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arXiv:2404.14056 · International Conference on Communications

Covert Multi-Access Communication with a Non-Covert User

Abdelaziz Bounhar, Mireille Sarkiss, Michèle Wigger

Published Jun 9, 2024• 2 citations
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Abstract

In this paper, we caracterize the fundamental limits of a communication system with three users (i.e., three transmitters) and a single receiver where communication from two covert users must remain undetectable to an external warden. Our results show a tradeoff between the highest rates that are simultaneously achievable for the three users. They further show that the presence of a non-covert user in the system can enhance the capacities of the covert users under stringent secret-key constraints. To derive our fundamental limits, we provide an information-theoretic converse proof and present a coding scheme that achieves the performance of our converse result. Our coding scheme is based on multiplexing different code phases, which seems to be essential to exhaust the entire tradeoff region between the rates at the covert and the two non-covert users. This property is reminiscent of the setup with multiple non-covert users, where multiplexing is also required to exhaust the entire rate-region.

DOI
10.1109/icc51166.2024.10622567

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In this paper, we caracterize the fundamental limits of a communication system with three users (i.e., three transmitters) and a single receiver where communication from two covert users must remain undetectable to an external warden. Our results show a tradeoff between the highest rates that are simultaneously achievable for the three users. They further show that the presence of a non-covert user in the system can enhance the capacities of the covert users under stringent secret-key constraints. To derive our fundamental limits, we provide an information-theoretic converse proof and present a coding scheme that achieves the performance of our converse result. Our coding scheme is based on multiplexing different code phases, which seems to be essential to exhaust the entire tradeoff region between the rates at the covert and the two non-covert users. This property is reminiscent of the setup with multiple non-covert users, where multiplexing is also required to exhaust the entire rate-region.
This paper establishes the fundamental limits of a multi-access system where multiple users communicate to a legitimate receiver in presence of an external warden. Only a specific subset of the users, called covert users, needs their communication to remain undetected to the warden, while the remaining non-covert users have no such constraint. The fundamental limits show a tradeoff between the different rates that are simultaneously achievable at the various users in function of the secret-key rates that the different users share with the legitimate receiver. Interestingly, the presence of the non-covert users can enhance the capacities of the covert users, especially under stringent secret-key budgets. Our findings underscore the essential requirement of employing a multiplexing (coded time-sharing) strategy to exhaust the fundamental region of all rates that are simultaneously achievable at the covert and the non-covert users. As a side-product of our results, we also establish the covert-capacity secret-key tradeoff for standard single-user and multi-access covert communication systems (without non-covert users), i.e., the largest covert rates that are achievable under given secret-key rate budgets. Previous works had only established the minimum secret-key rates required at largest covert rates.
This paper establishes the fundamental limits of a two-user single-receiver system where communication from User 1 (but not from User 2) needs to be undetectable to an external warden. Our fundamental limits show a tradeoff between the highest rates (or square-root rates) that are simultaneously achievable for the two users. Moreover, coded time-sharing for both users is fundamentally required on most channels, which distinguishes this setup from the more classical setups with either only covert users or only non-covert users. Interestingly, the presence of a non-covert user can be beneficial for improving the covert capacity of the other user.
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.
The fundamental limits of covert communication, where a message is sent from transmitter Alice to intended recipient Bob without detection by an attentive adversary warden Willie, has been considered extensively in recent years at the physical layer. The covert throughput depends critically on the warden's understanding of the characteristics of the radio environment and the type of receiver that he employs, and, as expected, the throughput increases when the warden has some uncertainty about the environment or some non-idealities in his receiver. In this paper, we consider the covert throughput when the adversary is only able to observe the medium access control (MAC) layer in a wireless communication system. In particular, given that the system has a rate ofλ\lambdaλpackets per slot transmitted overnnnchannels by allowable system users, we study the allowable rateλa\lambda _aλa​by covert users while maintaining covertness from an attentive warden observing the channel status in a slotted ALOHA system. We characterize performance for wardens with different abilities to discern the number of packets on a given channel, ranging from simple receivers that detect only whether there was a packet present to complicated receivers that can determine the number of packets involved in any collision, and also consider intended recipients Bob with varying abilities to perform multi-packet reception. In contrast to prior work in covert communications, the application considered motivates the consideration of results for finite (often small) observation vector lengthsnnnat the adversary. Numerical results are provided both to illustrate the tightness of our achievability regions for the packet transmission rate of the covert transmitters and to demonstrate the covert throughput of the system as a function ofλ\lambdaλandnnn.
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.
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.