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Using linear programming to decode binary linear codes (2005)
| Venue: | IEEE TRANS. INFORM. THEORY |
| Citations: | 183 - 9 self |
BibTeX
@ARTICLE{Feldman05usinglinear,
author = {Jon Feldman and Martin J. Wainwright and David R. Karger},
title = {Using linear programming to decode binary linear codes},
journal = {IEEE TRANS. INFORM. THEORY},
year = {2005},
volume = {51},
number = {3},
pages = {954--972}
}
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Abstract
A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting “LP decoder” generalizes our previous work on turbo-like codes. A precise combinatorial characterization of when the LP decoder succeeds is provided, based on pseudocodewords associated with the factor graph. Our definition of a pseudocodeword unifies other such notions known for iterative algorithms, including “stopping sets, ” “irreducible closed walks, ” “trellis cycles, ” “deviation sets, ” and “graph covers.” The fractional distance ��— ™ of a code is introduced, which is a lower bound on the classical distance. It is shown that the efficient LP decoder will correct up to ��— ™ P I errors and that there are codes with ��— ™ a @ I A. An efficient algorithm to compute the fractional distance is presented. Experimental evidence shows a similar performance on low-density parity-check (LDPC) codes between LP decoding and the min-sum and sum-product algorithms. Methods for tightening the LP relaxation to improve performance are also provided.
Keyphrases
linear programming binary linear code fractional distance factor graph lp decoder new method deviation set lp relaxation graph cover precise combinatorial characterization efficient algorithm parity-check representation classical distance previous work low-density parity-check sum-product algorithm experimental evidence similar performance efficient lp decoder arbitrary binary linear code iterative algorithm turbo-like code trellis cycle approximate maximum-likelihood discrete memoryless symmetric channel
