Multilevel coded linear physical-layer network coding with extended mapping in Galois Field for Rayleigh fading two-way relay channels

In this paper, we propose a novel multilevel coded linear physical-layer network coding scheme with extended mapping (LPNC-EM) for Rayleigh fading two-way relay channels (TWRC). The relay node adaptively selects the linear generator matrix and directly maps the superimposed signal of the two users into the linear network coded combination over the hybrid Galois Field (GF(2²) or GF(2³)). The selection criterion ensures unambiguous decoding and maximizes the individual rate of each user. The LPNC-EM scheme forms two or three independent coding levels which facilitate the use of multilevel coding. This enables the hierarchical decode-and-forward paradigm as in [3]. The numerical results show that uncoded LPNC-EM outperforms the original physical-layer network coding (PNC) and can achieve a error performance as good as the 5QAM denoise-and-forward in [2]. Furthermore, the multilevel coded LPNC-EM also provides a superior error performance compared with the coded original PNC.