The deterministic multicast capacity of 4-node relay networks

In this paper, we completely characterize the deterministic capacity region of a four-node relay network with no direct links between the nodes, where each node communicates with the three other nodes via a relay. Towards this end, we develop an upper bound on the deterministic capacity region, based on the notion of a one-sided genie. To establish achievability, we use the detour schemes that achieve the upper bound by routing specific bits via indirect paths instead of sending them directly.