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.