Optimal Rate Rate-Diverse Wireless Network Coding
Abstract: This paper proposes an encoding/decoding framework for achieving the optimal channel capacities of the two two-user user broadcast channel where each user (receiver) has the message targeted for the other user (receiver) as side information. Since the link qualities of the channels from the base station to the two users are different, their respective single single-user non-broadcast broadcast channel capacities are also different. A goal is to simultaneously achieve/approa achieve/approach ch the single-user single nonbroadcast channel capacities of the two users with a single broadcast transmission by applying network coding. This is referred to as the rate-diverse rate wireless network coding problem. For this problem, this paper presents a capacity-achieving achieving framework based on linear linear-structured structured nested lattice codes. The significance of the proposed framework, besides its theoretical optimality, is that it suggests a general design principle for linear rate rate-diverse diverse wireless network coding going beyond the use of lattice codes. We refer to this design principle as the principle of virtual single single-user user channels. Guided by this design principle, we propose two implementations of our encoding/decoding framework using practical linear codes amenable to decod decoding ing with affordable complexities: the first implementation is based on Low Density Lattice Codes (LDLC) and the second implementation is based on Bit Bit-interleaved interleaved Coded Modulation (BICM). These two implementations demonstrate the validity and performance ad advantage vantage of our framework.