Exact Second-Order Asymptotics in Covert Communication Over Discrete Memoryless Channels

2026-09-21

AI Summary

本文解决了二进制离散无记忆信道中隐蔽通信的精确二阶渐近性问题，通过改进脉冲位置调制分析方法，消除了前人研究中的(n^{1/4})误差惩罚。

Abstract

We determine the exact second-order asymptotics of covert communication over binary-input discrete memoryless channels when covertness is measured by variational distance. Previous work by Tahmasbi and Bloch [IEEE Trans. Inf. Theory, Apr. 2019] characterized the first-order asymptotics and derived achievability and converse bounds on the second-order term, but these bounds do not match. The gap arises from an additional penalty of order \(n^{1/4}\) in the achievability bound. We show that this penalty can be removed through a sharper analysis of the distribution of the warden's output induced by pulse-position modulation. Specifically, we express the variational distance through the Bhattacharyya coefficient of two distributions and the expectation of a continuous function of the log-likelihood ratio. Because the resulting expectation involves a continuous function rather than the probability of a likelihood-ratio event, an analysis of the characteristic function combined with a Gaussian smoothing argument reduces the approximation error from \(O(n^{-1/4})\) (derived from the Berry--Esseen bound in prior work) to \(O(n^{-1/2})\). With this better controlled approximation error, we manage to derive a matching achievability result to the existing converse result, thus establishing the exact second-order asymptotics.

Problem

• covert communication
• discrete memoryless channels
• second-order asymptotics
• variational distance

Innovation

• second-order asymptotics
• covert communication
• variational distance
• Bhattacharyya coefficient
• Gaussian smoothing