Least Squares Superposition Codes of Moderate Dictionary Size, Reliable at Rates up to Capacity

Details Least Squares Superposition Codes of Moderate Dictionary Size, Reliable at Rates up to Capacity Least Squares Superposition Codes of Moderate Dictionary Size, Reliable at Rates up to Capacity

2010-06-18

arxiv.org/abs/1006.3780v1

Computer Science

Information Theory

17 pages, 4 figures, journal submission

Scientific paper

For the additive white Gaussian noise channel with average codeword power constraint, new coding methods are devised in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design, 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 small for all rates up to the Shannon capacity.

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