Design of Low-Density Parity-Check Codes for Half-Duplex Three-Phase Two-Way Relay Channels

In two-way relay channels, two terminal nodes exchange information with the help of a relay node. Designing practical coding schemes for such channels is challenging, especially when messages are encoded into multiple streams and a destination node receives signals from multiple nodes. In this paper, we prove an achievable region for half-duplex three-phase two-way relay channels. Furthermore, we propose low-density parity-check (LDPC) codes for such channels where two source codewords are encoded by systematic LDPC codes at the relay node. To analyze the performance of the codes, discretized density evolution is derived for the joint decoder at terminal nodes. Based on the discretized density evolution, degree distributions are optimized by iterative linear programming in 3 steps. The length of the obtained optimized codes is 26% longer than the theoretic one.