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IEEE Wireless Communications Letters

Covert Communication Over Gaussian Multiple-Access Channels With Feedback

Kang-Hee Cho, Si-Hyeon Lee

Published Jul 13, 2022• 9 citations
Publisher

Abstract

We consider the covert communication over the two-user Gaussian multiple access channel (GMAC) with causal feedback. It is shown that any causal feedback does not enlarge the covert capacity region and the time-division scheme is optimal for a class of channels, which includes the case where the warden observes what the legitimate receiver receives. For the proof, we derive an outer bound on the covert capacity region of general GMACs with noiseless causal feedback, which implies that the square-root law holds for arbitrary channel gains. Furthermore, the extension to multi-user case is presented.

DOI
10.1109/lwc.2022.3190477

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We consider the covert communication over the two-user Gaussian multiple access channel (GMAC) with causal feedback. It is shown that any causal feedback does not enlarge the covert capacity region and the time-division scheme is optimal for a class of channels, which includes the case where the warden observes what the legitimate receiver receives. For the proof, we derive an outer bound on the covert capacity region of general GMACs with noiseless causal feedback, which implies that the square-root law holds for arbitrary channel gains. Furthermore, the extension to multi-user case is presented.
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 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 investigate message identification over a K-sender Gaussian multiple access channel (K-GMAC). Unlike conventional Shannon transmission codes, the size of randomized identification (ID) codes experiences a doubly exponential growth in the code length. Improvements in the ID approach can be attained through additional resources such as quantum entanglement, common randomness (CR), and feedback. It has been demonstrated that an infinite capacity can be attained for a single-user Gaussian channel with noiseless feedback, irrespective of the chosen rate scaling. We establish the capacity region of both the K-sender Gaussian multiple access channel (K-GMAC) and the K-sender state-dependent Gaussian multiple access channel (K-SD-GMAC) when strictly causal noiseless feedback is available.
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.