Stealth Communication with Vanishing Power over Binary Symmetric Channels

Abstract

A framework for stealth communication with vanishing power (VP) is presented by studying binary symmetric channels. Coding theorems are proved by modifying Gallager's error exponents for VP and by applying resolvability exponents. The analysis unifies and generalizes existing rate bounds for covert and stealth communication.1) We introduce a framework for stealth communication that includes previously treated scenarios as special cases. In particular, we are interested in using vanishing power, as for covert communication, but with energy that scales as n α , 0 ≤ α < 1, with blocklength n. Observe that covert communication has α ≤ 1/2 while stealth communication as treated in [7], [8] has α = 1. 2) We prove coding theorems by using suitably modified Gallager exponents. This gives an alternative, and we believe simpler, approach to prove and understand achievability as compared to previous work. This paper is organized as follows. Sec. II introduces notation and classic error exponents. In Sec. III, we derive achievable codebook scaling constants for vanishing power (VP) communication by using modified error exponents. We apply these results in Sec. IV to prove achievability of VP stealth communication. Finally, we compare our results for the covert communication case with bounds from [2], [3], [6] in Sec. V.