One-shot achievability and converse bounds of Gaussian random coding in AWGN channels under covert constraint

Abstract

It is well known that finite blocklength plays an important role in the analysis of practical communication. This paper considers the achievability and converse bounds on the maximal channel coding rate (throughput) at a given blocklength and error probability in covert communication over AWGN channels. The covert constraint is in the form of an upper bound of total variation distance (TVD). For the achievability, Gaussian random coding scheme is adopted for convenience in the analysis of TVD. The classical results of finite blocklength regime are not applicable in this case. By revisiting [18], we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. The general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. We further show an interesting connection between attaining tight achievability and converse bounds and solving two total variation distance related minimax problems. Further comparison is made between the new achievability bound and existing one with deterministic codebooks. The TVD at the adversary is analyzed under the given coding scheme, and the power level induced by covert constraint is bounded by applications of divergence inequalities. Our thorough analysis thus leads us to a comprehensive characterization of the attainable throughput in covert communication over AWGN channels. The summary of the initial part of this paper was published in [29].

Total Variation Distance Based Performance Analysis of Covert Communication over AWGN Channels in Non-asymptotic Regime

“…When the channels are discrete memoryless, this question has been answered by Bloch's works [14] [15], where the exact second-order asymptotics of the maximal number of reliable and covert bits are characterized when the discrimination metrics are relative entropy, total variation distance (TVD) and missed detection probability, respectively. In [16] and [17], one-shot achievability and converse bounds of Gaussian random coding under maximal power constraint are presented, and also the TVD at the adversary is roughly estimated using Pinsker's inequality. There are several reasons for us to adopt Gaussian random codes.…”