Boosting reliability over AWGN networks with average power constraints and noiseless feedback

For the point-to-point additive white Gaussian noise (AWGN) channel with noiseless feedback and an average power constraint, Schalkwijk and Kailath's scheme achieves a doubly-exponential decay of the probability of error. While some coding schemes for networks with noiseless feedback incorporate variations on the Schalkwijk-Kailath scheme, they do not in general achieve better than single-exponential decays in their probabilities of error everywhere in their achievable rate regions. We give a technique that can boost the reliability as high as desired of any from a large class of block coding schemes for networks with feedback. The technique relies crucially on the average nature of the power constraints. We explain and illustrate our results in the context of Ozarow's feedback strategy for the AWGN multiple-access channel