New capacity upper bounds and coding aspects for some channels with causal CSIT

We study two channels with causal CSIT: a finite state channel with input constraints and a finite-battery energy harvesting channel, considered in [1] and for the latter [2]–[5]. The capacity of these channels remains open and the calculation of the upper bounds often has a complexity double exponential in the block size N. In this paper we obtain an alternative upper bound which has a complexity linear in N. While, for any N, this bound is looser than the bound in [1], since it can be readily computed for very large values of N, it leads to numerically tighter bounds in many cases. Furthermore, for the energy harvesting channel we calculate the pairwise error probabilities of the ML decoder, which provides a useful guideline for the code design.