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In this paper, a multi-source multi-relay cooperative wireless network withbinary modulation and binary network coding is studied. The system modelencompasses: i) a demodulate-and-forward protocol at the relays, where thereceived packets are forwarded regardless of their reliability; and ii) amaximum-likelihood optimum demodulator at the destination, which accounts forpossible demodulations errors at the relays. An asymptotically-tight andclosed-form expression of the end-to-end error probability is derived, whichclearly showcases diversity order and coding gain of each source. Unlike otherpapers available in the literature, the proposed framework has three maindistinguishable features: i) it is useful for general network topologies andarbitrary binary encoding vectors; ii) it shows how network code and two-hopforwarding protocol affect diversity order and coding gain; and ii) it accountsfor realistic fading channels and demodulation errors at the relays. Theframework provides three main conclusions: i) each source achieves a diversityorder equal to the separation vector of the network code; ii) the coding gainof each source decreases with the number of mixed packets at the relays; andiii) if the destination cannot take into account demodulation errors at therelays, it loses approximately half of the diversity order.

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