A Constrained Channel Coding Approach to Joint Communication and Channel Estimation

A joint communication and channel state estimation problem is investigated, in which reliable information transmission over a noisy channel, and high-fidelity estimation of the channel state, are simultaneously sought. The tradeoff between the achievable information rate and the estimation distortion is quantified by formulating the problem as a constrained channel coding problem, and the resulting capacity-distortion function characterizes the fundamental limit of the joint communication and channel estimation problem. The analytical results are illustrated through case studies, and further issues such as multiple cost constraints, channel uncertainty, and capacity per unit distortion are also briefly discussed.Comment: Submitted to ISIT 200

Joint Transmission and State Estimation: A Constrained Channel Coding Approach

A scenario involving a source, a channel, and a destination, where the destination is interested in {\em both} reliably reconstructing the message transmitted by the source and estimating with a fidelity criterion the state of the channel, is considered. The source knows the channel statistics, but is oblivious to the actual channel state realization. Herein it is established that a distortion constraint for channel state estimation can be reduced to an additional cost constraint on the source input distribution, in the limit of large coding block length. A newly defined capacity-distortion function thus characterizes the fundamental tradeoff between transmission rate and state estimation distortion. It is also shown that non-coherent communication coupled with channel state estimation conditioned on treating the decoded message as training symbols achieves the capacity-distortion function. Among the various examples considered, the capacity-distortion function for a memoryless Rayleigh fading channel is characterized to within 1.443 bits at high signal-to-noise ratio. The constrained channel coding approach is also extended to multiple access channels, leading to a coupled cost constraint on the input distributions for the transmitting sources

Communication over Quantum Channels with Parameter Estimation

Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also when CSI is not available. This model can be viewed as a form of quantum metrology, and as the quantum counterpart of the classical rate-and-state channel with state estimation at the decoder. Regularized formulas for the capacity-distortion regions are derived. In the special case of measurement channels, single-letter characterizations are derived for the strictly causal and causal settings. Furthermore, in the more general case of entanglement-breaking channels, a single-letter characterization is derived when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results by Boche et al. (2016) on classical-quantum channels. Bosonic dirty paper coding is introduced as a consequence, where we demonstrate that the optimum is not necessarily the MMSE estimator coefficient as in the classical setting