On Diversity Order and Coding Gain of Multisource Multirelay Cooperative Wireless Networks With Binary Network Coding

In this paper, a multisource multirelay cooperative wireless network with binary modulation and binary network coding is studied. The system model encompasses 1) a Demodulate-and-Forward (DemF) protocol at the relays, where the received packets are forwarded, regardless of their reliability, and 2) a maximum-likelihood optimum demodulator at the destination, which accounts for possible demodulation errors at the relays. An asymptotically tight and closed-form expression of the end-to-end error probability is derived, which showcases the diversity order and coding gain of each source. Unlike other papers available in the literature, the proposed framework has three main distinguishable features: 1) It is useful for general network topologies and arbitrary binary encoding vectors; 2) it shows how network code and two-hop forwarding protocol affect diversity order and coding gain; and 3) it accounts for realistic fading channels and demodulation errors at the relays. The framework provides four main conclusions: 1) Each source achieves a diversity order equal to the separation vector of the network code; 2) the design of diversity-achieving network codes is equivalent to the design of systematic block codes over fully interleaved point-to-point links; 3) the coding gain of each source decreases with the number of mixed packets at the relays; and 4) if the destination cannot take into account demodulation errors at the relays, it loses approximately half of the diversity order. Our theoretical findings are validated through extensive Monte Carlo simulations.