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IEEE Information Theory Workshop (ITW)

Covert communication over broadcast channels

Keerthi Suria Kumar Arumugam, Matthieu R. Bloch

Published Nov 1, 2017• 14 citations
Publisher

Abstract

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.

DOI
10.1109/itw.2017.8278022

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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.
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.
We consider a scenario in which two legitimate transmitters attempt to communicate with a legitimate receiver over a discrete memoryless Multiple-Access Channel (MAC), while escaping detection from an adversary who observes their communication through another discrete memoryless MAC. If the MAC to the legitimate receiver is “better” than the one to the adversary, in a sense that we make precise, then the legitimate users can reliably communicate on the order of √n bits per n channel uses with arbitrarily Low Probability of Detection (LPD) without using a secret key. We also identify the pre-constants of the scaling, which leads to a characterization of the covert capacity region.
We consider a covert communication scenario where a legitimate transmitter wishes to communicate simultaneously to two legitimate receivers while ensuring that the communication is not detected by an adversary, also called the warden. The legitimate receivers and the adversary observe the transmission from the legitimate transmitter via a three-user discrete or Gaussian memoryless broadcast channel. We focus on the case where the symbol is not redundant, i.e., the output distribution at the warden induced by the no-input symbol is not a mixture of the output distributions induced by other input symbols, so that the covert communication is governed by the square root law, i.e., at most Θ(n)\Theta(\sqrt{n})Θ(n​) bits can be transmitted over nnn channel uses. We show that for such a setting of covert communication over broadcast channels, a simple time-division strategy achieves the optimal throughputs. Our result implies that a code that uses two separate optimal point-to-point codes each designed for the constituent channels and each used for a fraction of the time is optimal in the sense that it achieves the best constants of the n\sqrt{n}n​-scaling for the throughputs. Our proof strategy combines several elements in the network information theory literature, including concave envelope representations of the capacity regions of broadcast channels and El Gamal's outer bound for more capable broadcast channels.
We consider a covert communication scenario where a transmitter wishes to communicate simultaneously to two legitimate receivers while ensuring that the communication is not detected by an adversary, the warden. The legitimate receivers and the adversary observe the transmission from the transmitter via a three-user discrete or Gaussian memoryless broadcast channel. We focus on the case where the “no-input” symbol is not redundant, i.e., the output distribution at the warden induced by the no-input symbol is not a mixture of the output distributions induced by other input symbols, so that the covert communication is governed by the square root law, i.e., at most Θ(√n) bits can be transmitted over n channel uses. We show that for such a setting, a simple time-division strategy achieves the optimal throughputs for a non-trivial class of broadcast channels; this is not true for communicating over broadcast channels without the covert communication constraint. Our result implies that a code that uses two separate optimal point-to-point codes each designed for the constituent channels and each used for a fraction of the time is optimal in the sense that it achieves the best constants of the √n-scaling for the throughputs. Our proof strategy combines several elements in the network information theory literature, including concave envelope representations of the capacity regions of broadcast channels and El Gamal's outer bound for more capable broadcast channels.
We consider a covert communication scenario where a transmitter wishes to communicate simultaneously to two legitimate receivers while ensuring that the communication is not detected by an adversary, the warden. The legitimate receivers and the adversary observe the transmission from the transmitter via a three-user discrete or Gaussian memoryless broadcast channel. We focus on the case where the "no-input" symbol is not redundant, i.e., the output distribution at the warden induced by the no-input symbol is not a mixture of the output distributions induced by other input symbols, so that the covert communication is governed by the square root law, i.e., at most Θ(n)Θ(\sqrt{n})Θ(n​) bits can be transmitted over nnn channel uses. We show that for such a setting, a simple time-division strategy achieves the optimal throughputs for a non-trivial class of broadcast channels; this is not true for communicating over broadcast channels without the covert communication constraint. Our result implies that a code that uses two separate optimal point-to-point codes each designed for the constituent channels and each used for a fraction of the time is optimal in the sense that it achieves the best constants of the n\sqrt{n}n​-scaling for the throughputs. Our proof strategy combines several elements in the network information theory literature, including concave envelope representations of the capacity regions of broadcast channels and El Gamal's outer bound for more capable broadcast channels.
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.