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arXiv · 0910.1121

LP Decoding meets LP Decoding: A Connection between Channel Coding and Compressed Sensing

Alexandros G. Dimakis·Pascal O. Vontobel
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Abstract

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.

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Alexandros G. Dimakis, Pascal O. Vontobel. 2009-10-06. LP Decoding meets LP Decoding: A Connection between Channel Coding and Compressed Sensing. https://arxiv.org/abs/0910.1121

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