First and Second Order Asymptotics in Covert Communication

Abstract

We study the first- and second-order asymptotics of covert communication over binary-input DMC for three different covertness metrics and under maximum probability of error constraint. When covertness is measured in terms of the relative entropy between the channel output distributions induced with and without communication, we characterize the exact first- and second-order asymptotics of the number of bits that can be reliably transmitted with a maximum 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 bound the second-order asymptotics. PPM achieves the optimal first-order asymptotics for all three metrics, as well as the optimal second-order asymptotics for relative entropy. The main conceptual contribution of this paper is to clarify how the choice of a covertness metric impacts the information-theoretic limits of covert communications. The main technical contribution underlying our results is a detailed expurgation argument to show the existence of a code satisfying the reliability and covertness criteria.

References in corpus (1)

• Strong Converse for a Degraded Wiretap Channel via Active Hypothesis Testing

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• Bounds on Covert Capacity with Sub-Exponential Random Slot Selection
• Total Variation Distance Based Performance Analysis of Covert Communication over AWGN Channels in Non-asymptotic Regime
• Fundamental Limits of Covert Bit Insertion in Packets
• Covert Communication over Adversarially Jammed Channels
• Covert Identification over Binary-Input Discrete Memoryless Channels
• Stealthy Communication over Adversarially Jammed Multipath Networks
• Undetectable Radios: Covert Communication under Spectral Mask Constraints