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IEEE International Symposium on Information Theory (ISIT)

Stealthy Communication over Noisy Channels: Channel Capacity and The Role of Randomization

Abdalla Ibrahim, Johannes Rosenberger, Boulat A. Bash, Holger Boche, Christian Deppe

Published Jun 1, 2026• 0 citations
Publisher
DOI
10.1109/isit62367.2026.11653641

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In this work, we aim to design a stealthy secret key generation (SSKG) scheme for a completely concealed communication system. More specifically, the data transmission is accomplished by covert communications, which requires additional keys to guarantee the covertness when Bob's channel quality is worse than a warden Willie's in a special definition. However, normal SKG schemes may raise Willie's attention and violate the design goal. Therefore, we resort to the SSKG. The derived results show that the SK capacity lower and upper bounds of the source-model SKG are not affected by the additional stealth constraint. This result implies that we can attain the stealthy SKG capacity for free when the common randomness observed at each node forms a Markov chain. We then prove that the sufficient condition to attain the SK capacity can be relaxed from physical to stochastic degradedness. In order to underline the practical relevance, we also derive a sufficient condition to attain the degradedness by the usual stochastic order for the fast fading Gaussian Maurer's (satellite) model for the source of common randomness.
To conceal the behavior of communications, we may adopt covert or stealthy communications under different scenarios and demands. However, when legitimate users have worse channels than the eavesdropper, the legitimate users may need additional keys to attain the concealment. Normal secret key generation (SKG) schemes may raise Willie's attention due to the public discussion breaking the concealment. Therefore, in this work, we investigate how to conceal the SKG itself, especially according to the stealth constraint. We prove that if the virtual channel between the common random source observed by the legitimate Alice and Bob, namely, X and Y, respectively, is more capable than that between Bob and Willie (the warden), namely, Y and Z, respectively, the same stealthy SK rate as in the case without stealth constraint can be achieved. Furthermore, if (X, Y, Z) form a Markov chain, then the key capacity of the SKG with the stealth constraint can be achieved for free.
In this chapter, we develop the notion of secrecy capacity , which plays a central role in physical-layer security. The secrecy capacity characterizes the fundamental limit of secure communications over noisy channels, and it is essentially the counterpart to the usual point-to-point channel capacity when communications are subject not only to reliability constraints but also to an information-theoretic secrecy requirement. It is inherently associated with a channel model called the wiretap channel , which is a broadcast channel in which one of the receivers is treated as an adversary. This adversarial receiver, which we call the eavesdropper to emphasize its passiveness, should remain ignorant of the messages transmitted over the channel. The mathematical tools, and especially the random-coding argument, presented in this chapter are the basis for most of the theoretical research in physical-layer security, and we use them extensively in subsequent chapters. We start with a review of Shannon's model of secure communications (Section 3.1), and then we informally discuss the problem of secure communications over noisy channels (Section 3.2). The intuition we develop from loose arguments is useful to grasp the concepts underlying the proofs of the secrecy capacity and motivates a discussion of the choice of an information-theoretic secrecy metric (Section 3.3). We then study in detail the fundamental limits of secure communication over degraded wiretap channels (Section 3.4) and broadcast channels with confidential messages (Section 3.5).