An Efficient Pseudocodeword Search Algorithm for Linear Programming Decoding of LDPC Codes

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 heuristically 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 code...

• Type: Journal
• Year: 2008
• Where: TIT
• Authors: Michael Chertkov, Mikhail G. Stepanov
• Keywords: Codeword, Low-density Parity-check, Relaxed Polytope, TIT 2008