In this paper, we study network-coded cooperative diversity (NCCD) systems comprising multiple sources, one relay, and one destination, where the relay detects the packets received from all sources and performs Galois field network coding before forwarding a single packet to the destination. We develop a simple generalized cooperative maximum-ratio combining scheme for the destination which achieves a similar performance as optimal maximum-likelihood combining. Furthermore, assuming independent Rayleigh fading for all links of the network, we provide a mathematical framework for the analysis of the error performance of NCCD systems in the high signal-to-noise ratio regime. Based on this framework, we derive simple and elegant closed-form expressions for the asymptotic symbol and bit error rates of NCCD systems. The derived error rate expressions are valid for arbitrary numbers of sources, arbitrary modulation schemes, and arbitrary constellation mappings and provide significant insight into the impact of various system and channel parameters on performance. These expressions can also be exploited for optimization of the constellation mapping as well as for formulation of various NCCD system optimization problems including optimal power allocation, relay selection, and relay placement. Simulation results confirm the accuracy of the presented analysis and reveal that the performance of NCCD systems can be considerably improved by optimizing the constellation mapping and the power allocation based on the developed analytical results.

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