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. We prove that if the generating distribution of the codebook is close to Dirac measure in the weak sense, then the corresponding output distribution at the adversary satisfies covert constraint in terms of most common divergences. This helps link the local differential geometry of the distribution of noise with covert constraint. For the converse, the optimality of Gaussian distribution for minimizing KL divergence under second order moment constraint is extended from dimension $1$ to dimension $n$. It helps to establish the 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）上界δ的隐蔽约束条件下，通过n次信道使用在AWGN信道中实现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√(nδ log e)和(2)^{1/2}(nδ)^{1/4}(log e)^{3/4}·Q^{-1}(ε)。在可达性证明中，我们采用了信息几何中的准ε邻域概念。我们证明：若码本生成分布在弱收敛意义上接近狄拉克测度，则对手端对应的输出分布满足基于最常用散度的隐蔽约束。这一结论有助于建立噪声分布的局部微分几何与隐蔽约束之间的关联。在逆定理方面，我们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至n维，从而建立满足隐蔽约束的码字平均功率上界，并进一步推导出基于隐蔽度量的直接逆界。