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

TL;DR

This paper analyzes the finite blocklength performance of Gaussian random coding in AWGN channels under covert constraints, focusing on total variation distance as a discrimination metric, and compares it with K-L distance.

Contribution

It provides analytic solutions and expansions for total variation distance in finite blocklength regimes, highlighting its importance over K-L distance for covert communication analysis.

Findings

Total variation distance is more convincing than K-L distance in finite blocklength regimes.

Analytic solutions and expansions for total variation distance are derived.

Convergence rates of total variation with respect to SNR are analyzed.

Abstract

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.