Piggyback a common message on bidirectional relaying

In a three-node network, a half-duplex relay node enables bidirectional communication between two nodes with a spectral efficient two phase protocol using interference cancellation. In the first phase, both nodes transmit a message to the relay node, which decodes the messages and broadcast a composition in the second phase. In this work, we add an additionally multicast communication from the relay node to the two receiving node to the bidirectional relay communication. We characterize the total sum-rate maximum of the bidirectional and additional relay rate. Furthermore, we show how additional relay rate can be interchanged with bidirectional rate achieving the same total sum-rate. Due to the spectral efficiency of the bidirectional relaying protocol the total sum-rate behavior is dominated by the sum-rate optimal rate pair of the bidirectional broadcast phase.