Covert Communication over Noisy Channels: A Resolvability Perspective

TL;DR

This paper introduces a channel resolvability-based coding scheme enabling covert communication over noisy channels, achieving improved key size requirements and extending results to Gaussian channels.

Contribution

It generalizes covert communication schemes using channel resolvability, reducing key size from log n to sqrt n, and extends results to Gaussian channels with no secret key needed when the receiver's channel is better.

Findings

Achieves covert communication with sqrt(n) bits using sqrt(n) key bits.

Allows covert communication without secret key if receiver's channel is better.

Extends covert communication results to Gaussian channels.

Abstract

We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals through another discrete memoryless channel. We develop a coding scheme based on the principle of channel resolvability, which generalizes and extends prior work in several directions. First, it shows that, irrespective of the quality of the channels, it is possible to communicate on the order of $\sqrt{n}$ reliable and covert bits over $n$ channel uses if the transmitter and the receiver share on the order of $\sqrt{n}$ key bits; this improves upon earlier results requiring on the order of $\sqrt{n}\log n$ key bits. Second, it proves that, if the receiver's channel is "better" than the warden's channel in a sense that we make precise, it is possible to communicate on the order of $\sqrt{n}$ reliable and covert bits over $n$ channel uses without a secret key; this generalizes earlier results established for binary symmetric channels. We also identify the fundamental limits of covert and secret communications in terms of the optimal asymptotic scaling of the message size and key size, and we extend the analysis to Gaussian channels. The main technical problem that we address is how to develop concentration inequalities for "low-weight" sequences; the crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities.