The First and Second Order Asymptotics of Covert Communication over AWGN Channels

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

Finite Blocklength Analysis of Gaussian Random coding in AWGN Channels under Covert constraints II: A Viewpoint of Total Variation Distance

Covert communication over an additive white Gaussian noise (AWGN) channel with finite block length is investigated in this paper. The attention is on the covert criterion, which has not been considered in finite block length circumstance. As an accurate quantity metric of discrimination, the variation distance with given finite block length n and signal-noise ratio (snr) is obtained. We give both its analytic solution and expansions which can be easily evaluated. It is shown that K-L distance, which is frequently adopted as the metric of discrimination at the adversary in asymptotic regime, is not convincing in finite block length regime compared with the total variation distance. Moreover, the convergence rate of the total variation with different snr is analyzed when the block length tends to infinity. The results will be very helpful for understanding the behavior of the total variation distance and practical covert communication

Finite Blocklength Analysis of Gaussian Random Coding in AWGN Channels under Covert Constraint

This paper considers the achievability and converse bounds on the maximal channel coding rate at a given blocklength and error probability over AWGN channels. The problem stems from covert communication with Gaussian codewords. By re-visiting [18], we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. Such general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. Further comparison is made between the new achievability bounds and existing one with deterministic codebooks.Comment: 18 page