Covert communication over an additive white Gaussian noise (AWGN) channel with finite block length is investigated in this paper. The attention is on the covert criterion, which has not been considered in finite block length circumstance. As an accurate quantity metric of discrimination, the variation distance with given finite block length n and signal-noise ratio (snr) is obtained. We give both its analytic solution and expansions which can be easily evaluated. It is shown that K-L distance, which is frequently adopted as the metric of discrimination at the adversary in asymptotic regime, is not convincing in finite block length regime compared with the total variation distance. Moreover, the convergence rate of the total variation with different snr is analyzed when the block length tends to infinity. The results will be very helpful for understanding the behavior of the total variation distance and practical covert communication.

翻译：本文研究了在加性高斯白噪声（AWGN）信道中，有限块长下的隐蔽通信问题。重点考察了在有限块长情形下尚未被考虑的隐蔽准则。作为判别性的精确量化指标，本文推导了给定有限块长n和信噪比下的变差距离，并给出了其解析解及易于评估的展开形式。结果表明，在渐近体制下常被用作敌手判别性指标的K-L距离，在有限块长体制下较全变差距离缺乏说服力。此外，分析了不同信噪比下全变差随块长趋于无穷时的收敛速率。这些结果将有助于理解全变差距离的行为及实际隐蔽通信。