  We study a fading linear finite-field relay network having multiple
source-destination pairs. Because of the interference created by different
unicast sessions, the problem of finding its capacity region is in general
difficult. We observe that, since channels are time-varying, relays can deliver
their received signals by waiting for appropriate channel realizations such
that the destinations can decode their messages without interference. We
propose a block Markov encoding and relaying scheme that exploits such channel
variations. By deriving a general cut-set upper bound and an achievable rate
region, we characterize the sum capacity for some classes of channel
distributions and network topologies. For example, when the channels are
uniformly distributed, the sum capacity is given by the minimum average rank of
the channel matrices constructed by all cuts that separate the entire sources
and destinations. We also describe other cases where the capacity is
characterized.
