Multi-level physical-layer network coding for Gaussian two-way relay channels

In this paper, we propose the multi-level physical-layer network coding (MPLNC) for two-way relay channels (TWRC) to optimize the relay performance. In the proposed MPLNC scheme, each source node involves multiple linear binary codes for encoding, one per modulation level. The relay node receives these streams of signals and attempts to decode superimposed network codewords at each modulation level. We first derive the constellation constrained capacity for TWRC, and then prove that MPLNC can approach the channel capacity if and only if binary code rates are properly chosen for both source nodes. Furthermore, to facilitate practical implementation MPLNC, the design criteria for the proposed MPLNC scheme is investigated, which includes the rate design rule, the decoding order design rule and the labeling strategy design rule. Also discussed is the relation between MPLNC and bit-interleaved coded modulation (BICM)-based PLNC. Our analysis and simulation results indicate that MPLNC has a significant performance advantage in comparison to the BICM-based PLNC.