It is well known that finite blocklength analysis plays an important role in evaluating performances of communication systems in practical settings. 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 given in terms of an upper bound on total variation distance (TVD) between the distributions of eavesdropped signals at an adversary with and without presence of active and legitimate communication, respectively. 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 exploiting and extending canonical approaches, 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 based minimax and maxmin problems. The TVD constraint is analyzed under the given random coding scheme, which induces bounds on the transmission power through divergence inequalities. Further comparison is made between the new achievability bounds and existing ones derived under deterministic codebooks. Our thorough analysis thus leads us to a comprehensive characterization of the attainable throughput in covert communication over AWGN channels.
As claimed in International Telecommunications Union (ITU) Recommendation ITU-R M.2160, 6G communication systems require extremely high-security and low-latency communication, necessitating the study of covert communication operating at finite blocklengths. In the point-to-point (P2P) setting, covert communication enables a transmitter to send messages reliably over a noisy channel to a legitimate receiver without being detected by any third party. Under the covertness metric of Kullback–Leibler divergence (KLD), we derive exact second-order asymptotics for P2P covert communication over a multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) channel. In particular, our theoretical benchmarks refine the first-order asymptotics of Wang and Bloch (TIFS 2021), which is known as the square root law by showing that the non-asymptotic maximal number of transmitted messages has a back off that scales in the order
Θ(n41) beyond the first-order term scaling in the order
Θ(n21) when the blocklength is
n. Thus, our second-order asymptotic bound provides a better approximation to the finite blocklength performance of optimal codes. Furthermore, compared with the single antenna result of Yu et al. (arXiv:2305.17924v3), we demonstrate the impact of the number of antennas
m and reveal spatial diversity gains of MIMO, advocating the use of MIMO for covert communication to achieve a high transmission rate. To prove our results, we extend the quasi-
η-neighborhood framework from single-antenna real value channels to multi-antenna complex value MIMO channels. To ensure covertness, the transmission power vanishes as the blocklength
n increases. Thus, we judiciously analyze the finite blocklength performance of MIMO communication by modifying critical steps concerning the Berry–Esseen Theorem to deal with vanishing second and third absolute moments of information densities that rely on blocklength, which is in stark contrast with the non-covert case.
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.