Scalar Gaussian Wiretap Channel: Bounds on the Support Size of the Secrecy-Capacity-Achieving Distribution

Abstract

This work studies the secrecy-capacity of a scalar-Gaussian wiretap channel with an amplitude constraint on the input. It is known that for this channel, the secrecy-capacity-achieving distribution is discrete with finitely many points. This work improves such result by showing an upper bound of the order $\frac{A^{2}}{\sigma_{1}^{2}}$ where A is the amplitude constraint and $\sigma_{1}^{2}$ is the variance of the Gaussian noise over the legitimate channel.