Least Squares Superposition Codes of Moderate Dictionary Size Are Reliable at Rates up to Capacity
Authors:
Top Cited Papers
- 31 January 2012
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 58 (5) , 2541-2557
Abstract
For the additive white Gaussian noise channel with average codeword power constraint, coding methods are analyzed 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 (maximum likelihood), tailored to the assumed form of codewords being linear combinations of elements of the design. Communication is shown to be reliable with error probability exponentially small for all rates up to the Shannon capacity.Keywords
All Related Versions
This publication has 58 references indexed in Scilit:
- False Discovery Rate Control With GroupsJournal of the American Statistical Association, 2010
- Norms of random submatrices and sparse approximationComptes Rendus Mathematique, 2008
- For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solutionCommunications on Pure and Applied Mathematics, 2006
- Decoding by Linear ProgrammingIEEE Transactions on Information Theory, 2005
- An iterative thresholding algorithm for linear inverse problems with a sparsity constraintCommunications on Pure and Applied Mathematics, 2004
- Uncertainty principles and ideal atomic decompositionIEEE Transactions on Information Theory, 2001
- Matching pursuits with time-frequency dictionariesIEEE Transactions on Signal Processing, 1993
- A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network TrainingThe Annals of Statistics, 1992
- Broadcast channelsIEEE Transactions on Information Theory, 1972
- Probability Inequalities for Sums of Bounded Random VariablesJournal of the American Statistical Association, 1963