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We study a fading linear finite-field relay network having multiplesource-destination pairs. Because of the interference created by differentunicast sessions, the problem of finding its capacity region is in generaldifficult. We observe that, since channels are time-varying, relays can delivertheir received signals by waiting for appropriate channel realizations suchthat the destinations can decode their messages without interference. Wepropose a block Markov encoding and relaying scheme that exploits such channelvariations. By deriving a general cut-set upper bound and an achievable rateregion, we characterize the sum capacity for some classes of channeldistributions and network topologies. For example, when the channels areuniformly distributed, the sum capacity is given by the minimum average rank ofthe channel matrices constructed by all cuts that separate the entire sourcesand destinations. We also describe other cases where the capacity ischaracterized.

Sum capacity of multi-source linear finite-field relay networks with fading