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In this paper, we characterize the informationtheoretic capacity scaling of wireless ad hoc networks with n randomly distributed nodes. By using an exact channel model from Maxwell's equations, we successfully resolve the conflict in the literature between the linear capacity scaling byÖzgür et al. and the degrees of freedom limit given as the ratio of the network diameter and the wavelength λ by Franceschetti et al. In dense networks where the network area is fixed, the capacity scaling is given as the minimum of n and the degrees of freedom limit λ −1 to within an arbitrarily small exponent. In extended networks where the network area is linear in n, the capacity scaling is given as the minimum of n and the degrees of freedom limit √ nλ −1 to within an arbitrarily small exponent. Hence, we recover the linear capacity scaling byÖzgür et al. if λ = O(n −1 ) in dense networks and if λ = O(n −1/2 ) in extended networks. Otherwise, the capacity scaling is given as the degrees of freedom limit characterized by Franceschetti et al. For achievability, a modified hierarchical cooperation is proposed based on a lower bound on the capacity of multiple-input multiple-output channel between two node clusters using our channel model. Index Terms-Capacity scaling, channel correlation, cooperative multiple-input multiple-output (MIMO), degrees of freedom, hierarchical cooperation, Maxwell's equations, physical limit, wireless ad hoc networks.

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.

We consider streaming data transmission over a discrete memoryless channel. A new message is given to the encoder at the beginning of each block and the decoder decodes each message sequentially, after a delay of T blocks. In this streaming setup, we study the fundamental interplay between the rate and error probability in the central limit and moderate deviations regimes and show that i) in the moderate deviations regime, the moderate deviations constant improves over the block coding or non-streaming setup by a factor of T and ii) in the central limit regime, the second-order coding rate improves by a factor of approximately √ T for a wide range of channel parameters. For both regimes, we propose coding techniques that incorporate a joint encoding of fresh and previous messages. In particular, for the central limit regime, we propose a coding technique with truncated memory to ensure that a summation of constants, which arises as a result of applications of the central limit theorem, does not diverge in the error analysis.Furthermore, we explore interesting variants of the basic streaming setup in the moderate deviations regime. We first consider a scenario with an erasure option at the decoder and show that both the exponents of the total error and the undetected error probabilities improve by factors of T . Next, by utilizing the erasure option, we show that the exponent of the total error probability can be improved to that of the undetected error probability (in the order sense) at the expense of a variable decoding delay.Finally, we also extend our results to the case where the message rate is not fixed but alternates between two values.

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