Joint Relay Selection and Network Coding for Error-Prone Two-Way Decode-and-Forward Relay Networks

In a two-way relay network (TWRN), the optimal joint relay selection (RS) and network coding (NC) (O-RS-NC) scheme, which searches all the relay combinations to select a best relay subset, requires high computational complexity and significant amount of feedback. To address this issue, two joint RS and NC (RS-NC) schemes, referred to as a joint single RS and NC (S-RS-NC) and a joint dual RS and NC (D-RS-NC), are proposed based on decode-and-forward (DF) protocol for error-prone TWRNs. Specifically, for the S-RS-NC scheme, a single relay is selected to minimize the sum bit error rate (BER) of the TWRN. The S-RS-NC scheme is simple to implement, but it suffers from a relatively large signal-to-noise ratio (SNR) loss compared to the O-RS-NC scheme. To reduce the SNR loss, a D-RS-NC scheme is proposed. In the D-RS-NC scheme, one or two relays are selected to minimize the sum BER of the network. Because the source and relay transmission powers (E_S and E_R) have different impacts on the equivalent SNR of the TWRN, the RS criterion is designed based on different ratios of E_S and E_R. BER lower-bounds for these schemes are derived and verified by simulations to be tight asymptotically. Both analytical and simulation results show that the proposed RS-NC schemes are superior to the conventional RS without NC scheme when 2E_S>E_R. In most practical applications, for example, a wireless sensor network, all the nodes transmit at the same power, where the proposed RS-NC schemes perform better than the conventional RS without NC scheme.