An Efficient Pseudocodeword Search Algorithm for Linear Programming Decoding of LDPC Codes
Chertkov, M.
Stepanov, M.G.
Los Alamos Nat. Lab. (LANL), Los Alamos;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: April 2008
Volume: 54,
Issue: 4
On page(s): 1514-1520
ISSN: 0018-9448
INSPEC Accession Number: 9943627
Digital Object Identifier: 10.1109/TIT.2008.917682
Current Version Published: 2008-03-21
Abstract
In linear programming (LP) decoding of a low-density parity-check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords. In order to quantify LP decoding it is important to study vertexes of the relaxed polytope, so-called pseudocodewords. We propose a technique to heuristcally create a list of pseudocodewords close to the zero codeword and their distances. Our pseudocodeword-search algorithm starts by randomly choosing configuration of the noise. The configuration is modified through a discrete number of steps. Each step consists of two substeps: one applies an LP decoder to the noise-configuration deriving a pseudocodeword, and then finds configuration of the noise equidistant from the pseudocodeword and the zero codeword. The resulting noise configuration is used as an entry for the next step. The iterations converge rapidly to a pseudocodeword neighboring the zero codeword. Repeated many times, this procedure is characterized by the distribution function of the pseudocodeword effective distance. The efficiency of the procedure is demonstrated on examples of the Tanner code and Margulis codes operating over an additive white Gaussian noise (AWGN) channel.
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