On the capacity of some channels with channel state information

Channels whose output conditional probability depends on a time-varying state have been widely studied. Depending on the assumptions on the channel state and on the availability of channel state information (CSI) at the transmitter and at the receiver, a whole range of problems rises, each related to some physical situation of interest. Driven by the growing interest in mobile wireless communications, numerous works have been devoted to assessing the information theoretic limits of Gaussian fading channels, which can be modeled as the continuous counterpart of the discrete channels. We deal with channels with causal transmitter CSI. In general, capacity achieving codes are constructed over an extended alphabet of functions (usually indicated as strategies) that map sequences of transmitter CSI values onto input symbols. Here, we are interested in finding conditions such that the capacity achieving codes can be constructed directly on the channel input alphabet