Biblio

Covert communication, i.e., communication with a low probability of detection (LPD), has attracted a huge body of work. Recent studies have concluded that the maximal covert coding rate of the discrete memoryless channels and the additive white Gaussian noise (AWGN) channels is diminishing with the blocklength: the maximum information nats that can be transmitted covertly and reliably over such channels is only on the order of the square root of the blocklength. In this paper, we study covert communication over multiple-input multiple-output (MIMO) AWGN channels. We derive the order-optimal scaling law of the number of covert nats when the maximal covert coding rate of MIMO AWGN channels is diminishing with the blocklength. Furthermore, we provide a comparative discussion for the case in which secrecy and energy undetectability constraints are combined.

We propose a coding scheme for covert communication over additive white Gaussian noise channels, which extends a previous construction for discrete memoryless channels. We first show how sparse signaling with On-Off keying fails to achieve the covert capacity but that a modification allowing the use of binary phase-shift keying for "on" symbols recovers the loss. We then construct a modified pulse-position modulation scheme that, combined with multilevel coding, can achieve the covert capacity with low-complexity error-control codes. The main contribution of this work is to reconcile the tension between diffuse and sparse signaling suggested by earlier information-theoretic results.

We consider the problem of covert communication over a state-dependent channel, where the transmitter has non-causal knowledge of the channel states. Here, “covert” means that the probability that a warden on the channel can detect the communication must be small. In contrast with traditional models without noncausal channel-state information at the transmitter, we show that covert communication can be possible with positive rate. We derive closed-form formulas for the maximum achievable covert communication rate (“covert capacity”) in this setting for discrete memoryless channels as well as additive white Gaussian noise channels. 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.