On the Capacity Achieving Input of Amplitude Constrained Vector Gaussian Wiretap Channel

Antonino Favano; Luca Barletta; Alex Dytso

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arXiv · 2202.00586

On the Capacity Achieving Input of Amplitude Constrained Vector Gaussian Wiretap Channel

Antonino Favano·Luca Barletta·Alex Dytso

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Abstract

This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap channel under the peak-power constraint. This work determines the largest peak-power constraint $\bar{\mathsf{R}}_n$ such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the small-amplitude regime. The asymptotic of $\bar{\mathsf{R}}_n$ as $n$ goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy-capacity is also characterized in a form amenable for computation. Furthermore, several numerical examples are provided, such as the example of the secrecy-capacity achieving distribution outside of the small amplitude regime.

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Antonino Favano, Luca Barletta, Alex Dytso. 2022-02-01. On the Capacity Achieving Input of Amplitude Constrained Vector Gaussian Wiretap Channel. https://arxiv.org/abs/2202.00586

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