Capacity-achieving Feedback Scheme for Gaussian Finite-State Markov Channels with Channel State Information

In this paper, we propose capacity-achieving communication schemes for Gaussian finite-state Markov channels (FSMCs) subject to an average channel input power constraint, under the assumption that the transmitters can have access to delayed noiseless output feedback as well as instantaneous or delayed channel state information (CSI). We show that the proposed schemes reveals connections between feedback communication and feedback control.