Sparse Superposition Codes: Fast and Reliable at Rates Approaching Capacity with Gaussian Noise

For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. Both encoding and decoding are computationally feasible. The codewords are linear combinations of subsets of vectors from a given dictionary, with the possible messages indexed by the choice of subset. An adaptive successive decoder is developed, with which communication is shown to be reliable with error probability exponentially small for all rates below the Shannon capacity.