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：本文研究了在高斯白噪声信道中，在KL散度上界δ的隐蔽约束下，通过n次信道使用所能实现的最大吞吐量的渐近特性。研究表明，最大吞吐量的一阶和二阶渐近量分别为$\sqrt{nδ\log e}$和$(2)^{1/2}(nδ)^{1/4}(\log e)^{3/4}\cdot Q^{-1}(ε)$。可达性证明中采用的技术源于信息几何中的拟ε邻域概念。对于有限码长n，生成分布选取为一系列方差递减的截断高斯分布。递减规律的精心设计使得在输出分布满足隐蔽约束的条件下，主信道吞吐量在渐近意义上达到最大化。在逆命题证明中，将二阶矩约束下最小化KL散度的高斯分布最优性从一维推广到n维。基于此，我们建立了满足隐蔽约束的码平均功率上界，进而推导出基于隐蔽度量的直接逆命题界。