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Allerton Conference on Communication, Control, and Computing

Efficient implementation of linear programming decoding

Mohammad Hossein Taghavi, Amin Shokrollahi, Paul H. Siegel

Published Sep 1, 2008• 11 citations
Publisher

Abstract

This paper explores ideas for fast linear programming (LP) decoding of low-density parity-check (LDPC) codes. We first propose a modification of adaptive LP decoding, and prove that it performs LP decoding by solving a number of linear programs that contain at most one linear constraint derived from each of the parity-check constraints. Then, as a step toward designing an efficient LP solver that exploits the structure of LDPC codes, we study a sparse interior-point implementation for solving this sequence of linear programs. Since the most complex part of each iteration of the interior-point algorithms is to solve a (usually ill-conditioned) system of linear equations for finding the step direction, we propose a framework for designing preconditioners to be used with the iterative methods for solving these systems. The effectiveness of the proposed approach is demonstrated via both analytical and simulation results.

DOI
10.1109/allerton.2008.4797586

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