Broadcast Capacity Region of Two-Phase Bidirectional Relaying

Abstract: In a three-node network a half-duplex relay node enables bidirectional communication between two nodes with a spectral efficient two phase protocol. In the first phase, two nodes transmit their message to the relay node, which decodes the messages and broadcast a re-encoded composition in the second phase. In this work we determine the capacity region of the broadcast phase. In this scenario each receiving node has perfect information about the message that is intended for the other node. The resulting set of achievable rates of the two-phase bidirectional relaying includes the region which can be achieved by applying XOR on the decoded messages at the relay node. We also prove the strong converse for the maximum error probability and show that this implies that the $[\eps_1,\eps_2]$-capacity region defined with respect to the average error probability is constant for small values of error parameters $\eps_1$, $\eps_2$.