We study the fundamental limits of covert communications over general memoryless additive-noise channels. We assume that the legitimate receiver and the eavesdropper share the same channel and therefore see the same outputs. Under mild integrability assumptions, we find a general upper bound on the square-root scaling constant, which only involves the variance of the logarithm of the probability density function of the noise. Furthermore, we show that, under some additional assumptions, this upper bound is tight. We also provide upper bounds on the length of the secret key required to achieve the optimal scaling.
We study the fundamental limits of covert communications over general memoryless additive-noise channels. We assume that the legitimate receiver and the eavesdropper share the same channel and therefore see the same outputs. Under mild integrability assumptions, we find a general upper bound on the square-root scaling constant, which only involves the variance of the logarithm of the probability density function of the noise. Furthermore, we show that, under some additional assumptions, this upper bound is tight. We also provide upper bounds on the length of the secret key required to achieve the optimal scaling.
Physical-layer security aims to exploit the randomness inherent in communication channels in order to guarantee confidentiality even against computationally unlimited attackers. In this thesis, we focus on covert communication, also known as “communication with low probability of detection”. This is a scenario where a transmitter and receiver try to prevent an eavesdropper from making a good guess on whether a communication is ongoing or not. We assume that the receiver and the eavesdropper share the same channel and therefore see the same outputs. In this scenario, the transmitter shares a key with the legitimate receiver to provide the necessary advantage to detect the communication and reliably decode the message. Asymptotically, the amount of information that can be sent reliably and covertly scales like the square root of the number of channel uses; this is known as the square root law of covert communication.We study the corresponding scaling constant of the square root law for general memoryless channels including non-Gaussian additive noise, as well as Gaussian channels with memory. In the latter case, we show that the scaling constant is the same as over the memoryless Gaussian channel. For continuous memoryless channels, under mild integrability conditions, we show that the scaling constant is upper bounded by a simple expression which only involves the variance of the logarithm of the probability density function of the noise. Moreover, we show that under some additional assumptions, this upper bound is tight. Furthermore, we provide upper bounds on the length of the secret key required to achieve covertness.The second objective of this work is to investigate the limits of covert communication over continuous memoryless channels in the finite blocklength regime. We provide bounds for the first and second-order asymptotics for covert communication over an AWGN channel under a maximal error probability criterion and for the first-order asymptotics under an average error probability criterion.
We establish the fundamental limits of covert communication over quantum channels, focusing on both finite-dimensional classical-quantum (CQ) channels and the infinite-dimen\-sional lossy thermal-noise bosonic channel. For general memoryless CQ channels, we characterize when covert communication is possible and prove a square root law (SRL): at most Ln+o(n) bits can be reliably transmitted covertly over n uses of the channel where L is the channel-dependent covert capacity. We derive a single-letter expression for L and show that the required pre-shared secret key also scales as n under mild conditions. We also identify and characterize corner cases where either constant-rate or zero-rate covert communication is possible. For the bosonic channel, we prove that the SRL holds and derive exact covert capacities under different resource assumptions. In particular, we show that the covert secrecy and covert entanglement generation capacities both equal the covert classical capacity without entanglement-assistance, Lno-EA, and show that the required pre-shared classical secret key scales as n. We also find that quadrature phase-shift keying (QPSK) achieves the optimal covert capacity, outperforming binary modulation in contrast to the classical channel setting. When Alice and Bob instead share entanglement, the covert classical capacity improves to LEAnlogn+o(nlogn), though this scaling is sensitive to noise in the entangled resource. Finally, we propose a practical covert transceiver and simulate its performance compared to recently experimentally-tested transceivers under realistic conditions.
We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product a ofninput states is used:LSRLn+o(n)covert bits (but no more) can be reliably transmitted innuses of classical-quantum channel, whereLSRL>0is a channel-dependent constant that we callcovert capacity. We also show that ensuring covertness requiresJSRLn+o(n)bits secret key shared by the communicating parties prior to transmission, whereJSRL≥0is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on allnchannel uses. We determine the single-letter expressions forLSRLandJSRL, and establish conditions whenJSRL=0(i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.
In this paper, we consider fundamental communication limits over a compound channel. Covert communication in the information-theoretic context has been primarily concerned with fundamental limits when the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. This paper, however, considers an alternative, and no less important, setting in which the object to be masked is the state of the compound channel. Such a communication model has applications in the prevention of malicious parties seeking to jam the communication signal when, for example, the signal-to-noise ratio of a wireless channel is found to be low. Our main contribution is the establishment of bounds on the throughput-key region when the covertness constraint is defined in terms of the total variation distance. In addition, for the scenario in which the key length is infinite, we provide a sufficient condition for when the bounds coincide for the scaling of the throughput, which follows the square-root law. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.
We extend previous results on covert communication over the additive white Gaussian noise channel to two other types of additive noise channels. The first is the Gaussian channel with memory, where the noise sequence is a Gaussian vector with an arbitrary invertible covariance matrix. We show that the fundamental limit for covert communication over such a channel is the same as over the channel with white, i.e., memoryless, Gaussian noise. The second type of channel we consider is one with memoryless generalized Gaussian noise. For such a channel we prove a general upper bound on the dominant term in the maximum number of nats that can be covertly communicated over n channel uses. When the shape parameter p of the generalized Gaussian noise distribution is in the interval (0,1], we also prove a matching lower bound.
We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel, while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals through another discrete memoryless channel. We develop a coding scheme based on the principle of channel resolvability, which generalizes and extends prior work in several directions. First, it shows that irrespective of the quality of the channels, it is possible to communicate on the order of √n reliable and covert bits over n channel uses if the transmitter and the receiver share on the order of √n key bits. This improves upon earlier results requiring on the order of √n log n key bits. Second, it proves that if the receiver's channel is better than the warden's channel in a sense that we make precise, it is possible to communicate on the order of √n reliable and covert bits over n channel uses without a secret key. This generalizes earlier results established for binary symmetric channels. We also identify the fundamental limits of covert and secret communications in terms of the optimal asymptotic scaling of the message size and key size, and we extend the analysis to Gaussian channels. The main technical problem that we address is how to develop concentration inequalities for low-weight sequences. The crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities.