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.
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