LP decoding meets LP decoding: A connection between channel coding and compressed sensing

This is a tale of two linear programming decoders, namely channel coding linear programming decoding (CC-LPD) and compressed sensing linear programming decoding (CS-LPD). So far, they have evolved quite independently. The aim of the present paper is to show that there is a tight connection between,...

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Bibliographic Details
Published in2009 47th Annual Allerton Conference on Communication, Control, and Computing pp. 8 - 15
Main Authors Dimakis, A.G., Vontobel, P.O.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2009
Subjects
Channel coding
Compressed sensing
Decoding
Error correction
Linear code
Linear programming
Noise robustness
Parity check codes
Sparse matrices
Symmetric matrices
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ISBN9781424458707
1424458706
DOI10.1109/ALLERTON.2009.5394826

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Summary:This is a tale of two linear programming decoders, namely channel coding linear programming decoding (CC-LPD) and compressed sensing linear programming decoding (CS-LPD). So far, they have evolved quite independently. The aim of the present paper is to show that there is a tight connection between, on the one hand, CS-LPD based on a zero-one measurement matrix over the reals and, on the other hand, CC-LPD of the binary linear code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows one to translate performance guarantees from one setup to the other.
ISBN:9781424458707
1424458706
DOI:10.1109/ALLERTON.2009.5394826