¥ © AWGN ·Ê£· ©´£­ ´Ã m ¬Â ¥³£ Ï´§³ à ¬¯ n´  m´ ³

N0/2 ´ ³ Ë ¬³ ´ ¯m´ §³ y(t) ² » ³ ³©¯¤m´ ©§´ t = kTx Ï´Å­nÆ nÂ É §Ï´ ³ n¯£»§ rk ´ ³ Ë É ²Å n n¯£»§¯¶ º {am,k} ç² {rk} Å ´¥¯¯ à ¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ ´ 15

Ã É Ã§² ´¥qÂ É ¬¯ £¶ ¶ ´ 3 u 3 à m´ È ¯ ´ ·Ë m´ SNR ·ÊÅ nÂ É Æ ´£¬£ ´¥ (7.70)

£¹Ê¯ V2 = N0/(2T)

¥» ·Ê 7.16 ì ¬£¥¥ ² ¯ ¥² ·ÊÅ n ´¥qÂ É Ã m´ È ©´£¥º Ã¥ ¯ ¬³ ´

¥ © ¬¹Ê¯ ³ ¸ ¥² ³ m´ È ·Ê ©´£ º 3 Tb/in2 £¹Ê¯Â¬n à y ¹¯ m´ SNR ·Ê¥² n¯ Å n ¹Ê¯

Ï´Å­n£· BER = 10–4 ´ ¥» ©m´¥² ·ÊÅ n “1D target” £·¬£¥¥ ² n¯¤¬º Å ² ·Ê¥² ·Ê

Å n “Asymmetric 2D target” £·¬£¥¥ ² ·¬º Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯¬³ ´ ¥ © ¬¹Ê¯ ³ ¸ £· ©´£¥º Ã¥ £´ Å Ï´ ¯  ·¤© ³ ¥» ·Ê 7.17 ì ¬£¥¥ ² ¯ ¥² ·ÊÅ n ´¥qÂ É Ã m´ È

©´£¥º Ã¥ ¯ TMR ¥² ³ m´ È ·Ê ©´£ º 3 Tb/in2 ¸Ê ©m´¥² ·ÊÅ n “Asymmetric 2D

target” £·¬£¥¥ ² · ©m´¥² ·ÊÅ n ´¥qÂ É Ã ¯¹Ê È ¯ ´ ·Ë £¹Ê¯ TMR £· ©´£¥º Ã¥ £´ É

²¬m § Ï´Å­n m¯ ¬³ ´ £·§³ « ²Æ£m¬££´ ¥£´ ¸Ë ¸ Ï´Å­n ´¥qÂ É Ã ¬££´ ¥£·¬£¥¥ ² n¯¤ ©m´ ´¥qÂ É ·Ê£·£º£Â É ª» ¤q

7.7.3 ¬£¥¥ ² ¯ ¥² BPMR à © Ï´Ë ´ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 4.6.2 ¥² ·ÊÅ n ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë ( ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³

¥²­©m´ © ¥ ¥© ­´Ã ¯¡ q粩 ¥ ¯ ¥­³¬Ã¯§ · · ·) [3, 21] ¬´£´¥ m©¤Â ¶Ê£¬£¥¥ ²

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การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดิจิทัล Signal Processing for Digital Data Storage

45

SNR required to achieve BER = 10

-4

(in dB)

50

1D target Zero-corner 2D target Symmetric 2D target Asymmetric 2D target

40

35

30

25

0

0.5

1

1.5

2

2.5

Media noise amount (%)

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

¥» ·Ê 7.16 ¬£¥¥ ² ¯ ¥² ·ÊÅ n ´¥qÂ É Ã m´ È ·Ê£· § ¥² ¯ ¬³ ´ ¥ © ¬¹Ê¯ ³ ¸

36

SNR required to achieve BER = 10

-4

(in dB)

38

34

1D target Zero-corner 2D target Symmetric 2D target Asymmetric 2D target

32

30

28

26

24 0

5

10

15

20

TMR amount (%)

7

บทที่

¥» ·Ê 7.17 ¬£¥¥ ² ¯ ¥² ·ÊÅ n ´¥qÂ É Ã m´ È ·Ê£· § ¥² ¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³

¯ ¥² Æ n m¯ n´ £´ £¹Ê¯Â ·¤ ³ ¥² ·ÊÆ£mÅ n ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë ³ ³ Ë Å ¬m© ·Ë ²Ã¬ ¬£¥¥ ² ¯ ¥² BPMR ·ÊÅ n ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë ·Ë

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u 1,k u 0,k u1,k

a 1,k

a 0,k

zk

uˆ0,k

a1,k

¥» ·Ê 7.18 ( ) © ¥Â n´¥­³¬ ç² ( ) © ¥ ¯ ¥­³¬ ·Ê m¯Â ¶Ê£Â n´Æ Å ¥² BPMR Å ¥» ·Ê 7.2

 ¹Ê ¯ ´  ¶ ´¥ ¯ ¥­³¬Ã © Ï´Ë n¯ Å n ³ ¥² ·Ê »  n´¥­³¬ (coded system)

³ ³ Ë ¥² BPMR ·ÊÆ£m »  n´¥­³¬ (uncoded system) Å ¥» ·Ê 7.2 ¬´£´¥ Ï´Å­nÂ É ¥² ·Ê »  n´¥­³¬Æ nÄ ¤ ´¥Â ¶Ê£© ¥Â n´¥­³¬Ã§²© ¥ ¯ ¥­³¬ ·Êì Å ¥» ·Ê 7.18  n´Æ Å ¥» ·Ê 7.2

³Ê ¹¯ © ¥¢´ ¬m ¶ m´©¬´¥ (message bits) ¯ à m§²Ã ¥É {um,k} ¬Ï´­¥³ m {0, r1}

Ï´ © 3640 ¶ m¯Ã ¥É »  n´¥­³¬ n©¤¥­³¬Ã¯§ · · · ¥ ¶Ã (3, 27) ·Ê£·¯³ ¥´¥­³¬Â m´ ³

8/9 [17] Ï´Å­nÂ É §Ï´ ³ n¯£»§ ¯ à m§²Ã ¥É {am,k} ´ 4095 ¶ m¯Ã ¥É ³ ì Å ¥» ·Ê

7.18 ( ) £¹Ê¯Â£ ¥¶ q ´¥¶ ·Â É Å Ã m§²­§³ £·Â§ ­ ¸Ê Ï´ © 3 ³© ç²Å à m§²Ã ©£·Â§ ­ ¸Ê Ï´ © 27 ³© ´ ³ Ë §Ï´ ³ n¯£»§ {am,k} É ² » n ¯  n´ m¯ ¬³ ´ H ´£¥» ·Ê 7.2 Å ² ·Ê

© ¥¢´ ¥³ n¯£»§Â¯´ q º ¯ ¯· ©¯Æ§Â ¯¥q zk Å ¥» ·Ê 7.2 ² » n ¯  n´Æ Å ¯· ©¯Æ§Â ¯¥q

à  ¯¥qÄ [21] ´£ ·Êì Å ¥» ·Ê 7.18 ( ) ¸Ê Â É ´¥ Ï´ ´ ¥m©£ ³ ¥²­©m´ © ¥ ¥© ­´

SOVA à ¬¯ £¶ ¶ (2D-SOVA detector) [120] 粩 ¥ ¯ ¥­³¬Ã¯§ · · · Ä ¤ ´¥ ¯ ¥­³¬ ï§ · · · ²¯¤m» ¹Ë ´ ¯ ¯³§ ¯¥¶ ¸£ ´¥ m´ m´©¬´¥ (Message-Passing) [17] ·Ê£· ´¥© Ï´Ë

¢´¤Å Ï´ © 3 ¥¯ É ²Æ nÂ É m´ ¥²£´ ¯ ¶ m´©¬´¥ ¯ à ¥É §´ ­¥¹¯ uˆ0,k ´£ ·Ê n¯ ´¥

Å ´ ¶ ³ ¶© ¥ ¥© ­´ 2D-SOVA ·ÊÅ n Ê· ·Ë ²£· ³ Ë ¯ ´¥ Ï´ ´ ­£¹¯ ³ © ¥

¥© ­´ SOVA à ¬¯ ¶ª ´ (bi-directional SOVA) [42] ´£ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 3.5

 ·¤ à mà ¢´  ¥§§¶¬ ·ÊÅ nÅ © ¥ ¥© ­´ 2D-SOVA ²£· Ï´ © ¬ ´ ² Q £´ ¸Ë , £·Â¬n ¬´ ´£´ ©m´¬¯ ¬n ·Ê©¶Ê ¯¯ ´ à m§²¬ ´ ², ­¥¹¯£·Â¬n ¬´ ´£´ ©m´­ ¸Ê ¬n Å Ã m§² ´¥

 §·Ê¤ ¬ ´ ² ´ ¬ ´ ² u Æ ¤³ ¬ ´ ² q (­£¹¯ ³ à ¢´  ¥§§¶¬ ·ÊÅ nÅ © ¥ ¥© ­´

©·Â ¯¥q ¶¬¯ £¶ ¶) ¸Ê ¸Ë ¯¤m» ³ §³ « ² ¯ ´¥qÂ É ¬¯ £¶ ¶ ÊÅ· nÅ ¥² ¯¤m´ Æ¥ É ´£ n´¥² BPMR

Å n ´¥qÂ É ­ ¸Ê £¶ ¶ (1D target) ¯· ©¯Æ§Â ¯¥qà  ¯¥qÄ É ²Å n© ¥ ¥© ­´ SOVA [19, 42] (à ¥ ¶­¥¹¯Ã ¬¯ ¶ª ´ ÉÆ n ´£ ·Ê¯ ¶ ´¤Å ­³© n¯ ·Ê 3.4 ç² 3.5) à © ¥ ¥© ­´ 2D-SOVA

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-1

10

2

3.5 Tb/in

-2

10

BER

4 Tb/in2 -3

10

3 Tb/in2

-4

10

1D target Zero-corner 2D target Symmetric 2D target 15

20

25

30

35

40

SNR (dB)

´¥ §¯ m¯Æ ·Ë ²Â ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² BPMR à © Ï´Ë ·ÊÅ n ´¥qÂ É 3

à ¹¯ 1D target, Zero-corner 2D target, ç² Symmetric 2D target Ä ¤¯· ©¯Æ§Â ¯¥q ÊÅ· n ²£· Ï´ © Ã É Â m´ ³ 15 Ã É Ã§² m´ SNR ² ¶ ¤´£Ä ¤

1 ¬ SNR 10 log10 2 ­­­ RT ®

(7.76)

£·­ m ©¤Â É Â ¶Â § (dB) £¹Ê¯ V2 = N0/(2T) ç² R = 8/9 ¹¯¯³ ¥´¥­³¬Ã¯§ · · · ¥» ·Ê 7.19

 ¥·¤  ·¤ ¬£¥¥ ² ¯ ¥² BPMR à © Ï´Ë ·ÊÅ n ´¥qÂ É Ã m´ È ´¥© Ï´Ë ¥¯ ·Ê­n´ ¸Ê ² ©m´¥² ·ÊÅ n “Symmetric 2D target” £·¬£¥¥ ² · ©m´¥² ·ÊÅ n “Zero-corner 2D

การออกแบบทารเก็ตและอีควอไลเซอรสำหรับระบบ BPMR

¥» ·Ê 7.19 ¬£¥¥ ² ¯ ¥² BPMR à © Ï´Ë ·ÊÅ n ´¥qÂ É Ã m´ È ´¥© Ï´Ë ¥¯ ·Ê­n´

target” ç² “1D target” Ä ¤Â ´²¯¤m´ ¤¶Ê £¹Ê¯ ©´£ º n¯£»§¬» È

7

7.8 ¬¥º n´¤

บทที่

Å ´ ¶ ³ ¶© ¥ ¥© ­´ PRML ¤³ ¬´£´¥ Ï ´£´Å nÅ ´¥ ¥© ­´ n¯£»§ ¯ ¥² BPMR Æ n

 m  ·¤© ³ ¥² ´¥ ³ ¸ n¯£»§ ·ÊÅ n ³ ³©Ê Æ Å ³ º ³ ¯¤m´ Æ¥ É ´£¬£¥¥ ² ¯ © ¥ ¥© ­´

PRML ² ¸Ë ¯¤m» ³ ©´£Â­£´²¬£ ¯ ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q Ê·Å nÅ ¥² ³ ³ Ë Å ·Ë ¸ Æ n¯ ¶ ´¤©¶ · ´¥¯¯ à ´¥qÂ É ­ ¸Ê £¶ ¶Ã§²¬¯ £¶ ¶ 粯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶Ã§²¬¯ £¶ ¶ Ã

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m´ È ¬Ï´­¥³ Å n ´ Å Ã m§²¬ ´ ´¥ q ³ Ë ·Ë Â É Â ¥´²©m´ ´¥qÂ É Ã§²¯· ©¯Æ§Â ¯¥q Ê· ·¬´£´¥ m©¤§ § ¥² ·Ê ¶ ´ ISI ç² ITI Å ¥² BPMR Æ n¯¤m´ £· ¥²¬¶ ¶¢´ 2

´ ´¥ §¯ ©m´ “1D target” ­£´²¬Ï´­¥³ Å nÅ ¥² ·Ê£· ©´£ º n¯£»§ n ¯¤ (d 2.5

Tb/in ), “Zero-corner 2D target” ­£´²¬Ï´­¥³ Å nÅ ¥² ·Ê£· ©´£ º n¯£»§ ´ §´ (2.5 – 3

Tb/in2), 粓Symmetric 2D target” ç² “Asymmetric 2D target” ­£´²¬Ï´­¥³ Å nÅ ³

¥² ·Ê£· ©´£ º n¯£»§¬» È (t 3 Tb/in2) ¯ ´ ·Ë ¤³ ©m´ “Symmetric 2D target” Æ£m­£´²

¬Ï´­¥³ Å nÅ ¥² ·Ê£· § ¥² ¯ à ¥É £¶¬Â¥ ¶¬Â ¥ ³ 粯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶£·¬£¥¥ ² · ©m´¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ à m n¯ Å n ³ ¥² ·Ê£· 3 ­³©¯m´ ¸Ê ¤³ Ï´Æ n¤´ Å ´ ¶ ³ ¶

7.9 Ã ¸ ­³ n´¤ 1.

 ·¤ Ä ¥Ã ¥£ SCILAB  ¹Ê¯¯¯ à 1.1) ´¥qÂ É ­ ¸Ê £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ 1.2) ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤q粯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ 1.3) ´¥qÂ É ¬¯ £¶ à ¶ ¬££´ ¥Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ 1.4) ´¥qÂ É ¬¯ £¶ à ¶ ¯¬££´ ¥Ã§²¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶ 1.5) ´¥qÂ É ¬¯ £¶ à ¶ §²¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶

2.

 ¥·¤  ·¤ ©´£Ã m´ ¥²­©m´ ¯· ©¯Æ§Â ¯¥q­ ¸Ê £¶ ¶Ã§²¯· ©¯Æ§Â ¯¥q¬¯ £¶ ¶

3.

©´ à ¢´  ¥§§¶¬Ä ¤§²Â¯·¤ (ì ¬ ´ ² ¬n ¬´ ´ ç² n¯£»§ ¥² ϴ¬n ¬´ ´ ³ Ë ­£ ) £¹Ê¯ n¯£»§¯¶ º ¹¯ {–1, 1} ¯

3.1) ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤qà ¬££´ ¥ ·Ê Ï´­ Ä ¤¬£ ´¥ (7.64) 3.2) ´¥qÂ É ¬¯ £¶ à ¶ ¬££´ ¥ ·Ê Ï´­ Ä ¤¬£ ´¥ (7.67) 3.3) ´¥qÂ É ¬¯ £¶ à ¶ ¯¬££´ ¥ ·Ê Ï´­ Ä ¤¬£ ´¥ (7.15) 4.

¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ © ¥ ¥© ­´ 2D-SOVA Ä ¤§²Â¯·¤ ¥n¯£ ³ Ë ¤ ³©¯¤m´ ´¥

Ï´ © ¬Ï´­¥³

4.1) ´¥qÂ É ¬¯ £¶ ¶ Ê£ · ·£º£Â É ª» ¤qà ¬££´ ¥ 4.2) ´¥qÂ É ¬¯ £¶ à ¶ ¬££´ ¥

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·Ê 8 Â Ä Ä§¤· HAMR ´ ·Ê §m´©Å ·Ê 6 Â Ä Ä§¤· BPMR Â É ­ ¸Ê Å ­§´¤È Â Ä Ä§¤· Ê·¯´ ² Ï ´£´Å n ¶Ê£ ©´£ º n¯£»§Å °´¥q ¶¬ qÆ ¥¡q Å­nÆ n£´ ©m´ 1 Tb/in2 [117] à mÅ ³ º ³ ³ ©¶ ³¤ Ï´§³ à nÆ ³ ­´

m´ È ·Ê ·Ê¤© n¯ ³ ´¥¬¥n´ ¥² BPMR ¸Ë £´Å n ´ ¥¶  m ´¥¬¥n´ ¬¹Ê¯ ³ ¸ ·Ê£· ´¥ Ï´Ã

(bit-patterned media), ´¥Ã n ³ ­´ n¯ ¶ §´ Å ´¥Â ·¤ (written-in error) 粯¹Ê È Â ¥´² ¥²¤²Â©§´¯³ Å §n ·Ë

¬Ï´­¥³ Å ·Ë ² §m´© ¸ ¹Ë ´ Â Ä Ä§¤· ´¥ ³ ¸  ¶ ãm­§É ·ÊÅ n ©´£¥n¯  n´ m©¤53

(HAMR: heat-assisted magnetic recording) ­¥¹¯Â¥·¤ ¬³ Ë È ©m´ “Â Ä Ä§¤· HAMR” [78,

128, 129] ¸Ê ¹¯Â É ¯· Â Ä Ä§¤·­ ¸Ê ·Ê Ï´§³ Â É ·Ê¬ Å ¯ ¥¶«³ n» §¶ °´¥q ¶¬ qÆ ¥¡q ³Ê©Ä§

 ¥´² ¯ ´ m©¤Â ¶Ê£ ©´£ º n¯£»§Æ n£´ ©m´ 1 Tb/in2 çn© ¤³ ¬´£´¥ Ï ´£´Å n ´ ¥¶ Å °´¥q

¶¬ qÆ ¥¡q Æ n¢´¤Å ¥²¤²Â©§´¯³ Å §n ·Ë ( ´ ©m´ ² Ï ´£´Å n ´ m¯ Â Ä Ä§¤· BPMR) ¯ ´ ·Ë

Å ·Ë ²¯ ¶ ´¤­§³ ´¥ Ï´ ´ ç²Ã Ï´§¯ m¯ ¬³ ´ ¯ ¥² HAMR  ¹Ê¯Å­n n»¯m´

¥´ ¸ ¥²Â É m´ È ·Ê ·Ê¤© n¯ ³ ´¥ Ï ´¥² HAMR £´Å n ´ ¥¶ ¥©£ ³ Ë Ã¬ ³©¯¤m´

´¥ Ï´§¯ ¥² HAMR à à © ¯ 54 (longitudinal HAMR system) ç²Ã à © ³ Ë

(perpendicular HAMR system) [130 – 134]  ¹Ê¯ª¸ «´¬£¥¥ ² ¯ ¥² £¹Ê¯Â ·¤ ³

´¥´£¶Â ¯¥q m´ È Â m ϴí m ¯ § ¯¥q §³ « ² ¯ ­³©Â ·¤ ç²­³©¯m´ ç² º ¬£ ³ ¶ ´

ãm­§É ¯ ¬¹Ê¯ ³ ¸ Â É n 53

การออกแบบทาร เทคโนโลยีเก็HAMR ตและอีควอไลเซอรสำหรับระบบ BPMR

² ³ Ë ¸ Â É Æ Æ n©m´Â Ä Ä§¤· BPMR ¯´ ²¤³ Æ£m Ï´£´Å n ´ Æ n ¥¶ Å °´¥q ¶¬ qÆ ¥¡q ¢´¤Å

87

บทที่ บทที่

Â Ä Ä§¤· HAMR ­¥¹¯Â¥·¤ ©m´ “Â Ä Ä§¤· ´¥ ³ ¸ à ư ¥¶ (hybrid recording technology)” n¯ Ï ´£´ ¥²¤º q Å n¥m©£ ³ ¥² ´¥ ³ ¸  ¶ ãm­§É à à © ¯ , ¥² ´¥ ³ ¸  ¶ ãm­§É à à © ³ Ë , ­¥¹¯¥² BPMR (bit-

54

patterned magnetic recording) ÉÆ n  ¹Ê¯ m©¤Â ¶Ê£ ©´£ º n¯£»§Å­n£´ ©m´Â ¶£Æ n¯· ­§´¤Â m´ ³© [128, 129] ¥² HAMR à à © ¯ ­£´¤ ¸ Â Ä Ä§¤· HAMR ·ÊÅ n ´ ¥m©£ ³ ¥² ´¥ ³ ¸  ¶ ãm­§É à à © ¯

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8.1 Ï ´ ´¥Â ¶Ê£ ©´£ º n¯£»§ ¯ °´¥q ¶¬ qÆ ¥¡q Ï´Æ nÄ ¤ ´¥§ ¹Ë ·Ê (­¥¹¯ ¥¶£´ ¥) ´¥ ³ Â É n¯£»§

­ ¸Ê ¶ ¢´¤Å ¬¹Ê¯ ³ ¸ Ä ¤ ³Ê©Æ ¬¹Ê¯ ³ ¸ ¥² ¯ n©¤Â ¥  ¶ ãm­§É ´ Â§É Ï´ © £´ ¥©£ ³© ³ Â É ¯ º¢´ (particle) ·Ê£· ¥¶£´ ¥ V Ä ¤ ·Êà m§²Â ¥ ²£· m´¬³£ ¥²¬¶ ¶ÃÎ ¯ Æ¯Ä ¥¯ ·

à à  ·Ê¤© Ku (uniaxial anisotropy coefficient) ¸Ê n´ Ku £· m´£´ É ² Ï´Å­n¤´ m¯ ´¥  §·Ê¤ à § ¶ª ´ ¬¢´ ©´£Â É Ã£m­§É (magnetization) ¯ ¶ n¯£»§

Å ´ ¶ ³ ¶ §³ ´ ï Æ¯Ä ¥¯ · ¯ à m§²¯ º¢´ £· m´Â m´ ³ Ep = KuV ¸Ê Å n

Â É ³©©³ ¬ ·¤¥¢´ ¯ ¯ º¢´ [43] §m´© ¹¯ n´ Ï´­ Å­n §³ ´  ¶ ©´£¥n¯ ·Ê ¶ ¸Ë ´

¬¢´ é §n¯££· m´Â m´ ³ ET = kBT £¹Ê¯ kB ¹¯ m´ ³©Ä § qã (Boltzmann’s constant)

£· m´Â m´ ³ 1.38×10–23 »§ m¯Â §©¶ (joules per Kelvin) ç² T ¹¯¯º ­¢»£¶ (temperature) £·­ m ©¤Â É Â §©¶ ³ ³ Ë ¶ n¯£»§ ·ÊÂ É ¯¤m»Å ¬¹Ê¯ ³ ¸ ²£·Â¬ ·¤¥¢´ É m¯Â£¹Ê¯ EP KV u pC ET kBT

(8.1)

£¹Ê¯ E ¹¯ Ï´ ©  ɣ © ·Ê£· m´£´ ( m E t 60) Ä ¤ ³©Ê Æ ¬£ ´¥ (8.1) ² ¯ ¸ · Ï´ ³ ¯

´¥Â ¶Ê£ ©´£­ ´Ã m  ¶ ¹Ë ·Ê (areal density) ­¥¹¯ ©´£ º n¯£»§ ¯ °´¥q ¶¬ qÆ ¥¡q ¸Ê Â¥·¤ ³ ³©Ê Æ ©m´ “ · Ï´ ³ »Â ¯¥q ´¥´Ã£  ¶ 55 (superparamagnetic limit)” [1, 43]

 ¹Ê ¯ ´ m´ kBT Å ¬£ ´¥ (8.1) Â É m´ ³© ³ ³ Ë ©¶ · ´¥Â ¶Ê£ ©´£ º n¯£»§Ä ¤ ´¥§

¥¶£´ ¥ V ¸ Ï´Â É n¯ Å n ´ ³ ¬¹Ê¯ ³ ¸ ·Ê£· m´ Ku ¬» £´ ¸Ë  ¹Ê¯Å­n KuV £· m´  ¶£Ã§²

¬¯ §n¯ ³ ¬£ ´¥ (8.1) ¯¤m´ Æ¥ É ´£Å ´ ¶ ³ ¶ m´ Ku ²Ã ¥ ³ ¥ ³ “ m´¬¢´ § §n´ ãm­§É Hc (coercivity)” [43] ¸Ê ­£´¤ ¸ ¥¶£´ ¬ ´£Ã£m­§É ·Ê n¯ Å n ¹Ê¯ Ï´Å­n¬¢´ ©´£

Â É Ã£m­§É ¯ ¶ n¯£»§£· ¶ª ´  §·Ê¤ à § Æ Å ¶ª ¥ n´£56  ¥´² ² ³ Ë Â£¹Ê¯ Ku £· m´£´

É­£´¤ ©´£©m´ Hc £· m´£´ n©¤ ¸Ê § ·Ê ´££´ É ¹¯­³©Â ·¤ ² n¯ Å n¬ ´£Ã£m­§É ·Ê£· ©´£Â n£ ¬» £´ (£´ ©m´ m´ Hc) Å ´¥Â ·¤ ¶ n¯£»§§ Æ ³ Â É Å ¬¹Ê¯ ³ ¸ Æ n¯¤m´ £·Â¬ ·¤ ¥¢´

¯ ´ ·Ë©¶ · ´¥Â ¶Ê£ ©´£ º n¯£»§Ä ¤ ´¥§ ¥¶£´ ¥ V É ©¥ Ï´ ¸ ¸ ©´£Â n£ ¯ ¬ ´£Ã£m­§É £´ ¬º ·Ê­³©Â ·¤ Å ³ º ³ ¬´£´¥ ¬¥n´ Æ n n©¤  ¥´² ²Â É ³© Ï´ ³ m´£´ ¬º ¯ Ku (­¥¹¯ Hc)

55

n´ E Å ¬£ ´¥ (8.1) £· m´ n ¯¤Â ¶ Æ É ² Ï´Å­n£·Ä¯ ´¬¬» ·Ê n¯£»§ ¶ 0 ²Â ¶ ´¥Â §·Ê¤ à § ¶ª ´ ¬¢´ ©´£Â É

56

m´¬¢´ § §n´ ãm­§É Hc ¤³ ¬´£´¥ Å n ¯ ¸ ©´£ m´¤ ¯ ´¥Â ·¤ ¶ n¯£»§§ Æ ³ Â É Å ¬¹Ê¯ ³ ¸ ³Ê ¹¯

ãm­§É Æ Â É n¯£»§ ¶ 1 (ç²Å ´ §³ ³ ) ¬¹Ê¯ ³ ¸ ·Ê£· m´ Hc n ¯¤ ɬ´£´¥  ·¤ ¶ n¯£»§§ Æ Å ¬¹Ê¯ ³ ¸ Æ n m´¤ (Å n¬ ´£Ã£m­§É ´ ­³©Â ·¤ Æ£m£´ )

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¬¢´ § §n´ ãm­§É

Hc

T ¥» ·Ê 8.1 ¥² © ´¥Â ·¤ n¯£»§ ¯ ¥² HAMR

·Ê¥² ¬´£´¥ ¥¯ ¥³ Æ n ³ ³ Ë ¯´ ¬¥º Æ n©m´ ©´£­ ´Ã m  ¶ ¹Ë ·Ê¬» ¬º ¯ Â Ä Ä§¤· ´¥ ³ ¸

à à © ³ Ë ·ÊÅ nÅ °´¥q ¶¬ qÆ ¥¡q ³ º ³ ² » Ï´­ n©¤ ³ ³¤ ·Ê¬Ï´ ³ ¬¯ ¯¤m´ ¹¯ · Ï´ ³ »Â ¯¥q ´¥´Ã£  ¶ ç² ©´£Â n£ ¯ ¬ ´£Ã£m­§É £´ ¬º ·Ê­³©Â ·¤ ¬´£´¥ ¬¥n´ Æ n

Â Ä Ä§¤· HAMR ¹¯Â É Â Ä Ä§¤·­ ¸Ê ·Ê¬´£´¥ m©¤Â ¶Ê£ ©´£­ ´Ã m  ¶ ¹Ë ·ÊÆ n£´ ©m´

· Ï´ ³ ¯ Â Ä Ä§¤· ´¥ ³ ¸ à à © ³ Ë ·Ê Ï´§³ Å nÅ °´¥q ¶¬ qÆ ¥¡q ³ º ³ Ä ¤Â Ä Ä§¤· HAMR ¯´ª³¤ ¥²Ä¤ q ¯ ©´£ ¥¶ ·Ê©m´ “¬¢´ § §n´ ãm­§É Hc ²Ã ¥ ³ ³ ¯º ­¢»£¶”

เทคโนโลยี HAMR

8.2 ­§³ ´¥Â ·¤ n¯£»§ ¯ ¥² HAMR

´£ ·Êì Å ¥» ·Ê 8.1 §m´© ¹¯ m´¬¢´ § §n´ ãm­§É ¯ ¬¹Ê¯ ³ ¸ ²§ § £¹Ê¯¬¹Ê¯ ³ ¸ ³ Ë

» Ï´Å­n£·¯º ­¢»£¶¬» (­¥¹¯ » Ï´Å­n¥n¯ ) ç²Å ´ §³ ³

n´ Ï´­ Å­n “ ¥¶Â© A” ¹¯ ¥¶Â© ·Ê n¯ ´¥ ²Â ·¤ ¶ n¯£»§§ Æ ³ Â É Å ¬¹Ê¯ ³ ¸

³ ³ Ë ¥² © ´¥Â ·¤ n¯£»§Å ¥² HAMR ¬´£´¥ ¯ ¶ ´¤Æ n ³ ·Ë Â¥¶Ê£ n ¥¶Â© A ²£·

8

บทที่

¯º ­¢»£¶ ¶ (­¥¹¯¯º ­¢»£¶­n¯ ) ϴí m ­£´¤Â§ 1 Å ¥» ·Ê 8.1 ¸Ê £· m´ Hc ¬» ´ ³ Ë

¥² HAMR ² Ï´ ´¥Â ¶Ê£ ©´£¥n¯ Å­n ³ ¥¶Â© A  m ´¥Å nì § ¯¥q¤¶  n´Æ ¥ ¥¶Â© A É ² Ï´Å­n ¥¶Â© A £·¯º ­¢»£¶¬» ¸Ë Â¥¹Ê¯¤È £´ ¸ ϴí m ­£´¤Â§ 2 ¸Ê £· m´ Hc n ¯¤ ©m´

©´£Â n£ ¯ ¬ ´£Ã£m­§É ·Ê­³©Â ·¤ ¬´£´¥ ¬¥n´ Æ n ( ¸ Ï´Å­n ·¤ ¶ n¯£»§Â n´Æ Å ¥¶Â© A

Æ n m´¤ Ä ¤Å n ©´£Â n£ ¯ ¬ ´£Ã£m­§É Æ£m£´ ) ´ ³ Ë É Ï´ ´¥Â ·¤ ¶ n¯£»§Â n´Æ Å ¥¶Â© A

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ç²Â£¹Ê¯Â ·¤ ¶ n¯£»§Â¬¥É Â¥·¤ ¥n¯¤Ã§n© ¥² HAMR ² Ï´Å­n ¥¶Â© A Â¤É ³©§ ¯¤m´ ¥© ¥ɩ §³  n´¬m»¯º ­¢»£¶ ¶ ϴí m ­£´¤Â§ 1 ·Ê£· m´ Hc ¬» ¸Ê £· § Ï´Å­n ¶ n¯£»§ ·Ê ·¤  n´Æ ³ Â É Å ¥¶Â© A £·Â¬ ·¤¥¢´ ¬» (Æ£m£· ³ ­´Â¥¹Ê¯ · Ï´ ³ »Â ¯¥q ´¥´Ã£  ¶ )

Ä ¤ ³Ê©Æ Â Ä Ä§¤· HAMR ² n¯ » Ï ´£´Å n¥m©£ ³ ¥² ´¥ ³ ¸  ¶ ãm­§É Ã

·ÊÅ n ³ ³Ê©Æ 57  ¹Ê¯Â ¶Ê£ ©´£ º n¯£»§Å­n£´ ©m´Â ¶£­§´¤Â m´ [128, 129] Ä ¤ ¥² © ´¥Â ·¤

n¯£»§§ Æ ³ Â É Å ¬¹Ê¯ ³ ¸ ²Â É Æ ´£ ·Ê¯ ¶ ´¤ n´ n à m¬Ï´­¥³ ¥² © ´¥¯m´ ç² ´¥

¯ ¥­³¬ n¯£»§ ²¤³ ­£¹¯ ³ ·ÊÅ n¯¤m»Å ¥² ´¥ ³ ¸  ¶ ãm­§É à ·ÊÅ n ³ ³Ê©Æ ( ³Ê ¹¯ ¤³ Å n­³©¯m´ 粩 ¥¢´ ¥³ à  ¶£ ·ÊÅ nÅ °´¥q ¶¬ qÆ ¥¡q ³ º ³ )  ¥´² ² ³ Ë ²Â­É Æ n©m´

­§³ ´¥ Ï´ ´ ¯ Â Ä Ä§¤· HAMR »Â­£¹¯ m´¤ à mÅ ´ ¶ ³ ¶ ´¥ Ï ´Â Ä Ä§¤· HAMR

£´Å n ´ ¥¶ ² n¯ ¥¯¬m© ¥² ¯ ¯¹Ê È ·Ê Ï´§³ ³ ´¯¤m»Å ² ·Ë  m ¥² Ï ´¬m ì (light delivery system), ­³©Â ·¤ à thermo-magnetic, ¬m© m¯ ¥²¬´ ¥²­©m´ ­³©Â ·¤ ç² ´

³ ¸ (head-disk interface), ç²¥² Ï´ ©´£Â¤É (cooling system) ·Ê¬´£´¥ Ï´Å­n ¥¶Â©

·Ê ·¤ ¶ n¯£»§§ Æ Å ¬¹Ê¯ ³ ¸ £·¯º ­¢»£¶§ § ¯¤m´ ¥© ¥ɩ (¢´¤Å 1 ´Ä ©¶ ´ · [132])

Â É n [128, 135] ¯¤m´ Æ¥ É ´£ ´¥¯¯ à ¬m© ¥² ¯ m´ È Â­§m´ ·Ë  ¹Ê¯Å­n¥² £·¬£¥¥ ²

¬» ¬º ¤³ ² n¯ Ï´ ¸ ¸ ´¥­´ m´Â­£´² ·Ê¬º (optimization) Å ¢´ ¥©£ ¯ ³ Ë ¥² n©¤

8.3 ¹Ë ´ à ϴ§¯ ©¶§Â§·¤£- ¯£¬ ɯ  ¶ ©´£¥n¯ à ϴ§¯ ©¶§Â§·¤£- ¯£¬ ɯ (Williams-Comstock model) [136] Â É Ã Ï´§¯  ¶ ©¶Â ¥´²­q

·ÊÅ n¯ ¶ ´¤§³ « ²Â ´² ¯ ´¥Â §·Ê¤ ¬ ´ ²58 (transition characteristics) ·Ê ¶ ´ ´¥Â ·¤

¶ n¯£»§§ Æ ³ Â É Å ¬¹Ê¯ ³ ¸ ¯ ¥² ´¥ ³ ¸  ¶ ãm­§É à à © ¯ ¯¤m´ Æ¥ É ´£

Å · .ª. 2004 Rausch et al. [131] Æ n ϴ¬ ¯©¶ · ´¥¥©£ § ¥² ·Ê ¶ ´ ©´£¥n¯ ­¥¹¯

 ¥Â ·¤ q ¶ ©´£¥n¯ (thermal gradient)  n´Æ Å Ã Ï´§¯ ·Ë  ¹Ê¯Å n­´§³ « ²Â ´² ¯

´¥Â §·Ê¤ ¬ ´ ² ¯ ¥² HAMR à à © ¯ Ä ¤Ã Ï´§¯ Å­£m ÊÆ· n ²Â¥·¤ ©m´ “à ϴ§¯

©¶§Â§·¤£- ¯£¬ ɯ  ¶ ©´£¥n¯ (thermal Williams-Comstock model)” ¸Ê Ï´Å­n ¥´ ¸ §

¥² ¯ ´¥ Ï´Å­n¬Ê ¹¯ ³ ¸ £·¯º ­¢»£¶¬» ¸Ë ·Ê£· m¯¬¢´ § §n´ ãm­§É Hc 粬¢´ ãm­§É n´ (remanent magnetization) Mr [43, 137] Å ¬¹Ê¯ ³ ¸

57

Å ·Ê ·Ë¥² ´¥ ³ ¸  ¶ ãm­§É à ·ÊÅ n ³ ³©Ê Æ (conventional magnetic recording system) ­£´¤ ¸ ¥² ´¥

58

§³ « ²Â ´² ¯ ´¥Â §·Ê¤ ¬ ´ ² ·Ê n¯ ´¥ ¥´ ¹¯ ϴí m º ª» ¤q §´ ç² ©´£¤´© ¯ ´¥Â §·Ê¤ ¬ ´ ² ¯

³ ¸  ¶ ãm­§É à à © ¯ ­¥¹¯Ã à © ³ Ë ·ÊÅ nÅ °´¥q ¶¬ qÆ ¥¡q ³ º ³ ¬¢´ ©´£Â É Ã£m­§É ¥¶Â© ·Ê£· ´¥Â ·¤ ¶ n¯£»§§ Æ Å ¬¹Ê¯ ³ ¸

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Å ­³© n¯ ·Ë ²¯ ¶ ´¤­§³ ´¥ Ï´ ´ ¯ à ϴ§¯ ©¶§Â§·¤£- ¯£¬ ɯ  ¶ ©´£¥n¯

 ¹Ê¯Å­n n»¯m´ ¥´ ¸ §Æ m´ È ·Ê ·Ê¤© n¯ ³ ´¥ ³ ´Ã Ï´§¯ ·Ë ¸Ë £´ ¥©£ ³ Ë ¬´£´¥ Ï ´Æ

Å n Ï´§¯ ¥² (simulation)  ¹Ê¯ª¸ «´§³ « ²Â ´² n´ m´ È ¯ ¥² HAMR

8.3.1 Ä ¥Æ¡§q¯º ­¢»£¶ Å ¥² HAMR £¹Ê¯¬¹Ê¯ ³ ¸ » Ï´Å­n¥n¯ n©¤Â§Â ¯¥q ¬¢´ § §n´ ãm­§É Hc ¯ ¬¹Ê¯ ³ ¸ ²£·§³ « ² ´¥ ¥² ´¤Ã  ´¬q ·¤ (Gaussian distribution) ç² n´¬¹Ê¯ ³ ¸ Æ£m£· ´¥Â §¹Ê¯ ·Ê

¯º ­¢»£¶Å ´ ³ ¸ T(x) É ²£·§³ « ² ´¥ ¥² ´¤Ã  ´¬q ·¤  m ³ ­¥¹¯£·Ä ¥Æ¡§q ¯º ­¢»£¶ (temperature profile)  m´ ³

r2 ¬ T x Tpeak exp 2 ­­­ 300 2Tt ®­

(8.2)

£·­ m ©¤Â É Â §©¶ (K: kelvin) £¹Ê¯ Tpeak ¹¯¯º ­¢»£¶¬» ¬º ·ÊÅ n£·­ m ©¤Â É ¯ ª´Â §Â ·¤¬ (qC),

r ¹¯¥²¤² ´ ´ º ª» ¤q §´ ¯ Ä ¥Æ¡§q¯º ­¢»£¶Æ ¤³ ϴí m ·Ê¬ Å £·­ m ©¤Â É ´Ä £ ¥ (nm), Vt = FWHM / 2.35, FWHM (full width half max) ¹¯ ©´£ ©n´ ¯ Ä ¥Æ¡§q¯º ­¢»£¶

ϴí m ·Ê¯º ­¢»£¶£· m´Â É ¥¸Ê ­ ¸Ê ¯ ¯º ­¢»£¶¬» ¬º £·­ m ©¤Â É ´Ä £ ¥ [131], ç² 300 ¯¤m» Ê· º Ï´Â ¶ ϴí m (0, 0) Å ¥² ¶ ³ ´¥q ·Â ·¤ (Cartesian coordinate system) É

²Æ n©m´ r2 = x2 + z2 Ä ¤ ·Ê x ç² z ¹¯ ¶ª ´ Å Ã © ´£Ã ¥É (along-track) ç² ¶ª ´ Å Ã © ©´ à ¥É (cross-track) ´£§Ï´ ³ ³ ³ Ë ¬£ ´¥ (8.2)  ·¤ Å­£mÆ nÂ É z2 ¬ x2 ¬ T x Tpeak exp 2 ­­­ exp 2 ­­­ 300 2Tt ®­ 2Tt ®­

เทคโนโลยี HAMR

¹¯ m´¯º ­¢»£¶­n¯ £·­ m ©¤Â É Â §©¶ ¯ ´ ·Ë n´ Ï´­ Å­n º ª» ¤q §´ ¯ Ä ¥Æ¡§q¯º ­¢»£¶

(8.3)

¥» ·Ê 8.2 ì Ä ¥Æ¡§q¯º ­¢»£¶ ÊÆ· n ´ ¬£ ´¥ (8.3) ¬Ï´­¥³ Vt = 382 nm ç² Tpeak = 200 qC

¸Ê ì Å­nÂ­É ¸ §³ « ² ´¥ ¥² ´¤ ¯ ¯º ­¢»£¶ ³ Ë Å Ã © ´£Ã ¥É ç²Å à © ©´ à ¥É

8

บทที่

¯¤m´ Æ¥ É ´£ n´Æ£m ¶ ´¥ ´ ´¥ ¥² ´¤ ¯ ¯º ­¢»£¶Å à © ©´ à ¥É É ²Æ n©m´ ´¥ ¥² ´¤

¯ ¯º ­¢»£¶ ¬¹Ê¯ ³ ¸ Å Ã © ´£Ã ¥É £· m´Â m´ ³

2¬ x c ­­ ­ 300 T x Twrite exp 2Tt2 ®­­­

(8.4)

เลม 3 : การออกแบบวงจรภาครับขั้นสูง Volume III : Advanced Receiver Design

267

Temperature (K)

500 450

400 350

300 1000 500

1000 500

0 Cross-track position (nm)

0

-500

-500 -1000

-1000

Along-track position (nm)

¥» ·Ê 8.2 Ä ¥Æ¡§q¯º ­¢»£¶ ÊÆ· n ´ ¬£ ´¥ (8.3) ¬Ï´­¥³ Vt = 382 nm ç² Tpeak = 200 qC

£¹Ê¯ c ¹¯ ϴí m Å Ã © ´£Ã ¥É º ª» ¤q §´ ¯ Ä ¥Æ¡§q¯º ­¢»£¶Â£¹Ê¯Â ·¤ ³ º Ï´Â ¶

­¥¹¯ º ¯n´ ¯¶ (£·­ m ©¤Â É ´Ä £ ¥) ç² Twrite ¹¯¯º ­¢»£¶Å ² ·Ê Ï´§³  ·¤ ¶ n¯£»§§ Æ

Å ¬¹Ê¯ ³ ¸ ¸Ê ¬³£ ³ q ³ ¯º ­¢»£¶¬» ¬º ³ ·Ë

z 2 ¬­ 0 ­ Twrite Tpeak exp 2T 2 ­­ t ®

(8.5)

· º ­¢»£¶Â m´ ³ Twrite Ä ¤ ·Ê z0 ¹¯ ϴí m Å Ã © ©´ à ¥É ·Ê£¯ ­£´¤Â­ º

´¥©¶Â ¥´²­q¥² HAMR Ä ¤Å nà ϴ§¯ ©¶§Â§·¤£- ¯£¬ ɯ  ¶ ©´£¥n¯ ² Ï´

´¥Ã m à m§²Ã ¥É ¯¯ Â É ­§´¤È à ¥É ¤m¯¤ (sub-track) ­¥¹¯ ´ ¥³ Ë Â¥·¤ ©m´ “Æ£Ä ¥Ã ¥É (microtrack)” [130] ¸Ê Å ¥ · ·Ë m´ Twrite ²­£´¤ ¸ ¯º ­¢»£¶ ¯ à m§²Æ£Ä ¥Ã ¥É ·Ê£· º