We consider the fundamental limits of reliable communication over a two-state compound channel when the state of the channel needs to be masked. Our model is closely related to an area of study known as covert communication, a setting in which the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. Our main contribution is the establishment of upper and lower bounds on the throughput-key length region when the constraint that quantifies how much the states are masked is defined to be the total variation distance between the channel output distributions of the two states. When length of the key is sufficiently large, we provide sufficient conditions for the bounds to coincide. Our results follow the so-called square-root law and hence are reminiscent of results in covert communications. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.
We consider the fundamental limits of reliable communication over a two-state compound channel when the state of the channel needs to be masked. Our model is closely related to an area of study known as covert communication, a setting in which the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. Our main contribution is the establishment of upper and lower bounds on the throughput-key length region when the constraint that quantifies how much the states are masked is defined to be the total variation distance between the channel output distributions of the two states. When length of the key is sufficiently large, we provide sufficient conditions for the bounds to coincide. Our results follow the so-called square-root law and hence are reminiscent of results in covert communications. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.
In this paper, we consider fundamental communication limits over a compound channel. Covert communication in the information-theoretic context has been primarily concerned with fundamental limits when the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. This paper, however, considers an alternative, and no less important, setting in which the object to be masked is the state of the compound channel. Such a communication model has applications in the prevention of malicious parties seeking to jam the communication signal when, for example, the signal-to-noise ratio of a wireless channel is found to be low. Our main contribution is the establishment of bounds on the throughput-key region when the covertness constraint is defined in terms of the total variation distance. In addition, for the scenario in which the key length is infinite, we provide a sufficient condition for when the bounds coincide for the scaling of the throughput, which follows the square-root law. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.
In this paper, we study covert communication over a compound discrete memoryless channel (DMC). There are two channel states in which one of them is arbitrarily chosen and remains fixed during the transmission. The objective is to reliably send a message from the transmitter to the receiver. An adversary who is observing the channel output should not be able to infer the channel state. Two covertness metrics are considered. In the first metric, covertness is measured using the KL-divergence of the channel output marginal of each state with a fixed distribution. Different cases where such a distribution can be specified, are studied. The optimal transmission rate of each case is established. In the second metric, the covertness is measured by using the total variation distance of the channel output marginals of the two states. Upper and lower bounds on the optimal transmission covert rate are derived. The bounds match for a special case and characterize the optimal throughput.
Physical-layer security aims to exploit the randomness inherent in communication channels in order to guarantee confidentiality even against computationally unlimited attackers. In this thesis, we focus on covert communication, also known as “communication with low probability of detection”. This is a scenario where a transmitter and receiver try to prevent an eavesdropper from making a good guess on whether a communication is ongoing or not. We assume that the receiver and the eavesdropper share the same channel and therefore see the same outputs. In this scenario, the transmitter shares a key with the legitimate receiver to provide the necessary advantage to detect the communication and reliably decode the message. Asymptotically, the amount of information that can be sent reliably and covertly scales like the square root of the number of channel uses; this is known as the square root law of covert communication.We study the corresponding scaling constant of the square root law for general memoryless channels including non-Gaussian additive noise, as well as Gaussian channels with memory. In the latter case, we show that the scaling constant is the same as over the memoryless Gaussian channel. For continuous memoryless channels, under mild integrability conditions, we show that the scaling constant is upper bounded by a simple expression which only involves the variance of the logarithm of the probability density function of the noise. Moreover, we show that under some additional assumptions, this upper bound is tight. Furthermore, we provide upper bounds on the length of the secret key required to achieve covertness.The second objective of this work is to investigate the limits of covert communication over continuous memoryless channels in the finite blocklength regime. We provide bounds for the first and second-order asymptotics for covert communication over an AWGN channel under a maximal error probability criterion and for the first-order asymptotics under an average error probability criterion.
We explore covert communication of qubits over an arbitrary quantum channel. Covert communication conceals the transmissions in the channel noise, ensuring that an adversary is unable to detect their presence. We show the achievability of a square root law (SRL) for quantum covert communication similar to that for classical:M(n)nqubits can be transmitted covertly and reliably overnuses of a general quantum channel. We lower boundM(n)with and without assistance from a two-way covert classical channel. In the former case, we quantify the number of classical covert bits sufficient for our protocol.
We consider the problem of covert communication over a state-dependent channel when the Channel State Information (CSI) is available either non-causally, causally, or strictly causally, either at the transmitter alone, or at both transmitter and receiver. Covert communication with respect to an adversary, called “warden,” is one in which, despite communication over the channel, the warden’s observation remains indistinguishable from an output induced by innocent channel-input symbols. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver, the codebook uncertainty is typically removed via a shared secret key that is unavailable to the warden. In contrast to previous work, we do not assume the availability of a large shared key at the transmitter and legitimate receiver. Instead, we only require a secret key with negligible rate to bootstrap the communication and our scheme extracts shared randomness from the CSI in a manner that keeps it secret from the warden, despite the influence of the CSI on the warden’s output. When CSI is available at the transmitter and receiver, we derive the covert capacity region. When CSI is only available at the transmitter, we derive inner and outer bounds on the covert capacity. We also provide examples for which the covert capacity is positive with knowledge of CSI but is zero without it.
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.