A Generalized Two-Way Relay Channel with Private Information for the Relay

In the conventional two-way relay channel, two sources exchange information with help from a relay. We introduce a generalized two-way relay channel where each source additionally sends private information to the relay. For this channel, we consider a protocol that consists of a multiple- access (MA) phase and a broadcast (BC) phase and obtain achievable rate regions for both phases. The MA phase is related to computation over the multiple-access channel (MAC). We show that our scheme achieves rates that always lie within half bit of the capacity region for computation over MAC, and is capacity achieving in the BC phase. This near optimality in the MA phase can be achieved by time sharing a capacity-achieving code for the MAC and a superposition code that uses a lattice code as its component code.