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 $\delta$ of Kullback-Leibler divergence (KL divergence). It is shown that the first and second order asymptotics of the maximal throughput are $\sqrt{n\delta \log e}$ and $(2)^{1/2}(n\delta)^{1/4}(\log e)^{3/4}\cdot Q^{-1}(\epsilon)$, 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Kullback-Leibler散度（KL散度）的上界$\delta$约束下，AWGN信道经$n$次信道使用所实现的最大吞吐量的渐进特性。研究表明，最大吞吐量的一阶和二阶渐进项分别为$\sqrt{n\delta \log e}$和$(2)^{1/2}(n\delta)^{1/4}(\log e)^{3/4}\cdot Q^{-1}(\epsilon)$。在可达性证明中，我们采用了信息几何中的拟$\varepsilon$-邻域概念。对于有限码长$n$，生成分布被选为方差递减的截断高斯分布族，其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，主信道吞吐量在渐进意义下达到最大化。在逆证明中，将高斯分布在二阶矩约束下最小化KL散度的最优性从一维推广至$n$维。基于此，我们建立了满足隐蔽约束的码字平均功率上界，进而推导出以隐蔽度量为表征的直接逆界限。