Covert Communication in the Presence of an Uninformed Jammer

TL;DR

This paper explores covert communication strategies in noisy channels with an uninformed jammer, demonstrating that Alice can reliably transmit (n) bits without detection even against an optimal detector by Willie, under various channel conditions.

Contribution

It generalizes covert communication to environments with an uninformed jammer and no restrictions on Willie's detector, showing (n) bits can be transmitted covertly.

Findings

Alice can transmit (n) bits covertly with constant power.

Threshold detection is optimal in some scenarios, but not always.

Covert communication remains feasible with an uninformed jammer and complex fading channels.

Abstract

Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to $\mathcal{O}(\sqrt{n})$ bits in $n$ channel uses. However, this assumes Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with $n$, thus conveying $\mathcal{O}(n)$ bits covertly and reliably in $n$ uses of an AWGN channel. Here, we consider covert communication of $\mathcal{O}(n)$ bits in $n$ channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume an uninformed "jammer" is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with $n$ even when Willie employs an optimal detector.