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IEEE International Symposium on Information Theory (ISIT)

Covert Communication over a Physically Degraded Relay Channel with Non-Colluding Wardens

Keerthi Suria Kumar Arumugam, Matthieu R. Bloch, Ligong Wang

Published Jun 1, 2018• 15 citations
Publisher

Abstract

We analyze a physically degraded relay channel, in which the transmitter sends a covert message to the legitimate receiver with the help of a relay. Two wardens, who do not collude with each other, monitor communication from the transmitter and the relay, respectively, through two Discrete Memoryless Channels (DMCs) to detect the presence of a covert message. The objective of the transmitter is to deliver the covert message successfully to the receiver without exceeding the covertness threshold of either warden. We identify the optimal asymptotic scaling of message and key bits and the dependence of the covert throughput on the two covertness thresholds.

DOI
10.1109/isit.2018.8437505

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We analyze a physically degraded relay channel, in which the transmitter sends a covert message to the legitimate receiver with the help of a relay. Two wardens, who do not collude with each other, monitor communication from the transmitter and the relay, respectively, through two Discrete Memoryless Channels (DMCs) to detect the presence of a covert message. The objective of the transmitter is to deliver the covert message successfully to the receiver without exceeding the covertness threshold of either warden. We identify the optimal asymptotic scaling of message and key bits and the dependence of the covert throughput on the two covertness thresholds.
We consider a scenario in which K transmitters attempt to communicate covert messages reliably to a legitimate receiver over a discrete memoryless multiple-access channel (MAC) while simultaneously escaping detection from an adversary who observes their communication through another discrete memoryless MAC. We assume that each transmitter may use a secret key that is shared only between itself and the legitimate receiver. We show that each of the K transmitters can transmit on the order of √n reliable and covert bits per n channel uses, exceeding which, the warden will be able to detect the communication. We identify the optimal pre-constants of the scaling, which leads to a complete characterization of the covert capacity region of the K-user binary-input MAC. We show that, asymptotically, all sum-rate constraints are inactive unlike the traditional MAC capacity region. We also characterize the channel conditions that have to be satisfied for the transmitters to operate without a secret key.
Covert communication aims to hide the existence of the transmissions to guarantee the security in wireless communications. In this letter, channel uncertainty is exploited to achieve covert communication in relay networks. The transmitter Alice sends messages to the legitimate receiver Bob with the help of a relay, while the warden Willie wants to detect the existence of the transmission. The channel uncertainty introduces confusions to degrade the performance of Willie's detection. We show that Alice can transmit O{O}O (n{n}n ) bits in n{n}n channel uses covertly with the help of relay and channel uncertainty. Numerical results are shown to illustrate the achievability and the performance of the considered scenario.
We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel, while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals through another discrete memoryless channel. We develop a coding scheme based on the principle of channel resolvability, which generalizes and extends prior work in several directions. First, it shows that irrespective of the quality of the channels, it is possible to communicate on the order of √n reliable and covert bits over n channel uses if the transmitter and the receiver share on the order of √n key bits. This improves upon earlier results requiring on the order of √n log n key bits. Second, it proves that if the receiver's channel is better than the warden's channel in a sense that we make precise, it is possible to communicate on the order of √n reliable and covert bits over n channel uses without a secret key. This generalizes earlier results established for binary symmetric channels. We also identify the fundamental limits of covert and secret communications in terms of the optimal asymptotic scaling of the message size and key size, and we extend the analysis to Gaussian channels. The main technical problem that we address is how to develop concentration inequalities for low-weight sequences. The crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities.
In this paper, we study covert communication over a compound discrete memoryless channel (DMC). There are two channel states in which one of them is arbitrarily chosen and remains fixed during the transmission. The objective is to reliably send a message from the transmitter to the receiver. An adversary who is observing the channel output should not be able to infer the channel state. Two covertness metrics are considered. In the first metric, covertness is measured using the KL-divergence of the channel output marginal of each state with a fixed distribution. Different cases where such a distribution can be specified, are studied. The optimal transmission rate of each case is established. In the second metric, the covertness is measured by using the total variation distance of the channel output marginals of the two states. Upper and lower bounds on the optimal transmission covert rate are derived. The bounds match for a special case and characterize the optimal throughput.
We analyze a two-receiver binary-input discrete memoryless broadcast channel, in which the transmitter communicates a common message simultaneously to both users and a covert message to only one of them while treating the other as an adversary. This model captures the problem of embedding covert messages in an innocuous codebook and generalizes previous models in which the innocent behavior corresponds to the absence of communication between legitimate users. We identify the exact asymptotic behavior of the number of reliable and covert bits when the rate of the innocuous codebook is close to the channel capacity of the adversary. In particular, our results characterize the dependence of the number of covert bits on the channel parameters and the characteristics of the innocent codebook.
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.