Performance of Ring-TCM codes over two-way relay fading channels using linear physical-layer network coding

This paper proposes a channel coded linear physical-layer network coding (LPNC) scheme for two-way relay (TWR) fading channel, where only the relay possesses the channel state information (CSI) in the multiple access (MAC) phase. This scheme employs the spectrally efficient Ring-Trellis Coded Modulation (Ring-TCM) codes to achieve a better performance for TWR communication systems that employs LPNC. The design criterion of the Ring-TCM code for TWR fading channel is discussed. We also propose a new algorithm to find the optimal network coding coefficients to resemble the channel fading coefficients of the node-to-relay channels. The relay estimates the end nodes´ message using the maximum a posteriori (MAP) decoding algorithm based on a joint trellis. Our simulation results show that the coded LPNC scheme significantly outperforms the uncoded LPNC scheme. It can also outperform the coded scheme that employs complete decoding (CD) scheme. Our simulation results also show that the proposed scheme can approach the cut-set bound at the high signal-to-noise ratio (SNR).