Performance analysis of distributed turbo coded scheme with two ordered best relays

In this study, the authors propose a distributed turbo coded (DTC) scheme utilising two best relays selected among multi-relays. In this scheme, the considered turbo encoder is a rate 1/3 parallel concatenated code composed of two recursive systematic convolutional codes. The systematic information sequence is transmitted directly to a destination, whereas the two parity sequences, one of which is interleaved, are transmitted through the two selected best relays. The authors derive a union bound for the frame error rate including an upper bounded closed form expression for the pairwise error probability of the DTC scheme with two ordered best relays (DTC-TBR) by utilising order of statistic, then the authors verify the analytical expression by simulations. Numerical results show that the proposed scheme outperforms the DTC scheme with a single best relay (DTC-SBR) because of the more selection gain of the DTC-TBR compared with those of DTC-SBR with the rise of number of relays.