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 derives upper and lower bounds on the capacity of the multiple-input single-output free-space optical intensity channel with signal-independent additive Gaussian noise subject to both an average-intensity and a peak-intensity constraint. In the limit where the signal-to-noise ratio (SNR) tends to infinity, the asymptotic capacity is specified, while in the limit where the SNR tends to zero, the exact slope of the capacity is given.

This paper studies the capacity of a general multiple-input multiple-output (MIMO) free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. The focus is on the scenario with more transmit than receive antennas. In this scenario, different input vectors can yield identical distributions at the output, when they result in the same image vector under multiplication by the channel matrix. We first determine the most energy-efficient input vectors that attain each of these image vectors. Based on this, we derive an equivalent capacity expression in terms of the image vector, and establish new lower and upper bounds on the capacity of this channel. The bounds match when the signal-to-noise ratio (SNR) tends to infinity, establishing the high-SNR asymptotic capacity. We also characterize the low-SNR slope of the capacity of this channel.

We consider the problem of communication over a continuous-time Poisson channel subject to a covertness constraint: The relative entropy between the output distributions when a message is transmitted and when no input is provided must be small. In the absence of both bandwidth and peak-power constraints, we show the covert communication capacity of this channel, in nats per second, to be infinity. When a peak-power constraint is imposed on the input, the covert communication capacity becomes zero, and the “square-root scaling law” applies. When a bandwidth constraint but no peak-power constraint is imposed, the covert communication capacity is again shown to be zero, but we have not determined whether the square-root law holds or not.

Consider the problem of distributed binary hypothesis testing with two terminals, where the decision is made at one of them (the “receiver”). We study the exponent of the error probability of the second type. Previously, an achievable exponent was derived by Shimokawa, Han, and Amari using a “quantization and binning” scheme. We propose a simple modification on the receiver’s decision rule in this scheme to attain a better exponent.