Fast Sparse Superposition Codes have Exponentially Small Error   Probability for R < C
  For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. The paper [IEEE Trans. Inform. Theory 55 (2012), 2541 - 2557] investigated decoding using the optimal maximum-likelihood decoding scheme. Here a fast decoding algorithm, called adaptive successive decoder, is developed. For any rate R less than the capacity C communication is shown to be reliable with exponentially small error probability. 
Antony Joseph, Andrew Barron
cs.IT math.IT math.ST stat.TH