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We study the capacity region of a deterministic 4-node network, where 3 nodescan only communicate via the fourth one. However, the fourth node is not merelya relay since it can exchange private messages with all other nodes. Thissituation resembles the case where a base station relays messages between usersand delivers messages between the backbone system and the users. We assume anasymmetric scenario where the channel between any two nodes is not reciprocal.First, an upper bound on the capacity region is obtained based on the notion ofsingle sided genie. Subsequently, we construct an achievable scheme thatachieves this upper bound using a superposition of broadcasting node 4 messagesand an achievable "detour" scheme for a reduced 3-user relay network.

The Deterministic Capacity of Relay Networks with Relay Private Messages