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IEEE Transactions on Information Forensics and Security

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

Shihao Yan, Biao He, Xiangyun Zhou, Yirui Cong, Arnold Lee Swindlehurst

Published Jun 11, 2018• 263 citations
Publisher

Abstract

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.

DOI
10.1109/tifs.2018.2846257

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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.
Covert communication has recently been recognized as a highly promising security technology that enables a transmitter Alice to reliably and covertly communicate with a receiver Bob without being detected by a malicious warden. Available works on covert communication mainly focus on scenarios with only one warden, while the fundamental limits of covert communication in more practical multi-warden scenarios remain largely unknown. This paper therefore investigates the fundamental limits of covert communication over an additive white Gaussian noise (AWGN) channel in the presence of multiple wardens. We first consider a scenario with two wardens and derive the maximum number of bits Alice can transmit to Bob over n channel uses while ensuring a negligible detection probability at wardens. We then generalize this result to the multi-warden case and find that the minimal power of wardens has impacts on the scaling law of the performance limits of covert communication over AWGN channels.
In this letter, we consider delay-constrained covert communications with the aid of a full-duplex (FD) receiver. Without delay constraints, it has been shown that the transmit power of artificial noise (AN) at the FD receiver should be random in order to enhance covert communications. In this letter, we show that transmitting AN with a fixed power indeed improve covert communications with delay constraints, since in a limited time period the warden cannot exactly learn its received power. This explicitly shows one benefit of considering practical delay constraints in the context of covert communications. We analyze the optimal transmit power of AN for either fixed or globally optimized transmit power of covert information, based on which we also determine the specific condition under which transmitting AN by the FD receiver can aid covert communications and a larger transmit power of AN always leads to better covert communication performance.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this assumes that Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with n, thus conveying O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of O(n) bits in n channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume that an uninformed “jammer” is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with n even when Willie employs an optimal detector.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(n)\mathcal{O}(\sqrt{n})O(n​) bits in nnn channel uses. However, this assumes Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with nnn, thus conveying O(n)\mathcal{O}(n)O(n) bits covertly and reliably in nnn uses of an AWGN channel. Here, we consider covert communication of O(n)\mathcal{O}(n)O(n) bits in nnn channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume an uninformed "jammer" is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with nnn even when Willie employs an optimal detector.
This paper investigates the achievable message transmission rate of covert communication over slow fading channels where the channel coefficient remains unchanged over a finite transmission block. Such communication is often implemented with an extremely low transmission power aiming to achieve low probability of detection by the eavesdropper and under tolerable probability of decoding error for the legitimate receiver. The exact expression of achievability and asymptotic covert bounds are derived, which are shown in accordance with the square root law in AWGN (Additive White Gaussian Noise) channels with large transmission blocks. The case that the eavesdropper has unknown channel state information is also studied in the paper.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this result is predicated on Willie having an accurate statistical characterization of the background noise. When Willie has uncertainty about his noise characteristics and his receiver is limited to a power detector, O(n) bits can be covertly delivered. Here, we establish covert communication of O(n) bits in n channel uses while: (i) generalizing the environment; and (ii) removing any restrictions on Willie's receiver. We consider the case where an additional node, called the "jammer", is present to help Alice and Bob communicate covertly. This jammer is termed "uninformed", as it does not know the content or timing of Alice's transmission. We consider both AWGN channels and a scenario with a block faded jammer with a single fade per codeword. In these scenarios, we are able to establish the optimality of the power detector for Willie, from which the achievability of reliable and covert communication at a positive rate follows.