High-rate sparse superposition codes with iteratively optimal estimates

Recently sparse superposition codes with iterative term selection have been developed which are mathematically proven to be fast and reliable at any rate below the capacity for the additive white Gaussian noise channel with power control. We improve the performance using a soft decision decoder with Bayes optimal statistics at each iteration, followed by thresholding only at the final step. This presentation includes formulation of the statistics, proof of their distributions, numerical simulations of the performance improvement, and useful identities relating a squared error risk to a posterior probability of error.