Joint Channel Estimation and Channel Decoding in Physical-Layer Network Coding Systems: An EM-BP Factor Graph Framework

This paper addresses the problem of joint channel estimation and channel decoding in physical-layer network coding (PNC) systems. In PNC, multiple users transmit to a relay simultaneously. PNC channel decoding is different from conventional multi-user channel decoding: specifically, the PNC relay aims to decode a network-coded message rather than the individual messages of the users. Although prior work has shown that PNC can significantly improve the throughput of a relay network, the improvement is predicated on the availability of accurate channel estimates. Channel estimation in PNC, however, can be particularly challenging because of 1) the overlapped signals of multiple users; 2) the correlations among data symbols induced by channel coding; and 3) time-varying channels. We combine the expectation-maximization (EM) algorithm and belief propagation (BP) algorithm on a unified factor-graph framework to tackle these challenges. In this framework, channel estimation is performed by an EM subgraph, and channel decoding is performed by a BP subgraph that models a virtual encoder matched to the target of PNC channel decoding. Iterative message passing between these two subgraphs allow the optimal solutions for both to be approached progressively. We present extensive simulation results demonstrating the superiority of our PNC receivers over other PNC receivers.