Error exponents of module-additive noise channels with side information atthe transmitter

Consider the optimum strategy for using channel state ("side") information in transmission over a module-additive noise channel, with state-dependent noise, where the receiver does not have access to the side information (SI) . Recent work showed that capacity-wise, the optimum transmitter shifts eac h code letter by a "prediction" of the noise sample based on the SI. We sho w that this structure achieves also the random-coding error exponent, and, therefore, is optimum at some range of rates below capacity. Specifically, the optimum transmitter predictor minimizes the Renyi entropy of the predic tion error; the Renyi order depends on the rate, and goes to one (correspon ding to Shannon entropy) for rates close to capacity. In contrast, it is sh own that this "prediction strategy" may not be optimal at low transmission rates.