Lattice Coding and Decoding for Multiple Multiple-Antenna Antenna Ergodic Fading Channels
Abstract: For ergodic fading, a lattice coding and decoding strategy is proposed and its performance is analyzed for the single single-input single-output output (SISO) and multiplemultiple input multiple-output output (MIMO) point point-to-point point channel as well as the multiplemultiple access channel (MAC), with channe channell state information available only at the receiver (CSIR). At the decoder a novel strategy is proposed consisting of a timetime varying equalization matrix followed by decision regions that depend only on channel statistics, not individual realizations. Our en encoder coder has a similar structure to that of Erez and Zamir. For the SISO channel, the gap to capacity is bounded by a constant under a wide range of fading distributions. For the MIMO channel under Rayleigh fading, the rate achieved is within a gap to capacit capacityy that does not depend on the signal-to-noise noise ratio (SNR), and diminishes with the number of receive antennas. The analysis is extended to the K -user user MAC where similar results hold. Achieving a small gap to capacity while limiting the use of CSIR to the equalizer qualizer highlights the scope for efficient decoder implementations, since decision regions are fixed, i.e., independent of channel realizations.