The Design of Protograph LDPC Codes for Channel-Coded Physical-layer Network Coding

For two-way relay channel-coded physical network coding (CPNC) systems with sufficiently low code rate, the separate complete decoding (SCD) scheme outperforms the joint channel-physical network coding (JCNC) scheme. Hence, this paper addresses the design of protograph LDPC codes to approach the SCD-based CPNC capacity. In fact, due to virtual erasures induced by CPNC transmission, the conventional protograph that approaches point to point (P2P) AWGN capacity may not perform well in SCD-based CPNC channel in terms of error rates. We then use the finite-length EXIT chart to calculate iterative decoding threshold of a joint code graph formed by two codes in the SCD. Furthermore, we investigate the serial separate complete decoding (S-SCD) and parallel separate decoding (PSCD). Simulation results show that with the S-SCD, the proposed protograph codes have within 0.9 dB of their capacity limits for rates from 1/3 to 3/5.