In order to improve the performance of long-distance communication and fulfill the requirement of wireless-power line two-way relay hybrid system, a physical layer network coding algorithm based on the BP decoding and the threshold approximation of relay probability density function is proposed in this paper. By analyzing the probability density distribution of the relay signals,the initial logarithm likelihood ratio formulas of relay coding signals are deduced after physical layer network coding,
and the BP decoding is carried out. Then the multidimensional
signal is simplified by using the threshold method. The simulation results have verified the validity and reliability of the proposed algorithm as an optimized power distribution factor. Under the premise of decreasing complexity, the proposed algorithm can effectively ensure the performance requirements of wireless-power line two-way relay hybrid system.