On the Secrecy Capacity of Wiretap Channels With Side Information at the Transmitter

The wiretap channel with causal/noncausal side information at the transmitter is an extension of the original wiretap channel of Wyner to the multi-user case and has been investigated by several authors. Although much effort has been made to establish the secrecy capacity, it is still elusive even if the wiretap channel is physically degraded. In this paper, for a physically degraded wiretap channel, we show a lower bound on the secrecy capacity for the causal case and an upper bound for the noncausal case. We also show that under a certain condition, the secrecy capacity for the causal case is the same as that for the noncausal case. To illustrate the usefulness of our theoretical result, we introduce the concept of a symmetric wiretap channel with state, for which the above condition is easily checked, and we give some examples in which the secrecy capacity can be computed numerically.