Finite-State Channel with Feedback and Causal State Information Available at the Encoder

We study a general finite-state channel (FSC) with the state being available to the encoder (causally) and output received from feedback. The FSC family is rich and includes, for instance, a channel with a Markovian state, in which the state has memory and is input-independent, and also cases, such as the energy harvesting model, where the state is input-dependent. For this general setting, we derive a new achievable rate. It is then shown that the achievable rate can be formulated as an infinite-horizon average-reward Markov decision process (MDP). The MDP formulation constitutes a rigorous tool to numerically compute and analytically prove achievable rates. Our achievable rate for the noiseless binary energy harvesting channel (BEHC) is comparable to existing achievable rates. Our scheme works for the noisy BEHC with feedback, and to the best of our knowledge, this is the first achievable rate given for that channel. Furthermore, our achievable rate achieves the capacity of two known unifilar FSCs with feedback, i.e., the trapdoor channel and the input-constrained binary erasure channel (BEC).