4.5 Article

Decoding by linear programming

Journal

IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 51, Issue 12, Pages 4203-4215

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2005.858979

Keywords

basis pursuit; decoding of (random) linear codes; duality in optimization; Gaussian random matrices; l(1) minimization; linear codes; linear programming; principal angles; restricted orthonormality; singular values of random matrices; sparse solutions to underdetermined systems

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This paper considers a natural error correcting problem with real valued input/output. We wish to recover an input vector f is an element of R-n from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y?

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