On the random coding exponent of nonlinear gaussian channels

A random coding theorem for nonlinear additive gaussian channels is presented. Modeling the channel's nonlinear behavior as a causal, stationary Volterra system and under maximum likelihood decoding, an upper bound on the average error probability is obtained. The proposed bound is deduced by deploying exponential martingale inequalities. Cubic nonlinearities are used as example to illustrate the validity of the random coding exponent and the usefulness of the proposed technique in the treatment of nonlinear channels.