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IEEE International Symposium on Information Theory (ISIT)

Covert Communication When Action-Dependent States is Available Non-Causally at the Transmitter

Hassan ZivariFard, Xiaodong Wang

Published Jun 25, 2023• 4 citations
Publisher

Abstract

This paper studies covert communication over channels with action-dependent states when the state is available non-causally at the encoder. Covert communication refers to reliable communication between a transmitter and a receiver while ensuring low probability of detection at an adversary, which we refer to as "warden". It is well known that in a point to point Discrete Memoryless Channel (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 positive covert and reliable communication rate, which is communication on the order of N bits over N channel uses, while the transmitter and the receiver share a secret key of negligible rate. We derive an achievable rate region by using block-Markov encoding and secret key generation from the Action-Dependent State Information (ADSI), which subsumes the best achievable rate region for channels with random states.

DOI
10.1109/isit54713.2023.10206650

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This paper studies covert communication over channels with action-dependent states when the state is available non-causally at the encoder. Covert communication refers to reliable communication between a transmitter and a receiver while ensuring low probability of detection at an adversary, which we refer to as "warden". It is well known that in a point to point Discrete Memoryless Channel (DMC), it is possible to communicate on the order of N\sqrt N 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 N\sqrt N N​ bits. This paper studies achieving positive covert and reliable communication rate, which is communication on the order of N bits over N channel uses, while the transmitter and the receiver share a secret key of negligible rate. We derive an achievable rate region by using block-Markov encoding and secret key generation from the Action-Dependent State Information (ADSI), which subsumes the best achievable rate region for channels with random states.
This paper studies covert communication over channels with Action-Dependent State Information (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 Discrete Memoryless Channel (DMC), it is possible to communicate on the order ofN\sqrt {N}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 ofN\sqrt {N}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 Additive White Gaussian Noise (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. A few other examples are also worked out in detail.
We consider the problem of covert communication over a state-dependent channel, for which the transmitter and the legitimate receiver have non-causal access to the channel state information. Covert communication with respect to an adversary, referred to as the “warden,” is one in which the distribution induced during communication at the channel output observed by the warden is identical to the output distribution conditioned on an inactive channel-input symbol. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver the codebook uncertainty is removed via a shared secret key that is unavailable to the warden. Unlike earlier work in state-dependent covert communication, we do not assume the availability of a shared key at the transmitter and legitimate receiver. Rather, a shared randomness is extracted at the transmitter and the receiver from the channel state, in a manner that keeps the shared randomness secret from the warden despite the influence of the channel state on the warden's output. An inner bound on the covert capacity, in the absence of an externally provided secret key, is derived.
We consider the problem of covert communication over a state-dependent channel when the Channel State Information (CSI) is available either non-causally, causally, or strictly causally, either at the transmitter alone, or at both transmitter and receiver. Covert communication with respect to an adversary, called “warden,” is one in which, despite communication over the channel, the warden’s observation remains indistinguishable from an output induced by innocent channel-input symbols. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver, the codebook uncertainty is typically removed via a shared secret key that is unavailable to the warden. In contrast to previous work, we do not assume the availability of a large shared key at the transmitter and legitimate receiver. Instead, we only require a secret key with negligible rate to bootstrap the communication and our scheme extracts shared randomness from the CSI in a manner that keeps it secret from the warden, despite the influence of the CSI on the warden’s output. When CSI is available at the transmitter and receiver, we derive the covert capacity region. When CSI is only available at the transmitter, we derive inner and outer bounds on the covert capacity. We also provide examples for which the covert capacity is positive with knowledge of CSI but is zero without it.
We consider the problem of covert communication over a state-dependent channel, where the transmitter has non-causal knowledge of the channel states. Here, “covert” means that the probability that a warden on the channel can detect the communication must be small. In contrast with traditional models without noncausal channel-state information at the transmitter, we show that covert communication can be possible with positive rate. We derive closed-form formulas for the maximum achievable covert communication rate (“covert capacity”) in this setting for discrete memoryless channels as well as additive white Gaussian noise channels. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.
We study covert communication and covert secret key generation with positive rates over channels with causal Channel State Information (CSI) at the transmitter. Specifically, we consider a state-dependent Discrete Memoryless Channel (DMC) where the transmitter has causal access to the CSI, and aims to communicate covertly with the receiver while simultaneously generating a covert secret key shared with the receiver. We derive an achievable rate region for this problem, which recovers as a special case the best-known results for covert communication over channels with CSI. To the best of our knowledge, our results are the first instance of achieving a positive rate for covert secret key generation.
We consider the problem of covert communication in the presence of a cooperative jammer. Covert communication refers to communication that is undetectable by an adversary, i.e., a scenario in which, despite ongoing communication, the output distribution observed by an adversary called the “warden” is indistinguishable from the distribution that would have been induced by an innocent channel-input symbol. It is known that in general, a transmitter and a receiver can communicate onlyO(n)O(\sqrt{n})O(n​)covert bits overnnnchannel uses, i.e., zero rate. This paper shows that a cooperative jammer can facilitate the communication of positive covert rates, subject to the transmitter having non-causal access to the jammer signal. An achievable rate region is calculated that highlights the relation between the covert communication rate, jammer's randomness (expressed as a rate), and rate of a secret key shared between transmitter and receiver.