Optimal Inputs for Some Classes of Degraded Wiretap Channels

In this paper, an analysis of an input distribution that achieves the secrecy capacity of a general degraded additive noise wiretap channel is presented. In particular, using convex optimization methods, an input distribution that achieves the secrecy capacity is characterized by conditions expressed in terms of integral equations. The new conditions are used to study the structure of the optimal input distribution for three different additive noise cases: vector Gaussian; scalar Cauchy; and scalar exponential.