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arXiv:2310.15519 · IEEE Transactions on Communications

Covert Communication With Gaussian Noise: From Random Access Channel to Point-to-Point Channel

Masahito Hayashi, M. A. Vázquez‐Castro

Published Nov 15, 2023• 9 citations
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Abstract

We propose a covert communication protocol for the spread-spectrum multiple random access with additive white Gaussian noise (AWGN) channel. No existing paper has studied covert communication for the random access channel. Our protocol assumes binary discrete phase-shift keying (BPSK) modulation, and it works well under imperfect channel state information (I-CSI) for both the legitimate and adversary receivers, which is a realistic assumption in the low power regime. Also, our method assumes that the legitimate users share secret variables in a similar way as the preceding studies. Although several studies investigated the covert communication for the point-to-point communication, no existing paper considers the covert communication under the above uncertainty assumption even for point-to-point communication. Our protocol under the above uncertainty assumption allowsO(n) legitimate senders andO(n/logn) active legitimate senders. Furthermore, our protocol can be converted to a protocol for point-to-point communication that works under the above uncertainty assumption.

DOI
10.1109/tcomm.2023.3332861

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We propose a covert communication protocol for the spread-spectrum multiple random access with additive white Gaussian noise (AWGN) channel. No existing paper has studied covert communication for the random access channel. Our protocol assumes binary discrete phase-shift keying (BPSK) modulation, and it works well under imperfect channel state information (I-CSI) for both the legitimate and adversary receivers, which is a realistic assumption in the low power regime. Also, our method assumes that the legitimate users share secret variables in a similar way as the preceding studies. Although several studies investigated the covert communication for the point-to-point communication, no existing paper considers the covert communication under the above uncertainty assumption even for point-to-point communication. Our protocol under the above uncertainty assumption allowsO(n) legitimate senders andO(n/logn) active legitimate senders. Furthermore, our protocol can be converted to a protocol for point-to-point communication that works under the above uncertainty assumption.
We consider the problem of covert communication over a state-dependent channel, where the transmitter has causal or noncausal knowledge of the channel states. Here, covert means that a warden on the channel should observe similar statistics when the transmitter is sending a message and when it is not. When a sufficiently long secret key is shared between the transmitter and the receiver, we derive closed-form formulas for the maximum achievable covert communication rate (covert capacity) for discrete memoryless channels and, when the transmitter's channel-state information (CSI) is noncausal, for additive white Gaussian noise (AWGN) channels. For certain channel models, including the AWGN channel, we show that the covert capacity is positive with CSI at the transmitter, but is zero without CSI. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.
This paper studies covert communication over channels with Action-Dependent State Information (ADSI) when the state is available either non-causally or causally at the transmitter. Covert communication refers to reliable communication between a transmitter and a receiver while ensuring a low probability of detection by an adversary, which we refer to as “warden”. It is well known that in a point-to-point Discrete Memoryless Channel (DMC), it is possible to communicate on the order ofN\sqrt {N}N​bits reliably and covertly over N channel uses while the transmitter and the receiver are required to share a secret key on the order ofN\sqrt {N}N​bits. This paper studies achieving reliable and covert communication of positive rate, i.e., reliable and covert communication on the order of N bits in N channel uses, over a channel with ADSI while the transmitter has non-causal or causal access to the ADSI, and the transmitter and the receiver share a secret key of negligible rate. We derive achievable rates for both the non-causal and causal scenarios by using block-Markov encoding and secret key generation from the ADSI, which subsumes the best achievable rates for channels with random states. We also derive upper bounds, for both non-causal and causal scenarios, that meet our achievable rates for some special cases. As an application of our problem setup, we study covert communication over channels with rewrite options, which are closely related to recording covert information on memory, and show that a positive covert rate can be achieved in such channels. As a special case of our problem, we study the Additive White Gaussian Noise (AWGN) channels and provide lower and upper bounds on the covert capacity that meet when the transmitter and the receiver share a secret key of sufficient rate and when the warden’s channel is noisier than the legitimate receiver channel. As another application of our problem setup, we show that cooperation can lead to a positive covert rate in Gaussian channels. A few other examples are also worked out in detail.
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.
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.
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.
The problem of covert communication over Multiple-Input Multiple-Output (MIMO) Additive White Gaussian Noise (AWGN) channels is investigated, in which a transmitter attempts to reliably communicate with a legitimate receiver while avoiding detection by a passive adversary. The covert capacity of the MIMO AWGN channel is characterized under a variational distance covertness constraint when the MIMO channel matrices are static and known. The characterization of the covert capacity is also extended to a class of channels in which the legitimate channel matrix is known but the adversary’s channel matrix is only known up to a rank and a spectral norm constraint.