The secrecy capacity of the semi-deterministic broadcast channel

In this paper, we study secure communications over a two-user semi-deterministic broadcast channel, i.e., one of the receivers is connected to the transmitter through a deterministic channel. We consider the case where the deterministic receiver is also the eavesdropper for the other receiver´s message. We derive the secrecy capacity region by showing that superposition encoding plus Gel´fand-Pinsker encoding is optimal. We find that due to the deterministic component of the channel, Gel´fand-Pinsker binning alone is enough to achieve perfect secrecy. We also compare our scheme with the capacity-achieving scheme of Marton for the semi-deterministic broadcast channel where there is no secrecy constraint.