Optimal Throughput for Covert Communication Over a Classical-Quantum Channel

This paper considers the problem of communication over a memoryless classical-quantum wiretap channel subject to the constraint that the eavesdropper on the channel should not be able to learn whether the legitimate parties are using the channel to communicate or not. Specifically, the relative entropy between the output quantum states at the eavesdropper when a codeword is transmitted and when no input is provided must be sufficiently small. Extending earlier works, this paper proves the "square-root law" for a broad class of classical-quantum channels: the maximum amount of information that can be reliably and covertly transmitted over $n$ uses of such a channel scales like $\sqrt{n}$. The scaling constant is also determined.Comment: Corrected version of a paper presented at ITW 2016. In the ITW paper, the denominator in the main formula (10) was incorrect. The current version corrects this mistake and adds an appendix for its derivatio

Covert communication with finite blocklength in AWGN channels

Covert communication is to achieve a reliable transmission from a transmitter to a receiver while guaranteeing an arbitrarily small probability of this transmission being detected by a warden. In this work, we study the covert communication in AWGN channels with finite blocklength, in which the number of channel uses is finite. Specifically, we analytically prove that the entire block (all available channel uses) should be utilized to maximize the effective throughput of the transmission subject to a predetermined covert requirement. This is a nontrivial result because more channel uses results in more observations at the warden for detecting the transmission. We also determine the maximum allowable transmit power per channel use, which is shown to decrease as the blocklength increases. Despite the decrease in the maximum allowable transmit power per channel use, the maximum allowable total power over the entire block is proved to increase with the blocklength, which leads to the fact that the effective throughput increases with the blocklength.ARC Discovery Projects Grant DP15010390

Finite Blocklength Analysis of Gaussian Random Coding in AWGN Channels under Covert Constraint

This paper considers the achievability and converse bounds on the maximal channel coding rate at a given blocklength and error probability over AWGN channels. The problem stems from covert communication with Gaussian codewords. By re-visiting [18], we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. Such general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. Further comparison is made between the new achievability bounds and existing one with deterministic codebooks.Comment: 18 page

Delay-Intolerant Covert Communications with Either Fixed or Random Transmit Power

In this paper, we study delay-intolerant covert communications in additive white Gaussian noise (AWGN) channels with a finite block length, i.e., a finite number of channel uses. Considering the maximum allowable number of channel uses to be N, it is not immediately clear whether the actual number of channel uses, denoted by n, should be as large as N or smaller for covert communications. This is because a smaller n reduces a warden’s chance to detect the communications due to fewer observations, but also reduces the chance to transmit information. We show that n=N is indeed optimal to maximize the amount of information bits that can be transmitted, subject to any covert communication constraint in terms of the warden’s detection error probability. To better make use of the warden’s uncertainty due to the finite block length, we also propose to use uniformly distributed random transmit power to enhance covert communications. Our examination shows that the amount of information that can be covertly transmitted logarithmically increases with the number of random power levels, which indicates that most of the benefit of using random transmit power is achieved with just a few different power levels.This work was supported by the Australian Research Council’s Discovery Projects under Grant DP180104062

Fundamental Limits of Communication with Low Probability of Detection

This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. Specifically, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the "off" input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.Comment: Version to appear in IEEE Transactions on Information Theory; minor typos in v2 corrected. Part of this work was presented at ISIT 2015 in Hong Kon

Finite Blocklength Analysis of Gaussian Random coding in AWGN Channels under Covert constraints II: A Viewpoint of Total Variation Distance

Covert communication over an additive white Gaussian noise (AWGN) channel with finite block length is investigated in this paper. The attention is on the covert criterion, which has not been considered in finite block length circumstance. As an accurate quantity metric of discrimination, the variation distance with given finite block length n and signal-noise ratio (snr) is obtained. We give both its analytic solution and expansions which can be easily evaluated. It is shown that K-L distance, which is frequently adopted as the metric of discrimination at the adversary in asymptotic regime, is not convincing in finite block length regime compared with the total variation distance. Moreover, the convergence rate of the total variation with different snr is analyzed when the block length tends to infinity. The results will be very helpful for understanding the behavior of the total variation distance and practical covert communication

The First and Second Order Asymptotics of Covert Communication over AWGN Channels

This paper investigates the asymptotics of the maximal throughput of communication over AWGN channels by $n$ channel uses under a covert constraint in terms of an upper bound $\delta$ of Kullback-Leibler divergence (KL divergence). It is shown that the first and second order asymptotics of the maximal throughput are $\sqrt{n\delta \log e}$ and $(2)^{1/2}(n\delta)^{1/4}(\log e)^{3/4}\cdot Q^{-1}(\epsilon)$, respectively. The technique we use in the achievability is quasi-$\varepsilon$-neighborhood notion from information geometry. We prove that if the generating distribution of the codebook is close to Dirac measure in the weak sense, then the corresponding output distribution at the adversary satisfies covert constraint in terms of most common divergences. This helps link the local differential geometry of the distribution of noise with covert constraint. For the converse, the optimality of Gaussian distribution for minimizing KL divergence under second order moment constraint is extended from dimension $1$ to dimension $n$. It helps to establish the upper bound on the average power of the code to satisfy the covert constraint, which further leads to the direct converse bound in terms of covert metric