On the rate-limited Gelfand-Pinsker problem

We study a rate-limited version of the well known problem of coding for channels with random parameters which was studied by Gelfand and Pinsker [1]. In particular, we consider a state-dependent channel when the transmitter is supplied with the state information at a rate R_e. We obtain a new upper bound on the capacity, C(R_e), for this channel. We explicitly evaluate this upper bound for the rate-limited dirty paper coding (DPC) problem and show that it strictly improves upon the DPC capacity for certain values of R_e.