An Optimal Decoding Strategy for Physical-layer Network Coding over Multipath Fading Channels

We present an optimal decoder for physical-layer network coding (PNC) in a multipath fading channels. Previous studies on PNC have largely focused on the single path case. For PNC, multipath not only introduces inter-symbol interference (ISI), but also cross-symbol interference (Cross-SI) between signals simultaneously transmitted by multiple users. In this paper, we assume the transmitters do not have channel state information (CSI). The relay in the PNC system, however, has CSI. The relay makes use of a belief propagation (BP) algorithm to decode the multipath-distorted signals received from multiple users into a network-coded packet. We refer to our multipath decoding algorithm as MP-PNC. Our simulation results show that, benchmarked against synchronous PNC over a one-path channel, the bit error rate (BER) performance penalty of MP-PNC under a two-tap ITU channel model can be kept within 0.5dB. Moreover, it outperforms a MUD-XOR algorithm by 3dB -- MUD-XOR decodes the individual information from both users explicitly before performing the XOR network-coding mapping. Although the framework of fading-channel PNC presented in this paper is demonstrated based on two-path and three-path channel models, our algorithm can be easily extended to cases with more than three paths.