Covert Communication via Action-Dependent States

TL;DR

This paper investigates the possibility of achieving reliable and positive-rate covert communication over channels with action-dependent states, using causal or non-causal state information at the transmitter, and introduces new coding schemes and bounds.

Contribution

It develops achievable rates and bounds for covert communication with action-dependent states, extending existing results to channels with causal and non-causal state information.

Findings

Positive covert rates are achievable with secret key sharing.

Bounds meet in special cases, confirming optimality.

Cooperation enhances covert capacity in Gaussian channels.

Abstract

This paper studies covert communication over channels with ADSI when the state is available either non-causally or causally at the transmitter. Covert communication refers to reliable communication between a transmitter and a receiver while ensuring a low probability of detection by an adversary, which we refer to as `warden'. It is well known that in a point-to-point DMC, it is possible to communicate on the order of $\sqrt{N}$ bits reliably and covertly over $N$ channel uses while the transmitter and the receiver are required to share a secret key on the order of $\sqrt{N}$ bits. This paper studies achieving reliable and covert communication of positive rate, i.e., reliable and covert communication on the order of N bits in N channel uses, over a channel with ADSI while the transmitter has non-causal or causal access to the ADSI, and the transmitter and the receiver share a secret key of negligible rate. We derive achievable rates for both the non-causal and causal scenarios by using block-Markov encoding and secret key generation from the ADSI, which subsumes the best achievable rates for channels with random states. We also derive upper bounds, for both non-causal and causal scenarios, that meet our achievable rates for some special cases. As an application of our problem setup, we study covert communication over channels with rewrite options, which are closely related to recording covert information on memory, and show that a positive covert rate can be achieved in such channels. As a special case of our problem, we study the AWGN channels and provide lower and upper bounds on the covert capacity that meet when the transmitter and the receiver share a secret key of sufficient rate and when the warden's channel is noisier than the legitimate receiver channel. As another application of our problem setup, we show that cooperation can lead to a positive covert rate in Gaussian channels.