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The document discusses a channel assignment algorithm for throughput optimization in multi-radio wireless mesh networks using network coding. It formulates the joint problem of random network coding, channel assignment, and broadcast link scheduling while taking into account opportunistic overhearing, interference constraints, coding constraints, number of channels, radios per node, and fairness between unicast connections. An auction-based suboptimal solution is developed for overall network throughput optimization. Evaluation shows the algorithm can effectively use multiple radios and channels and handle fairness issues from auctions, with promising gains over traditional routing solutions