An efficient decoding algorithm based on orthogonal projection method for asynchronous physical-layer network coding

This paper presents an efficient decoding scheme for asynchronous physical network coding (PNC) network. The proposed scheme incorporates linear orthogonal projection method into the asynchronous PNC network to eliminate the impact of inter-symbol interference caused by imperfect synchronisation. In terms of the number of floating-point operations to decode per collided information packet at relay, the speedups of the proposed algorithm over the existed optimal belief propagation (BP) decoding algorithm is around 1.32 for BPSK and 2.68 for QPSK, respectively. Numerical simulations confirm that the proposed scheme achieves a near performance with the optimal BP decoding algorithm at a much lower complexity. Moreover, the proposed decoding method has a much better bit-error rate performance than collision resolution method which is the first method proposed to extract collided packets in the asynchronous PNC model described by this paper.