Symbol-Level Constellation Shaping for Channel-coded Physical-layer Network Coding

In this paper, we present a system that performs joint channel coding and constellation shaping for physical-layer network coding (PNC) with quadrature amplitude modulation (QAM). Traditional bit-level PNC (based on the exclusive-OR) has been shown to be effective in increasing the system throughput, but requires a specific design of PNC mapping and shaping code when used with non-binary modulation in order to avoid ambiguity in bit-level detection. We show that PNC applied at symbol level does not present any ambiguity for QAM modulation, so that a wider range of PNC mapping and shaping code designs are possible. Furthermore, we show that the symbol-level PNC approach ensures a shaped signal transmission in both communication phases even with a simple denoising operation at the relay. The simplicity of this denoising operation also facilitates an achievable rate analysis, which is used in the design of shaping codes. Simulation results demonstrate that for end-to-end communication in a PNC system with 16-QAM, the proposed approach achieves a shaping gain of 0.75 dB at a bit error rate of 10-4 with a low-complexity (4, 2) shaping block code.