Limits of low-probability-of-detection communication over a discrete memoryless channel

This paper considers the problem of communication over a discrete memoryless 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 channel whose output distribution induced by the zero input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum number of bits that can be transmitted under this criterion scales like the square root of the blocklength. Exact expressions for the scaling constant are also derived.