  Although BICM can significantly improves the BER performance by iteration
processing between the demapping and the decoding in a traditional receiver,
its design and performance in PNC system has fewer studied. This paper
investigates a bit interleaved coded modulation (BICM) scheme in a Gaussian
two-way relay channel operated with physical layer network coding (PNC). In
particular, we first present an iterative demapping and decoding framework
specially designed for PNC. After that, we compare different constellation
mapping schemes in this framework, with the convergence analysis by using the
EXIT chart. It is found that the anti-Gray mapping outperforms the Gray
mapping, which is the best mapping in the traditional decoding schemes.
Finally, the numerical simulation shows the better performance of our framework
and verifies the mapping design.
