On the deterministic multicast capacity of bidirectional relay networks

In this paper, we completely characterize the deterministic multicast capacity region of the symmetric two-pair bidirectional half duplex relay network with private messages. Towards this end, we first develop a new upper bound on the deterministic capacity region, based on the notion of a one-sided genie. We then proceed to construct novel detour schemes that achieve the upper bound by routing the bits intended for a certain receiver through the network rather than sending it directly. To the best of the authors´ knowledge, this scenario corresponds to one of the rare cases where coding, across levels and time, is needed to achieve the deterministic capacity of the network.