We consider the problem of coding to ensure covert communication, which involves ensuring reliable communication between two legitimate parties while simultaneously guaranteeing a low probability of detection by an eavesdropper. Specifically, we develop an optimal low-complexity coding scheme that achieves the information-theoretic limits of covert communications over binary-input discrete memoryless channels (BI-DMCs). To justify our design, we first consider a regime in which information theory proves the possibility of covert communication without shared secret key and show the impossibility of achieving information-theoretic limits using linear codes without secret key. We then circumvent this impossibility by introducing non-linearity into the coding scheme through the use of pulse position modulation (PPM) and multilevel coding (MLC). This MLC-PPM scheme exhibits several appealing properties; in particular, for an appropriate decoder, the channel at a given level is independent of the total number of levels and the codeword length. We exploit these properties to show how one can use families of channel capacity- and channel resolvability-achieving codes to concretely instantiate a covert communication scheme.

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 propose a forward reconciliation algorithm for covert key generation based on pulse-position modulation (PPM) and multilevel coding (MLC) with multistage decoding (MSD). This multilevel scheme not only allows one to concentrate the diffuse information content of the sparse signals used for covertness but also enables the use of independent codes at each level designed for stationary channels. In particular, we show that polar codes offer a low-complexity reconciliation-capacity achieving solution.

We develop a low-complexity coding scheme to achieve covert communications over binary symmetric channels. We circumvent the impossibility of covert communication with linear codes by introducing non-linearity through the use of pulse-position modulation (PPM) and multilevel coding (MLC). We show that the MLC-PPM scheme exhibits many appealing properties, in particular, the channel at a given index level remains the same as the number of level increases, which allows one to use families of capacity- and resolvability-achieving codes to concretely instantiate the covert communication scheme.

To achieve strong coordination in a network, nodes benefit from access to a source of common randomness. Most studies pertaining to strong coordination assume the existence of a source of common randomness accessible to all nodes in the network. This assumption, however, is not practical in a decentralized network. We analyze the problem of strong coordination in a three-terminal line network with common randomness available only at the first two nodes and assume that the actions of the first node are specified by an external agent. We use coding schemes developed for channel resolvability codes to characterize the strong coordination capacity region when the intermediate node is operating in a functional mode. A comparison of our coordination capacity region with a case in which all nodes have access to a common randomness shows that we have to increase the communication rate between the second and the third nodes to achieve the same coordination distribution.