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.
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.
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 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 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) 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 works have considered the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. These works generally assume a standard discrete-time model. But the assumption of a discrete-time model in standard communication scenarios is often predicated on its equivalence to a continuous-time model, which has not been established for the covert communications problem. Here, we consider the continuous-time channel directly and study if efficient covert communication can still be achieved. We assume that an uninformed jammer is present to assist Alice, and we consider additive white Gaussian noise (AWGN) channels between all parties. For a channel with approximate bandwidth W, we establish constructions such that O(WT) information bits can be transmitted covertly and reliably from Alice to Bob in T seconds for two separate scenarios: 1) when the path-loss between Alice and Willie is known; and 2) when the path-loss between Alice and Willie is unknown.
Covert communication, also known as low probability of detection (LPD) communication, prevents the adversary from knowing that a communication is taking place. Recent work has demonstrated that, in a three-party scenario with a transmitter (Alice), intended recipient (Bob), and adversary (Warden Willie), the maximum number of bits that can be transmitted reliably from Alice to Bob without detection by Willie, when additive white Gaussian noise (AWGN) channels exist between all parties, is on the order of the square root of the number of channel uses. In this paper, we begin consideration of network scenarios by studying the case where there are additional “friendly” nodes present in the environment that can produce artificial noise to aid in hiding the communication. We establish achievability results by considering constructions where the system node closest to the warden produces artificial noise and demonstrate a significant improvement in the throughput achieved covertly, without requiring close coordination between Alice and the noise-generating node. Conversely, under mild restrictions on the communication strategy, we demonstrate no higher covert throughput is possible. Extensions to the consideration of the achievable covert throughput when multiple wardens randomly located in the environment collaborate to attempt detection of the transmitter are also considered.
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(√n) bits can be sent from the transmitter to the receiver in n channel uses while lower-bounding α + β ≥ 1-ε for any ε > 0, where α and β 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(√n) bits can be sent in n LPD channel uses. Conversely, attempting to transmit more than O(√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→∞.
Covert communication conceals the transmission of the message from an attentive adversary. Recent work on the limits of covert communication in additive white Gaussian noise channels has demonstrated that a covert transmitter (Alice) can reliably transmit a maximum of O(√n) bits to a covert receiver (Bob) without being detected by an adversary (Warden Willie) in n channel uses. This paper focuses on the scenario where other “friendly” nodes distributed according to a two-dimensional Poisson point process with density m are present. We propose a strategy where the friendly node closest to the adversary, without close coordination with Alice, produces artificial noise. We show that this method allows Alice to reliably and covertly send O(min{n, mγ/2√n}) bits to Bob in n channel uses, where γ is the path-loss exponent. We also consider a setting where there are Nw collaborating adversaries uniformly and randomly located in the environment and show that in n channel uses, Alice can reliably and covertly send O(min{n, (mγ/2√n/Nwγ)}) bits to Bob when γ>2, and O(min{n, (m√n/Nw2log2Nw)}) when γ=2. Conversely, we demonstrate that no higher covert throughput is possible for γ>2.