Error exponents of modulo-additive noise channels with side information at the transmitter

Consider the optimum strategy for using channel state ("side") information in transmission over a modulo-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 each code letter by a "prediction" of the noise sample based on the SI. We show 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 Rényi entropy of the prediction error; the Rényi order depends on the rate, and goes to one (corresponding to Shannon entropy) for rates close to capacity. In contrast, it is shown that this "prediction strategy" may not be optimal at low transmission rates.