Secret communications over semi-deterministic broadcast channels

In this paper, we investigate secret communications over a two-user semi-deterministic broadcast channel, in which user 1´s channel is deterministic, while user 2´s channel is a discrete memoryless channel. The transmitter has two independent confidential messages, each of which is intended for one of the receivers, but is kept completely secret from the other. We first establish the secrecy capacity region of the semi-deterministic broadcast channel. Next, as a special case, we consider both channels are deterministic and compare the secrecy capacity region with the well-known general capacity region of the deterministic broadcast channel without secrecy constraint. Our result illustrates the fundamental loss of the transmission rates due to keeping the messages secret as well as the tradeoff between the communication rate and the perfect secrecy requirement.