On the capacity of some channels with channel state information

In this paper we study the capacity of some channels whose conditional outp ut probability distribution depends on a state process independent of the c hannel input and where channel state information (CSI) signals are availabl e both at the transmitter (CSIT) and at the receiver (CSIR), When the chann el state and the CSI signals are jointly independent and identically distri buted (i.i.d.), the channel reduces to a case studied by Shannon, In this c ase, we show that when the CSIT is a deterministic function of the CSIR, op timal coding is particularly simple. When the state process has memory, we provide a general capacity formula and we give some more restrictive condit ions under which the capacity has still a simple single-letter characteriza tion, allowing simple optimal coding, Finally, we turn to the additive whit e Gaussian noise (AWGN) channel with fading and we provide a generalization of some results about capacity with CSI for this channel. In particular, w e show that variable-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.