Bit Mapping Design for LDPC Coded BICM Schemes with Binary Physical-layer Network Coding

We propose a new low-density parity-check (LDPC) coded binary physical-layer network coding (PNC) scheme for Gaussian two-way relay channels. In this scheme, we introduce a bit mapper between the LDPC encoder and the modulator, which considers the unequal error protections brought by the high order PSK modulations. We add a new bipartite sub-channel graph consisting of sub-channels and variable nodes (VNs) to the Tanner graph and propose a progressive edge growth (PEG) algorithm to design the bit mapper. The design paradigm is to search for the bit mapping distribution with the lowest decoding threshold by using the extrinsic information transfer (EXIT) chart, and then establish the edges progressively between VNs and sub-channels according to the distribution. The proposed PEG algorithm is employed to design the bit mappers of the schemes with 8-PSK, 16-PSK, 64-PSK and 256-PSK. Simulation results show that the proposed schemes can considerably improve the bit error performance of the PNC XOR messages, compared to the schemes without bit mappers.