It is well known that finite blocklength analysis plays an important role in evaluating performances of communication systems in practical settings. This paper considers the achievability and converse bounds on the maximal channel coding rate (throughput) at a given blocklength and error probability in covert communication over AWGN channels. The covert constraint is given in terms of an upper bound on total variation distance (TVD) between the distributions of eavesdropped signals at an adversary with and without presence of active and legitimate communication, respectively. For the achievability, Gaussian random coding scheme is adopted for convenience in the analysis of TVD. The classical results of finite blocklength regime are not applicable in this case. By exploiting and extending canonical approaches, we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. The general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. We further show an interesting connection between attaining tight achievability and converse bounds and solving two total variation distance based minimax and maxmin problems. The TVD constraint is analyzed under the given random coding scheme, which induces bounds on the transmission power through divergence inequalities. Further comparison is made between the new achievability bounds and existing ones derived under deterministic codebooks. Our thorough analysis thus leads us to a comprehensive characterization of the attainable throughput in covert communication over AWGN channels.

中文翻译：

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隐蔽约束下AWGN信道高斯随机编码的有限块长度分析


众所周知，有限块长度分析在评估实际环境中通信系统的性能方面发挥着重要作用。本文考虑了 AWGN 信道上隐蔽通信中给定块长度和错误概率下最大信道编码率（吞吐量）的可实现性和逆界。隐蔽约束是根据对手处窃听信号的分布之间的总变化距离（TVD）的上限给出的，分别存在和不存在主动和合法通信。考虑到可实现性，为了方便TVD的分析，采用高斯随机编码方案。有限块长度机制的经典结果不适用于这种情况。通过利用和扩展规范方法，我们首先在最大或平均错误概率要求下为随机编码方案提出新的、更通用的可实现性界限。然后将一般界限应用于 AWGN 信道中的隐蔽通信，其中码字是根据高斯分布生成的，同时满足最大功率约束。我们进一步展示了获得严格可实现性和逆边界与解决两个基于总变分距离的极小极大和极大极小问题之间的有趣联系。在给定的随机编码方案下分析了 TVD 约束，该方案通过发散不等式引入了传输功率的界限。在新的可实现性界限和确定性密码本下导出的现有可实现性界限之间进行了进一步的比较。因此，我们的全面分析使我们能够全面表征 AWGN 信道上的隐蔽通信中可达到的吞吐量。