Fundamental Limits of Communication with Low Probability of Detection

TL;DR

This paper investigates the fundamental limits of covert communication over DMC and AWGN channels, establishing that the maximum information transmitted scales with the square root of blocklength under low detectability constraints.

Contribution

It derives the square root scaling law and exact constants for covert communication limits over DMC and AWGN channels, extending understanding of low-probability detection constraints.

Findings

Maximum information scales as the square root of blocklength.

Exact expressions for the scaling constants are provided.

Results apply to both DMC and AWGN channels.

Abstract

This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. Specifically, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the "off" input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.