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：本文研究了加性高斯白噪声信道中有限码长下的隐密通信。关注点在尚未被有限码长情形考量的隐密准则。作为一种精确的区分度量，本文得到了给定有限码长n和信噪比下的变差距离。我们给出了其解析解及易于计算的展开形式。研究表明，在渐进场景下常被用作对抗方区分度量的K-L距离，在有限码长情形下相对于总变差距离缺乏说服力。此外，分析了当码长趋于无穷时不同信噪比下总变差的收敛速度。这些结果对于理解总变差距离的行为及实际隐密通信具有重要参考价值。