A Novel Error Detection due to Joint CRC Aided Denoise-and-Forward Network Coding for Two-Way Relay Channels

In wireless two-way (TW) relay channels, denoise-and-forward (DNF) network coding (NC) is a promising technique to achieve spectral efficiency. However, unsuccessful detection at relay severely deteriorates the diversity gain, as well as end-to-end pairwise error probability (PEP). To handle this issue, a novel joint cyclic redundancy code (CRC) check method (JCRC) is proposed in this paper by exploiting the property of two NC combined CRC codewords. Firstly, the detection probability bounds of the proposed method are derived to prove its efficiency in evaluating the reliability of NC signals. On the basis of that, three JCRC aided TW DNF NC schemes are proposed, and the corresponding PEP performances are also derived. Numerical results reveal that JCRC aided TW DNF NC has similar PEP comparing with the separate CRC one, while the complexity is reduced to half. Besides, it demonstrates that the proposed schemes outperform the conventional one with log-likelihood ratio threshold