On the Diversity of Network-Coded Cooperation With Decode-and-Forward Relay Selection

In this paper, we study outage probability (OP) and diversity order of a M-source and N-relay wireless network that combines network coding (NC) and relay selection (RS). More specifically, a decode-and-forward (DF) relaying protocol is considered and the network-encoding vectors at the relays are assumed to constitute a maximum distance separable (MDS) code. Single relay selection (SRS) and multiple relay selection (MRS) protocols are investigated, where the best relay and the L best relays forward the network-coded packets to the destination, respectively. An accurate mathematical framework for computing the OP is provided and from its direct inspection the following conclusions on the achievable diversity are drawn: 1) the SRS protocol achieves diversity order equal to two regardless of M and N and 2) the MRS protocol achieves diversity order equal to L + 1 if L < M and equal to N + 1 if L >= M. These analytical findings are substantiated with the aid of Monte Carlo simulations, which also show that RS provides a better OP than NC based on repetition coding if L >= M.