LP Decoding meets LP Decoding: A Connection between Channel Coding and Compressed Sensing
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.
Cite
@article{arxiv.0910.1121,
title = {LP Decoding meets LP Decoding: A Connection between Channel Coding and Compressed Sensing},
author = {Alexandros G. Dimakis and Pascal O. Vontobel},
journal= {arXiv preprint arXiv:0910.1121},
year = {2009}
}
Comments
Appeared in the Proceedings of the 47th Allerton Conference on Communications, Control, and Computing, Allerton House, Monticello, Illinois, USA, Sep. 30 - Oct. 2, 2009. This version of the paper contains all the proofs that were omitted in the official version due to space limitations