On the capacity of some channels with channel state information

In this paper we study the capacity of some channels whose conditional output probability distribution depends on a state process independent of thechannel input and where channel state information (CSI) signals are available both at the transmitter (CSIT) and at the receiver (CSIR). When the channel state and the CSI signals are jointly i.i.d., the channel reduces to a case studied by Shannon. In this case, we show that when the CSIT is a deterministic function of the CSIR, optimal coding is particularly simple. When the state process has memory, we provide a general capacity formula and we give some more restrictive conditions under which the capacity has still a simple single-letter characterization, allowing simple optimal coding. Finally, we turn to the AWGN channel with fading and we provide a generalization of some results about capacity with CSI for this channel. In particular, we show thatvariable-rate coding (or multiplexing of several codebooks) is not needed to achieve capacity and, even when the CSIT is not perfect, the capacity achieving power allocation is of the waterfilling type.