Analysis of PAM Mapping for Convolutional-Coded Physical-Layer Network Coding

In this letter, we investigate iterative decoding for convolutional-coded physical-layer network coding operated with bit-interleaved coded modulation (BICM-PNC) over two-way relay channel (TWRC). The superimposed constellation at the relay from two users may not remain the same characteristic as the original modulation at the users. Thus, we first propose a design of mapping for PAM modulations at the users and enable the superimposed constellation of the maximum squared Euclidean weight (MSEW). Then, we analyze the PNC mappings by means of an extrinsic information transfer (EXIT) chart. The analysis and simulation results show that the proposed mapping can provide a good match to a given outer channel code. In particular, it achieves much better error performance than the conventional semi-Gray and binary-bit mappings at high SNR region for both 8-PAM and 16-PAM modulations.