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

Abstract

This paper investigates covert communication over an additive white Gaussian noise (AWGN) channel in finite block length regime on the assumption of Gaussian codebooks. We first review some achievability and converse bounds on the throughput under maximal power constraint. From these bounds and the analysis of TVD at the adversary, the first and second asymptotics of covert communication are investigated by the help of some divergences inequalities. Furthermore, the analytic solution of TVD, and approximation expansions which can be easily evaluated with given snr (signal noise ratio) are presented. In this way, the proper power level for covert communication can be approximated with given covert constraint of TVD, which leads to more accurate estimation of the power compared with preceding bounds. Moreover, the connection between Square Root Law and TVD is disclosed to be on the numerical properties of incomplete gamma functions. Finally, the convergence rates of TVD for snr = n −τ with τ > 0.5 and τ < 0.5 are studied when the block length tends to infinity, which extends the previous extensively focused work on τ = 0.5. Further elaboration on the effect of such asymptotic characteristics on the primary channel's throughput in finite block regime is also provided. The results will be very helpful for understanding the behavior of the total variation distance and practical covert communication.