Linear complexity approximate LP decoding of LDPC codes: Generalizations and improvements

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Abstract

The iterative algorithm, for low complexity linear programming (LP) decoding of low-density parity-check (LDPC) codes, proposed by Vontobel and Koetter, is considered. In this paper the convergence rate and computational complexity of this algorithm are studied using a scheduling scheme that we propose. In particular we are interested in obtaining a feasible vector in the LP decoding problem, with objective function value whose distance to the minimum, normalized by the block length, can be made arbitrarily small. It is shown that such a feasible vector can be obtained with linear, in the block length, computational complexity. Improved bounds on the convergence rate are also presented. The results extend to generalized LDPC (GLDPC) codes. It is also shown that previous results for LDPC and GLDPC codes, on the ability of the LP decoder to correct some fixed fraction of errors, hold with linear computational complexity when using the approximate iterative LP decoder.

Original languageEnglish
Title of host publication2008 5th International Symposium on Turbo Codes and Related Topics, TURBOCODING
Pages31-36
Number of pages6
DOIs
StatePublished - 2008
Event2008 5th International Symposium on Turbo Codes and Related Topics, TURBOCODING - Lausanne, Switzerland
Duration: 1 Sep 20085 Sep 2008

Publication series

Name2008 5th International Symposium on Turbo Codes and Related Topics, TURBOCODING

Conference

Conference2008 5th International Symposium on Turbo Codes and Related Topics, TURBOCODING
Country/TerritorySwitzerland
CityLausanne
Period1/09/085/09/08

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