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

TL;DR

This paper develops a numerical method to compute the secrecy capacity and optimal input distribution for a scalar Gaussian wiretap channel with a peak amplitude constraint, advancing understanding of secure communication under amplitude limits.

Contribution

It introduces a numerical procedure combining gradient ascent and Blahut-Arimoto algorithms to determine the secrecy capacity and optimal distributions under peak constraints.

Findings

Numerical computation of secrecy capacity under peak amplitude constraints.

Characterization of the optimal input distribution structure.

Enhanced understanding of secure communication limits with amplitude restrictions.

Abstract

This paper studies a scalar Gaussian wiretap channel where instead of an average input power constraint, we consider a peak amplitude constraint on the input. The goal is to obtain insights into the secrecy-capacity and the structure of the secrecy-capacity-achieving distribution. Capitalizing on the recent theoretical progress on the structure of the secrecy-capacity-achieving distribution, this paper develops a numerical procedure, based on the gradient ascent algorithm and a version of the Blahut-Arimoto algorithm, for computing the secrecy-capacity and the secrecy-capacity-achieving input and output distributions.