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... Similarly, [4] considered the achievability bounds on the maximal channel coding rate at a given blocklength and error probability over AWGN channels. In addition, [5], [6] investigated the throughput over quasi-static fading channels, revealing the fundamental difference in the design between the case of quasi-static fading channel and that of AWGN channel. More complex scenarios with multiple warders, multi-antenna sources and unmanned aerial vehicle aided networks were considered in [7]- [9]. ...

... However, the analysis and corresponding system designs about the proactive warder in [10]- [12] were based on an infinite blocklength assumption, which is no longer suitable for short-packet transmission. Besides, the results from the system with passive warders [5]- [9] can not be directly applied to the system with the proactive warder, since another jamming link exits between the warder and the destination in addition to communication and detection links. This compounds the challenges of both reliability and covertness in short-packet communications. ...

... Notably, from the perspective of Alice, only statistical CSI is available. Therefore, the average detection error probability is derived as the covertness metric [5]. ...

Wireless short-packet communications pose challenges to the security and reliability of the transmission. Besides, the proactive warder compounds these challenges, who detects and interferes with the potential transmission. An extra jamming channel is introduced by the proactive warder compared with the passive one, resulting in the inapplicability of analytical methods and results in exsiting works. Thus, effective system design schemes are required for short-packet communications against the proactive warder. To address this issue, we consider the analysis and design of covert and reliable transmissions for above systems. Specifically, to investigate the reliable and covert performance of the system, detection error probability at the warder and decoding error probability at the receiver are derived, which is affected by both the transmit power and the jamming power. Furthermore, to maximize the effective throughput, an optimization framework is proposed under reliability and covertness constraints. Numerical results verify the accuracy of analytical results and the feasibility of the optimization framework. It is shown that the tradeoff between transmission reliability and covertness is changed by the proactive warder compared with the passive one. Besides, it is shown that longer blocklength is always beneficial to improve the throughput for systems with optimized transmission rates. But when transmission rates are fixed, the blocklength should be carefully designed since the maximum one is not optimal in this case.

... Assume that Alice wants to communicate with Bob covertly in the main channel (Alice-Bob), and an adversary observes the communication process simultaneously in a wiretap (Alice-adversary) channel. If Alice knows the lower bound on wiretap channel noise, Alice can transmit O( √ N ) bits to Bob using N channel resources [22], [23] with an arbitrarily low probability of detection in additive white Gaussian channels, whose fundamental limit follows a square root law [22], [23]. However, the covert throughput of a communication channel that follows a square-root law is zero, i.e., lim N →∞ ...

... Assume that Alice wants to communicate with Bob covertly in the main channel (Alice-Bob), and an adversary observes the communication process simultaneously in a wiretap (Alice-adversary) channel. If Alice knows the lower bound on wiretap channel noise, Alice can transmit O( √ N ) bits to Bob using N channel resources [22], [23] with an arbitrarily low probability of detection in additive white Gaussian channels, whose fundamental limit follows a square root law [22], [23]. However, the covert throughput of a communication channel that follows a square-root law is zero, i.e., lim N →∞ ...

... Assume that an adversary performs two hypotheses tests on the information it receives to decide whether a D2D communication link is transmitting covert signals or not [23]- [25], which can be defined as ...

A device-to-device (D2D) communication link is vulnerable because it is relatively easy to be compromised by adversaries due to the fact that D2D terminals are power limited nodes. This article proposes a covert communication scheme that allows D2D communication links to transmit covert signals (e.g., privacy sensitive data) to ensure a low probability of detection. We allocate transmit powers of cellular and D2D noncovert signals following a fading D2D channel to add the uncertainty in adversary’s background noises. With the help of base station, cooperative power domain nonorthogonal multiple access and successive interference cancellation are used to decode covert signal. Depending on whether a D2D transmitter has the knowledge of adversary’s detection threshold, we derive minimum error probability to measure the covertness performance. Furthermore, we evaluate covert throughput, which is defined as a maximum average transmission rate of covert signal, subject to a given covertness performance.

... where f |ht,w| 2 (x) = e −x is the PDF of |h t,w | 2 . Substituting (14) and (15) into (22), and the proof can be completed after some algebraic operations. Note thatξ in (22) for µ > σ 2 w contains two parts, where the first part reflects the negative impact of the opportunistic jammer selection on the detection accuracy at W, and the second one arises due to the absence of the instantaneous CSI of h t,w . ...

... Substituting (14) and (15) into (22), and the proof can be completed after some algebraic operations. Note thatξ in (22) for µ > σ 2 w contains two parts, where the first part reflects the negative impact of the opportunistic jammer selection on the detection accuracy at W, and the second one arises due to the absence of the instantaneous CSI of h t,w . ...

In this paper, we study covert communications between {a pair of} legitimate transmitter-receiver against a watchful warden over slow fading channels. There coexist multiple friendly helper nodes who are willing to protect the covert communication from being detected by the warden. We propose an uncoordinated jammer selection scheme where those helpers whose instantaneous channel gains to the legitimate receiver fall below a pre-established selection threshold will be chosen as jammers radiating jamming signals to defeat the warden. By doing so, the detection accuracy of the warden is expected to be severely degraded while the desired covert communication is rarely affected. We then jointly design the optimal selection threshold and message transmission rate for maximizing covert throughput under the premise that the detection error of the warden exceeds a certain level. Numerical results are presented to validate our theoretical analyses. It is shown that the multi-jammer assisted covert communication outperforms the conventional single-jammer method in terms of covert throughput, and the maximal covert throughput improves significantly as the total number of helpers increases, which demonstrates the validity and superiority of our proposed scheme.

... However, limited storage resources and requirements of quick updates in modern communication systems require a finite, sometimes small, number of channel uses, and hence the results in the infinite blocklength regime do not hold anymore. Under finite blocklength, covert communication has been considered in the literature under AWGN and fading channels [14][15][16], where a single-antenna adversary was considered. ...

... The wireless links from Alice to Bob and Alice to Willie are subject to quasi-static Rayleigh fading channels, which constitute a suitable model for covert communications scenario under NLOS communications, and is commonly adopted in the literature [7,16]. Resultantly, corresponding to a large coherence time, the channel coefficients remain constant in a slot and change independently from one slot to the next. ...

Covert communication hides the transmission of a message from a watchful adversary while ensuring reliable information decoding at the receiver, providing enhanced security in wireless communications. In this letter, covert communication in the presence of a multi-antenna adversary and under delay constraints is considered. Under the assumption of quasi-static wireless fading channels, we analyze the effect of increasing the number of antennas employed at the adversary on the achievable throughput of covert communication. It is shown that in contrast to a single-antenna adversary, a slight increase in the number of adversary's antennas drastically reduces the covert throughput, even for relaxed covertness requirements.

... Obviously, MIMO techniques also proved useful for covert communication, and for achieving a positive rate [14], [15], [16]. The literature on the subject is diverse, with works also considering delay [17], [18], finite block length [19], [20], [21], [22] and tighter asymptotics [23]. ...

Covert communication, a sub-field of information security, is focused on hiding the mere existence of communication from unwanted listeners via the physical layer, i.e., via signal and noise characteristics, rather than assuming coding or secure protocols at the higher layers. In this work, we consider the problem of perfect covert communication in wireless networks. Specifically, harnessing an Intelligent Reflecting Surface (IRS), we turn our attention to schemes which allow the transmitter to completely hide the communication, with zero energy at the unwanted listener (Willie) and hence zero probability of detection. Applications of such schemes go beyond simple covertness, as we prevent detectability or decoding even when the codebook, timings and channel characteristics are known to Willie. That is, perfect covertness also ensures Willie is unable to decode, even assuming communication took place and knowing the codebook. We define perfect covertness, give a necessary and sufficient condition for it in IRS-assisted communication and define the optimization problem. For $N=2$ IRS elements we compute the probability of finding a solution and give the solution analytically. For $N>2$, we also analytically compute the probability of such a zero-detection solution, and show that it tends to $1$ as the number of IRS elements increases. We provide a perfectly covert scheme achieving it and prove its convergence. The results are also supported by simulation results, showing that a small amount of IRS elements allows for a positive rate at the legitimate user yet with zero probability of detection at an unwanted listener.

... While asymptotic behaviour gives us fundamental limits and important insights, it is critical to understand such systems with finite, realistic block lengths, demanded by either complexity or delay constraints. The first studies were in [32], [33], [34], [35], [36], [7], [37]. Needless to say, practical constrains such as limited delay and finite blocks, may limit the communication of Alice and Bob, yet, on the other hand, may limit the warden's ability to detect the communication, hence it is not a priori clear which will have a stronger effect. ...

Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the behavior of) a linear system, while keeping an observer, Willie, unable to decide if the system is indeed being controlled or not. We formally define the problem, under a model where Willie can only observe the system's output. Focusing on AR(1) systems, we show that when Willie observes the system's output through a clean channel, an inherently unstable linear system can not be covertly stabilized. However, an inherently stable linear system can be covertly controlled, in the sense of covertly changing its parameter or resetting its memory. Moreover, we give positive and negative results for two important controllers: a minimal-information controller, where Alice is allowed to use only $1$ bit per sample, and a maximal-information controller, where Alice is allowed to view the real-valued output. Unlike covert communication, where the trade-off is between rate and covertness, the results reveal an interesting \emph{three--fold} trade--off in covert control: the amount of information used by the controller, control performance and covertness.

... By eqs. (19) to (20), using Chebyshev's inequality, we have, ...

Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the parameters of) a linear system, while keeping an observer, Willie, unable to decide if the system is indeed being controlled or not. We formally define the problem, under two different models: (i) When Willie can only observe the system's output (ii) When Willie can directly observe the control signal. Focusing on AR(1) systems, we show that when Willie observes the system's output through a clean channel, an inherently unstable linear system can not be covertly stabilized. However, an inherently stable linear system can be covertly controlled, in the sense of covertly changing its parameter. Moreover, we give direct and converse results for two important controllers: a minimal-information controller, where Alice is allowed to used only $1$ bit per sample, and a maximal-information controller, where Alice is allowed to view the real-valued output. Unlike covert communication, where the trade-off is between rate and covertness, the results reveal an interesting \emph{three--fold} trade--off in covert control: the amount of information used by the controller, control performance and covertness. To the best of our knowledge, this is the first study formally defining covert control.

... With the square root law indicating that covert capacity is asymptotically zero, a positive covert rate has been proved to be achievable through creating the uncertainties of warden's received signals. The common methods for providing uncertainties are to exploit the randomness of transmitter power [11][12][13] and the cooperative jamming signal [14][15][16][17][18], the sample randomness caused by a finite channel use [19][20][21][22], and the uncertainty of the noise power [23][24][25][26], which are collectively called covertness sources here. However, the first two covertness sources are considered to be under potential security threats made by deep learning due to their artificial randomness of fixed distributions. ...

This paper studies multi-antenna covert communication exploiting a public communication link over the wireless fading channel. In particular, a relatively practical covert communication scenario is considered for the first time, where a warden with radiometer may improve its detection accuracy by jointly detecting uplink covert pilot and downlink covert communication. To this end, a joint covert communication system, jointly considering uplink covert pilot, imperfect channel state information issue and downlink covert communication, is proposed and further studied. Specifically, the detection performance of warden and the covertness performance of system are comprehensively studied, respectively. Afterwards, an optimization problem for covert capacity is formulated to maximize overall performance. Then, with our analysis and simplification, an optimal power allocation algorithm is designed for covert capacity accordingly. Our examination shows a win-win situation has been achieved in the proposed system, that is, covert communication would rarely affect the normal communication of public link and occupy its communication resources. Interestingly enough, we analytically find an invariance property of downlink covert communication that covertness performance is not impacted by noise levels or warden's position. Based on this extraordinary finding, we conclude that the downlink covert communication system can perfectly combat with a powerful warden adopting power trend test method, while the joint covert communication system may resist that through a pilot deception scheme. © 2021 The Authors. IET Communications published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology

... Furthermore, [28] has considered achieving covertness under strict delay requirements using a fullduplex receiver, where it has been shown that in contrast to asymptotically infinite channel uses, a fixed power artificial noise transmission helps improve covert communications. The authors in [29] have analyzed covert communications under finite blocklength in the presence of a multi-antenna Willie, while covert communications over slow fading channels under finite blocklength has been considered in [30], providing an upper bound on the total power satisfying a desired probability of detection by the adversary. ...

Covert communications enable a transmitter to send information reliably in the presence of an adversary, who looks to detect whether the transmission took place or not. We consider covert communications over quasi-static block fading channels, where users suffer from channel uncertainty. We investigate the adversary Willie's optimal detection performance in two extreme cases, i.e., the case of perfect channel state information (CSI) and the case of channel distribution information (CDI) only. It is shown that in the large detection error regime, Willie's detection performances of these two cases are essentially indistinguishable, which implies that the quality of CSI does not help Willie in improving his detection performance. This result enables us to study the covert transmission design without the need to factor in the exact amount of channel uncertainty at Willie. We then obtain the optimal and suboptimal closed-form solution to the covert transmission design. Our result reveals fundamental difference in the design between the case of quasi-static fading channel and the previously studied case of non-fading AWGN channel.

... Furthermore, [55] has considered achieving covertness under strict delay requirements using a full-duplex receiver, where it has been shown that in contrast to asymptotically infinite channel uses, a fixed power artificial noise transmission helps improve covert communications. The authors in [56] have analyzed covert communications under finite blocklength in the presence of a multi-antenna Willie, while covert communications over slow fading channels under finite blocklength has been considered in [57], providing an upper bound on the total power satisfying a desired probability of detection by the adversary. ...

Traditional approaches to wireless communication security (e.g., encryption) focus on maintaining the message integrity so that the contents are only accessible to the intended recipient. However, detection of the mere presence of a transmission can have a negative impact, violating the privacy of the communicating parties. In contrast, Covert Communications (also known as Low Probability of Detection Communications) hide the transmission of a message from a watchful adversary while ensuring a certain decoding performance at the receiver. In this thesis, we focus on exploiting any existing or induced uncertainties at the adversary, developing novel methods to achieve covertness in wireless scenarios. The insights gained from this thesis aim to help alleviate the ever increasing security and privacy concerns in future wireless networks. The first half of the thesis examines the use of artificial noise (AN) to cause sufficient confusion at the adversary such that message transmissions cannot be detected. We first consider a full-duplex information receiver, who generates AN of varying power causing uncertainty in the adversary's received signal statistics. Although the transmission of this AN causes self-interference, it provides the opportunity of achieving covertness under carefully managed transmit power levels. Here, we provide design guidelines for the choice of AN transmission power range. Furthermore, we demonstrate that if the transmission probability and AN power can be jointly optimized, the prior transmission probability of 0.5, which amounts to a random guess by the adversary, is not always the best choice for achieving maximum covertness. Rather, increasing the transmission probability beyond 0.5 allows an increase in the AN transmit power for satisfying a given covert rate requirement and can be the difference between achieving strong covertness and almost no covertness at all. Relying on the use of AN, we next consider achieving covertness in the domain of backscatter radio systems. We assume that the tag (containing the information) is passive and the reader (transceiver) controls the transmit power to keep the tag's response hidden. A non-conventional transmission scheme is proposed where the reader emits noise-like signal with transmit power varying across different communication slots. We analyse the conditions on the transmit power to achieve a target level of covertness, and illustrate the price a backscatter system has to pay, in terms of bit error rate, for achieving covert communication. In the second half of the thesis, we focus on scenarios where users suffer from uncertainty in their channel knowledge under quasi-static fading conditions. We first focus on the case where the adversary can make an infinite number of observations in a time slot, and a public action is used to provide cover for a secret action. It has been demonstrated that although channel uncertainty adversely effects the information at the intended receiver, it also provides the opportunity to hide any transmissions. Secondly, under a finite blocklength assumption, we investigate Willie's optimal detection performance in two extreme cases, i.e., the case of perfect channel state information (CSI) and the case of channel distribution information (CDI) only. It is shown that in the large detection error regime, Willie's detection performances in these two extreme cases are essentially indistinguishable, implying that the quality of CSI does not help Willie in improving his detection performance. We, thus, reveal fundamental differences in the design of covert transmissions for quasi-static fading channels in comparison to non-fading AWGN channels.

... In [6] [7], the first and second order asymptotics are investigated over discrete memoryless channels when the discrimination metrics are relative entropy, total variation distance (variational distance) and missed detection probability at a fixed significance level, respectively. For AWGN channels and slow fading channels, the maximal transmit power and the maximal transmit bits in finite block length were characterized in [8] and [9] by using the conclusion on the maximal throughput in [10] directly. ...

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.

... zero-mean Gaussian random variables. The square root law was found over AWGN channels [8] and slow fading channels [25]. Yan et al. [26] first studied delay-intolerant covert communications in AWGN channels with a finite block length. ...

Covert wireless communication or low probability of detection (LPD) communication that employs the noise or jamming signals as the cover to hide user's information can prevent a warden Willie from discovering user's transmission attempts. Previous work on this problem has typically assumed that the warden is static and has only one antenna, often neglecting an active warden who can dynamically adjust his/her location to make better statistic tests. In this paper, we analyze the effect of an active warden in covert wireless communications on AWGN channels and find that, having gathered samples at different places, the warden can easily detect Alice's transmission behavior via a trend test, and the square root law is invalid in this scenario. Furthermore, a more powerful warden with multiple antennas is harder to be deceived, and Willie's detection time can be greatly shortened.

... When the channels are discrete memoryless, this question has been answered by Bloch's works [14] [15], where the exact second-order asymptotics of the maximal number of reliable and covert bits are characterized when the discrimination metrics are relative entropy, variational distance (TV distance) and missed detection probability, respectively. For AWGN channels and slow fading channels, the maximal transmit power and the maximal transmit bits in finite block length are characterized in [16] and [17], respectively. In this work, we are interested in the question with"converse" direction: give an finite block length n and snr at the main channel, how much discrimination will it give rise to at the adversary with respect to the background noise. ...

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.

Multiantenna technique can provide a substantial rate gain for wireless communication; however, when applied in covert wireless communication, the potential detecting risk of pilot transmission is always neglected. In this article, for the first time, we consider the effect of pilot leakage on the performance of covert communication over a finite transmission blocklength. First, we construct a general analysis model of multiantenna joint covert communication (JTCC), where the uplink covert pilot, the imperfect channel estimation issues, and the downlink covert communication is taken into account. Second, we evaluate the covertness performance of the proposed system in which an independent detection scheme (IDS) and two joint detection schemes (JDSs) are adopted at an unintended warden, respectively. In particular, the closed-form expressions of tight average covert probability are derived under the different detection schemes. Third, we establish an optimization framework for the covert throughput maximization subject to the constraints of covertness, reliability, and blocklength. Moreover, a simple and robust solution is provided by jointly designing the pilot length and the transmit power. Numerical results highlight the advantages of the JTCC system in resisting pilot detection and indicate the tradeoff of pilot design between the achievable covertness, the required reliability, and the overall rate performance.

This paper considers beamforming techniques for covert communication over multiple input single output (MISO) channels with finite blocklength. We first show that the optimal input distribution for covert communication over complex Gaussian channels is circular symmetric complex Gaussian. By reviewing our previous results on the throughput of Gaussian random coding over additive white Gaussian noise (AWGN) channels, the achievability and converse bounds on the attainable throughput over MISO channels are analyzed. Then, the optimal beamforming strategies and their relationship with the transmitting power are thoroughly investigated in a variety of situations in terms of several types of channel state information available at both ends of the system. We reveal the fact that the maximal allowable transmit power is not constrained by covertness requirement when there is full channel information of the adversary, while there is an upper bound of the transmit power which is based on beamforming and an outage-based covertness criterion if there is only partial channel information of the adversary. Finally, numerical results are presented to show that the throughput of covert communication can be increased notably by adopting a proper beamforming strategy in MISO channels in comparison with the single antenna case.

In this paper, we study covert communications between a pair of legitimate transmitter-receiver against a watchful warden over slow fading channels. There coexist multiple friendly helper nodes who are willing to protect the covert communication from being detected by the warden. We propose an uncoordinated jammer selection scheme where those helpers whose instantaneous channel gains to the legitimate receiver fall below a pre-established selection threshold will be chosen as jammers radiating jamming signals to defeat the warden. By doing so, the detection accuracy of the warden is expected to be severely degraded while the desired covert communication is rarely affected. We then jointly design the optimal selection threshold and message transmission rate for maximizing covert throughput under the premise that the detection error of the warden exceeds a certain level. Numerical results are presented to validate our theoretical analyses. It is shown that the multi-jammer assisted covert communication outperforms the conventional single-jammer method in terms of covert throughput, and the maximal covert throughput improves significantly as the total number of helpers increases, which demonstrates the validity and superiority of our proposed scheme.

It is well known that finite blocklength analysis plays an important role in evaluating performances of communication systems in practical settings. This paper considers the achievability and converse bounds on the maximal channel coding rate (throughput) at a given blocklength and error probability in covert communication over AWGN channels. The covert constraint is given in terms of an upper bound on total variation distance (TVD) between the distributions of eavesdropped signals at an adversary with and without presence of active and legitimate communication, respectively. For the achievability, Gaussian random coding scheme is adopted for convenience in the analysis of TVD. The classical results of finite blocklength regime are not applicable in this case. By exploiting and extending canonical approaches, we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. The general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. We further show an interesting connection between attaining tight achievability and converse bounds and solving two total variation distance based minimax and maxmin problems. The TVD constraint is analyzed under the given random coding scheme, which induces bounds on the transmission power through divergence inequalities. Further comparison is made between the new achievability bounds and existing ones derived under deterministic codebooks. Our thorough analysis thus leads us to a comprehensive characterization of the attainable throughput in covert communication over AWGN channels.

Covert communications enable a transmitter to send information reliably in the presence of an adversary, who looks to detect whether the transmission took place or not. We consider covert communications over quasi-static block fading channels, where users suffer from channel uncertainty. We investigate the adversary Willie's optimal detection performance in two extreme cases, i.e., the case of perfect channel state information (CSI) and the case of channel distribution information (CDI) only. It is shown that in the large detection error regime, Willie's detection performances of these two cases are essentially indistinguishable, which implies that the quality of CSI does not help Willie in improving his detection performance. This result enables us to study the covert transmission design without the need to factor in the exact amount of channel uncertainty at Willie. We then obtain the optimal and suboptimal closed-form solution to the covert transmission design. Our result reveals fundamental difference in the design between the case of quasi-static fading channel and the previously studied case of non-fading AWGN channel.

This paper investigates covert communication over an additive white Gaussian noise (AWGN) channel in finite block length regime on the assumption of Gaussian codebooks. We first review some achievability and converse bounds on the throughput under maximal power constraint. From these bounds and the analysis of TVD at the adversary, the first and second asymptotics of covert communication are investigated by the help of some divergences inequalities. Furthermore, the analytic solution of TVD, and approximation expansions which can be easily evaluated with given snr (signal noise ratio) are presented. In this way, the proper power level for covert communication can be approximated with given covert constraint of TVD, which leads to more accurate estimation of the power compared with preceding bounds. Further elaboration on the effect of such asymptotic characteristics on the primary channels's throughput in finite block regime is also provided. The results will be very helpful for understanding the behavior of the total variation distance and practical covert communication.

Covert communication hides the transmission of a message from a watchful adversary, while ensuring reliable information decoding at the receiver, providing enhanced security in wireless communications. In this work, covert communication in the presence of a multi-antenna adversary and under delay constraints is considered. Under the assumption of quasi-static wireless fading channels, we analyze the effect of increasing the number of antennas employed at the adversary on the achievable throughput of covert communication. It is shown that in contrast to a single-antenna adversary, a slight increase in the number of adversary's antennas drastically reduces the covert throughput, even for relaxed covertness requirements.

This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the existing results, but also achieve stronger notions of secrecy.

Fundamental limits of covert communication have been studied in literature for different models of scalar channels. It was shown that, over n independent channel uses, O(√ n) bits can transmitted reliably over a public channel while achieving an arbitrarily low probability of detection (LPD) by other stations. This result is well known as square-root law and even to achieve this diminishing rate of covert communication, some form of shared secret is needed between the transmitter and the receiver. In this paper, we establish the limits of LPD communication over the MIMO AWGN channel. We define the notion of-probability of detection (-PD) and provide a formulation to evaluate the maximum achievable rate under the-PD constraint. Then, we show that the optimal input distribution is zero mean Gaussian distribution. Assuming channel state information (CSI) about the main channel only at the transmitter, we derive the optimal input covariance matrix, hence, establishing the-PD capacity. We evaluate-PD rates in the limiting regimes for the number of channel uses (asymptotic block length) and the number of antennas (massive MIMO). We show that, while the SRL still holds for the MIMO AWGN, the number of bits that can be transmitted covertly scales exponentially with the number of transmitting antennas. We establish the condition on the number of transmitting antennas required to achieve a non-diminishing rate with LPD. The practical implication of our result is that, MIMO has the potential to provide a substantial increase in the file sizes that can be covertly communicated subject to a reasonably low delay.

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.

The wiretap channel has been devised and studied first by Wyner, and subsequently extended to the case with nondegraded general wiretap channels by Csiszár and Körner. Focusing mainly on the stationary memoryless channel with cost constraint, we newly introduce the notion of reliability and secrecy functions as a fundamental tool to analyze and/or design the performance of an efficient wiretap channel system, including binary symmetric wiretap channels, Poisson wiretap channels, and Gaussian wiretap channels. Compact formulas for those functions are explicitly given for stationary memoryless wiretap channels. It is also demonstrated that, based on such a pair of reliability and secrecy functions, we can control the tradeoff between reliability and secrecy (usually conflicting), both with exponentially decreasing rates as block length (n) becomes large. Four ways to do so are given on the basis of rate shifting, rate exchange, concatenation, and change of cost constraint. In addition, the notion of the (delta ) secrecy capacity is defined and shown to attain the strongest secrecy standard among others. The maximized versus averaged secrecy measures is also discussed.

A transmitter Alice may wish to {\it reliably} transmit a message to a
receiver Bob over a binary symmetric channel (BSC), while simultaneously
ensuring that her transmission is {\it deniable} from an eavesdropper Willie.
That is, if Willie listening to Alice's transmissions over a {"significantly
noisier"} BSC than the one to Bob, he should be unable to estimate even whether
Alice is transmitting. Even when Alice's (potential) communication scheme is
publicly known to Willie (with {\it no} common randomness between Alice and
Bob), we prove that over $n$ channel uses Alice can transmit a message of
length ${\cal O}(\sqrt{n})$ bits to Bob, deniably from Willie. We also prove
information-theoretically order-optimality of our results.

This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability Â¿ isclosely approximated by C - Â¿(V/n) Q<sup>-1</sup>(Â¿) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion , and Q is the complementary Gaussian cumulative distribution function.

In 1893 Jacques Hadamard introduced the famous inequality concerning the determinant of the Gram matrix. The generalizations of this inequality are the main subject of considerations presented in this paper. Calculations executed for the gramian of order three revealed that the description of gramian hides a great potential enabling to strengthen essentially the Hadamard inequality. The research, undertaken in this direction, resulted in discovering the more subtle versions of the Hadamard inequality, also by involving the "language" of the positive semi-definite Hermitian matrices.

An effective security measure is defined that includes strong secrecy and
stealth communication. Effective secrecy ensures that a message cannot be
deciphered and that the presence of meaningful communication is hidden. To
measure stealth we use resolvability and relate this to binary hypothesis
testing. Results are developed for wire-tap channels and broadcast channels
with confidential messages.

We present a square root limit on the amount of information transmitted
reliably and with low probability of detection (LPD) over additive white
Gaussian noise (AWGN) channels. Specifically, if the transmitter has AWGN
channels to an intended receiver and a warden, both with non-zero noise power,
we prove that $o(\sqrt{n})$ bits can be sent from the transmitter to the
receiver in $n$ channel uses while lower-bounding $\alpha+\beta\geq1-\epsilon$
for any $\epsilon>0$, where $\alpha$ and $\beta$ respectively denote the
warden's probabilities of a false alarm when the sender is not transmitting and
a missed detection when the sender is transmitting. Moreover, in most practical
scenarios, a lower bound on the noise power on the channel between the
transmitter and the warden is known and $O(\sqrt{n})$ bits can be sent in $n$
LPD channel uses. Conversely, attempting to transmit more than $O(\sqrt{n})$
bits either results in detection by the warden with probability one or a
non-zero probability of decoding error at the receiver as $n\rightarrow\infty$.

THE problems of cryptography and secrecy systems furnish an interesting application of communication theory.1 In this paper a theory of secrecy systems is developed. The approach is on a theoretical level and is intended to complement the treatment found in standard works on cryptography.2 There, a detailed study is made of the many standard types of codes and ciphers, and of the ways of breaking them. We will be more concerned with the general mathematical structure and properties of secrecy systems.

Incluye bibliografía e índice

This is an account of the life of the author’s book Testing Statistical Hypotheses
, its genesis, philosophy, reception and publishing history. There is also some discussion of the position of hypothesis testing and the Neyman-Pearson theory in the wider context of statistical methodology and theory.

The lack of a low probability of detection (LPD) waveform is often
cited as one of the criteria against the use of commercial off-the-shelf
(COTS) communications systems in the tactical military environment.
However, there is rarely any quantitative evidence given to support this
understandable qualitative assertion. We propose a method for
quantitatively defining LPD that is based on well known principles of
communications theory and open sources of COTS system specifications.
Such a method of quantitatively defining LPD allows researchers working
in unclassified environments to consider the LPD characteristics of a
communications system while in the design phase, fair comparisons in LPD
characteristics between competing systems, and the potential for active
participation of the electronic warfare (EW) community in the up front
development of future tactical military communications systems