Second-Order Asymptotics in Covert Communication.

We study the second-order asymptotics of covert communication over binary-input DMC for three different metrics of covertness. When covertness is measured in terms of the relative entropy between the channel output distributions induced with and without communication, we characterize the exact second-order asymptotics of the number of bits that can be reliably transmitted with a probability of error less than $\epsilon$ and a relative entropy less than $\delta$. When covertness is measured in terms of the variational distance between the channel output distributions or in terms of the probability of missed detection for fixed probability of false alarm, we establish the exact first-order asymptotics and bounds on the second-order asymptotics. The main conceptual contribution of this paper is to clarify how the choice of a covertness metric impacts the information-theoretic limits of the number of covert and reliable bits. The main technical contribution of the underlying results is a detailed analysis of probability of existence of a code satisfying the reliability and covert criteria.