发表机构
Shanghai AI Laboratory; Shanghai Innovation Institute; Southern University of Science and Technology; Institute of Artificial Intelligence (TeleAI) of China Telecom（上海人工智能实验室; 上海创新研究院; 南方科技大学; 中国电信人工智能研究院（TeleAI））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对二元输入离散无记忆信道，通过精细分析脉冲位置调制下看守者输出的分布，将隐蔽通信二阶渐近性的近似误差从O(n^{-1/4})降至O(n^{-1/2})，从而确立精确的二阶渐近性。
AI 中文摘要
我们确定了当隐蔽性以变分距离度量时，二元输入离散无记忆信道上隐蔽通信的精确二阶渐近性。Tahmasbi和Bloch先前的工作[IEEE Trans. Inf. Theory, 2019年4月]刻画了一阶渐近性，并推导了二阶项的可达性和逆界，但这些界并不匹配。这一差距源于可达性界中一个阶为\(n^{1/4}\)的额外惩罚。我们证明，通过对脉冲位置调制所引发的看守者输出分布进行更精细的分析，可以消除这一惩罚。具体而言，我们通过两个分布的Bhattacharyya系数以及对数似然比的连续函数的期望来表达变分距离。由于所得的期望涉及连续函数而非似然比事件的概率，特征函数分析与高斯平滑论证相结合，将近似误差从\(O(n^{-1/4})\)（由先前工作中的Berry-Esseen界得出）降低到\(O(n^{-1/2})\)。凭借这一更好控制的近似误差，我们成功推导出与现有逆界匹配的可达性结果，从而确立了精确的二阶渐近性。
英文摘要
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.
