Achievable Rate Region of a Two Phase Bidirectional Relay Channel

In this work, the capacity region of the broadcast channel in a two phase bidirectional relay communication scenario is proved. Thereby, each receiving node has perfect knowledge about the message intended for the other node. The capacity region can be achieved using an auxiliary random variable taking two values, i.e., by the principle of time-sharing. The resulting achievable rate region of the two-phase bidirectional relaying includes the region which can be achieved by network coding applying XOR on the decoded messages at the relay node.