Capacity of a class of multi-source relay networks

We consider a relay network having K source-destination pairs. Finding the capacity region of such a network with multiple unicast sessions is in general difficult. By focusing on a special class of such networks, we show that the capacity can be found. Namely, we consider a linear finite-field channel model, which can model interference in the network. Furthermore, we assume time-varying channels. We propose a block Markov encoding and relaying scheme that exploits such channel variations. By comparing its achievable sum-rate with the general cut-set upper bound, we show the sum capacity can be characterized for a certain class of channel distributions and network topologies.