Design and Analysis of Multi-Level Physical-Layer Network Coding for Gaussian Two-Way Relay Channels

In this paper, we propose a multi-level physical-layer network coding (MPLNC) scheme that optimizes the relay performance for both symmetric and asymmetric traffic in a Gaussian two-way relay channel. The proposed MPLNC scheme enables each source to employ multiple linear binary codes for encoding, one per modulation level, and the relay node to decode superimposed network codewords at each modulation level. We first derive the achievable rate for the transmission of arbitrary constellations and then prove that MPLNC with multistage decoding (MPLNC/MSD) can achieve the achievable rate if binary code rates are properly chosen for both sources. Furthermore, the design criteria for the proposed MPLNC scheme is investigated, which includes the rate design rule and the labeling strategy. Moreover, we derive the error exponent and an upper bound of the overall error probability for MPLNC. Our analysis and simulation results show that MPLNC/MSD has a significant performance advantage in comparison to the existing bit-interleaved coded modulation (BICM)-based PLNC scheme.