Scalar Gaussian Wiretap Channel: Properties of 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 $\frac{\mathsf{A}}{{\sigma }_1^2}$ where $\mathsf{A}$ is the amplitude constraint and ${\sigma }_1^2$ is the variance of the Gaussian noise over the legitimate channel.

This is an extended version of a paper accepted to 2021 IEEE Information Theory Workshop (ITW)

References in corpus (1)

• The Degraded Discrete-Time Poisson Wiretap Channel

Cited by in corpus (1)

• Scalar Gaussian Wiretap Channel with Peak Amplitude Constraint: Numerical Computation of the Optimal Input Distribution