This paper investigates the asymptotics of the maximal throughput of communication over AWGN channels by $n$ channel uses under a covert constraint in terms of an upper bound $δ$ of Kullback-Leibler divergence (KL divergence). It is shown that the first and second order asymptotics of the maximal throughput are $\sqrt{nδ\log e}$ and $(2)^{1/2}(nδ)^{1/4}(\log e)^{3/4}\cdot Q^{-1}(ε)$, respectively. The technique we use in the achievability is quasi-$\varepsilon$-neighborhood notion from information geometry. For finite blocklength $n$, the generating distributions are chosen to be a family of truncated Gaussian distributions with decreasing variances. The law of decreasing is carefully designed so that it maximizes the throughput at the main channel in the asymptotic sense under the condition that the output distributions satisfy the covert constraint. For the converse, the optimality of Gaussian distribution for minimizing KL divergence under the second order moment constraint is extended from dimension $1$ to dimension $n$. Based on that, we establish an upper bound on the average power of the code to satisfy the covert constraint, which further leads to the direct converse bound in terms of covert metric.

翻译：本文研究了在隐蔽约束下，通过n次信道使用在AWGN信道上进行通信的最大吞吐量的渐近性，该隐蔽约束以Kullback-Leibler散度（KL散度）的上界δ表示。研究表明，最大吞吐量的一阶和二阶渐近性分别为$\sqrt{nδ\log e}$和$(2)^{1/2}(nδ)^{1/4}(\log e)^{3/4}\cdot Q^{-1}(ε)$。我们在可达性证明中使用的技术是信息几何中的拟ε邻域概念。对于有限块长n，生成分布被选为一族方差递减的截断高斯分布。方差递减规律经过精心设计，使得在输出分布满足隐蔽约束的条件下，主信道上的吞吐量在渐近意义上达到最大。对于逆命题，我们将在二阶矩约束下最小化KL散度的高斯分布的最优性从一维推广到n维。在此基础上，我们建立了为满足隐蔽约束而设计的码的平均功率的上界，这进一步推导出以隐蔽度量表示的直接逆命题界。