Noise prediction for channels with side information at the transmitter

The computation of channel capacity with side information at the transmitter side (but not at the receiver side) requires, in general, extension of the input alphabet to a space of “strategies,” and is often hard. We consider the special case of a discrete memoryless modulo-additive noise channel = + , where the encoder observes causally the random state that governs the distribution of the noise . We show that the capacity of this channel is given by