Network-coded SIR-based relay selection for multiple-relay TWRC

This paper considers a two-way relay channel (TWRC) that operates in a multiple-relay context with network-coded soft information relaying. During the relaying process, the log likelihood ratio sequence resulting from the network coding of the two soft-in soft-out decoders output sequences is supplied to a soft encoder. In order to mitigate the error-propagation due to the erroneous decoding at the relay, a method is proposed for modelling the soft estimated symbols at the output of the soft encoder which is mathematically convenient to work with. The signal-to-noise ratios of the equivalent one-hop channels towards each end-node are derived. Accordingly, the study proposes two relay selection (RS) schemes based on the network-coded soft information relaying, a sub-optimal Max-Min-based single RS scheme, and a double-side RS scheme. Closed-form expressions for the bit error rate performances and asymptotic pairwise error probabilities of the multiple-relay TWRC with the proposed RS schemes are derived. Monte-Carlo simulations are carried out to verify the accuracy of the analytical results.