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Sparse superposition codes are developed for the additive white Gaussian noise channel with average codeword power constraint. Codewords are linear combinations of subsets of vectors, with the possible messages indexed by the choice of subset. Decoding is by least squares, tailored to the assumed form of linear combination. Communication is shown to be reliable with error probability exponentially...
For the additive Gaussian noise channel with average codeword power constraint, sparse superposition codes and adaptive successive decoding is developed. Codewords are linear combinations of subsets of vectors, with the message indexed by the choice of subset. A feasible decoding algorithm is presented. Communication is reliable with error probability exponentially small for all rates below the Shannon...
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