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arXiv:2506.16581

Covert Communication over Physically-Degraded Alarm Two-Way Channels

Erdoğan, Tuna, Kann, Tyler, Nosratinia, Aria, Matthieu R. Bloch

Published Jun 19, 2025• 0 citations
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Abstract

We study covert communications over binary-input discrete memoryless alarm two-way channels, in which two users interact through a two-way channel and attempt to hide the presence of their communication from an eavesdropping receiver. The alarm two-way channel is one in which simultaneous transmissions by both users trigger an alarm at the eavesdropper, which captures the challenges and opportunities of cooperation beyond interference management. In particular, by characterizing the covert capacity region of two-way channels when using public time sharing, we show how cooperation strictly improves achievable covert communication throughputs. While our analysis falls short of characterizing the two-way covert capacity region for all two-way channels, we provide general achievable and converse bounds that illuminate the cooperation mechanisms that benefit covertness and are tight for a physically-degraded alarm two-way channels. Because of the unique nature of covert communications, our analysis also shows that the coordination required to avoid triggering alarms comes asymptotically "for free". The key technical challenge that we address is how to appropriately design auxiliary random variables in a multi-user covert communication setting subject to the square root law.

DOI
10.48550/arxiv.2506.16581

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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.
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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.
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This paper considers the covert identification problem in which a sender aims to reliably convey an identification (ID) message to a set of receivers via a binary-input discrete memoryless channel (BDMC), and simultaneously to guarantee that the communication is covert with respect to a warden who monitors the communication via another independent BDMC. We prove a square-root law for the covert identification problem. This states that an ID message of size exp(exp(Θ(√{ n})) can be transmitted over n channel uses. We then characterize the exact pre-constant in the Θ(·) notation. This constant is referred to as the covert identification capacity. We show that it equals the recently developed covert capacity in the standard covert communication problem, and somewhat surprisingly, the covert identification capacity can be achieved without any shared key between the sender and receivers. The achievability proof relies on a random coding argument with pulse-position modulation (PPM), coupled with a second stage which performs code refinements. The converse proof relies on an expurgation argument as well as results for channel resolvability with stringent input constraints.
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.