Feedback enlarges capacity region of two-way relay channel

We consider a two-way relay channel (TRC) in which two terminals exchange messages with the help of a relay between them. The two terminals transmit messages to the relay through the Multiple Access Channel (MAC) and the relay transmits messages to the two terminals through the Broadcast Channel (BC). We assume that the MAC and the BC do not interfere with each other, and each terminal receives signals only from the relay but not the other terminal. All the nodes are assumed to be full-duplex, which means that they can transmit and receive information at the same time. The TRC is said to be without feedback if each terminal node cannot use its previously received information for encoding its message. Otherwise, the TRC is said to be with feedback. We obtain an outer bound on the capacity region of the discrete memoryless TRC without feedback and prove that the outer bound is tighter than the cut-set outer bound. In addition, we show that using feedback can enlarge the capacity region of some discrete memoryless TRC.