with Side Information at the Transmitter

The basic problem that we will be looking at can be described as follows and is illustrated in Figure 1. The overall objective (as usual) is to reliably communicate a message m ∈ {1, . . . , 2nR} from the encoder to the decoder using the channel n times. The largest rate R for which this is possible is called the capacity of the channel. The channel that we can use is described by a conditional probability distribution p(y|x, s), where x ∈ X is the input to the channel, s ∈ S is the state of the channel, and y ∈ Y is the output of the channel. Initially, we will assume that the sets X , S, and Y are finite. The states of the channel are generated in an IID fashion using a given distribution p(s). The encoder uses his knowledge of the channel state and the message M to be