Diversity and Coding Gain of Multi-Source Multi-Relay Cooperative Wireless Networks with Binary Network Coding

In this paper, a multi–source multi–relay cooperative wireless network with binary network coding is studied. The system model encompasses: i) a demodulate–and–forward protocol at the relays, where the received packets are forwarded regardless of their reliability; and ii) a maximum–likelihood optimum decoder at the destination, which accounts for possible decoding errors at the relays. An asymptotically– tight and closed–form expression of the end-to-end error probability is derived, which clearly showcases diversity and coding gain of each source. Unlike other papers available in the literature, the proposed framework has three main distinguishable features: i) it is useful for general network topologies and arbitrary binary encoding vectors; ii) it shows how network code and two–hop forwarding protocol affect diversity and coding gain; and ii) it accounts for realistic fading channels and decoding errors at the relays. The framework provides three main conclusions: i) each source achieves a diversity order equal to the separation vector of the network code; ii) the coding gain of each source decreases with the number of mixed packets at the relays; and iii) if the destination cannot take into account decoding errors at the relays, it loses approximately half of the diversity order.