Non-linear network coding in two-way relaying discrete channels

In this paper, we present optimal network coding which can maximize achievable rate region in two-way relaying discrete channels, where there are two communicating nodes and one relaying node. We focus on a low-complexity relaying protocol termed the detect-and-forward (DtF) scheme, in which the relaying node does not require channel decoding but detection. We first analyze the achievable rate region of any digital network coding function including non-linear types. We then search for the optimal network code in favor of maximizing two kinds of performance measures: the sum rate and the product rate. For high SNR regimes, linear network codes like the exclusive-or (XOR) function can offer the maximum-achievable rate region. Whereas, for low SNR regimes, it is verified that non-linear network codes like the negate-or (NOR) function can outperform linear codes due to the effect of error occurrence at the intermediate relaying node.