Approximate iterative bayes optimal estimates for high-rate sparse superposition codes

This paper is concerned with sparse superposition codes with iterative term selection for additive white Gaussian noise channel with power control. In particular, we consider a soft decision decoder with Bayes optimal estimates at each step, presuming uniform prior on the choice of the terms that are sent. Bayes optimal estimates are formulated and shown to have a Martingale property that provides alternative representations of a posterior probability of error. Since the Bayes optimal estimates are infeasible, an approximation method is suggested. We analyze the performance of the approximation method in comparison with the infeasible estimates.