Low Complexity Majority-Logic Decoding for LDPC-Coded PNC Systems

In this letter, we propose majority-logic decoding (MLGD) algorithms of low complexity for low-density parity-check (LDPC) coded physical-layer network coding (PNC) in a two-way relay channel (TWRC). In particular, we decode the transmit combination of two-user messages from the superimposed signal and then map the XOR message of two users. By exploiting the superposition rules of PNC, we develop hard decision-based and reliability-based decoding algorithms, i.e., modified one-step MLGD (M-OSMLGD) and iterative soft reliability-based decoding (M-ISRB), to iteratively update the combination of two-user messages. Moreover, we propose an improved M-ISRB (IM-ISRB) decoding to update the external reliability of the combination of two-user messages in each iteration. Simulation results show that the proposed decoding algorithms can achieve effective an trade-off between complexity and decoding performance for LDPC-coded PNC systems.