Joint Channel-Network Decoding for Asynchronous Physical-Layer Network Coding

Symbol asynchrony is an important issue in practical implementation of physical-layer network coding (PNC). In this paper, we investigate the asynchronous convolutionally coded PNC over the two-way relay network (TWRN). Symbols from two users arrive at the relay with symbol misalignment. A joint channel-network decoder (JCND) for the relay is proposed. A salient feature for the proposed JCND is that it incorporates the code structure and the symbol misalignment jointly, and the cyclic structure for the channel code is not required to combat the integer symbol misalignment. Furthermore, we derive the bit error rate (BER) bound at the relay utilizing the error state diagram. Simulation results indicate that the performance of the proposed algorithm matches well with the bound.