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We consider the problem of covert communication over a state-dependent channel, for which the transmitter and the legitimate receiver have non-causal access to the channel state information. Covert communication with respect to an adversary, referred to as the “warden,” is one in which the distribution induced during communication at the channel output observed by the warden is identical to the output distribution conditioned on an inactive channel-input symbol. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver the codebook uncertainty is removed via a shared secret key that is unavailable to the warden. Unlike earlier work in state-dependent covert communication, we do not assume the availability of a shared key at the transmitter and legitimate receiver. Rather, a shared randomness is extracted at the transmitter and the receiver from the channel state, in a manner that keeps the shared randomness secret from the warden despite the influence of the channel state on the warden’s output. An inner bound on the covert capacity, in the absence of an externally provided secret key, is derived. 

We investigate the performance of discrete (coded) modulations in the full-duplex compress-forward relay channel using multilevel coding. We numerically analyze the rates assigned to component binary codes of all levels. LDPC codes are used as the component binary codes to provide error protection. The compression at the relay is done via a nested scalar quantizer whose output is mapped to a codeword through LDPC codes. A compound Tanner graphical model and information-exchange algorithm are described for joint decoding of both messages sent from the source and relay. Simulation results show that the performance of the proposed system based on multilevel coding is better than that based on BICM, and is separated from the SNR threshold of the known CF achievable rate by two factors consisting approximately of the sum of the shaping gain (due to scalar quantization) and the separation of the LDPC code implementation from AWGN capacity.