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arXiv:0802.1369 · Information Theory and Applications Workshop (ITA)

Interior-point algorithms for linear-programming decoding

Pascal O. Vontobel

Published Jan 1, 2008• 42 citations
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Abstract

Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the linear-programming decoder formulation.
DOI
10.1109/ita.2008.4601085

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Linear programming (LP) decoders can outperform currently used message-passing decoders in channel coding applications, but require prohibitively large complexity on even moderately sized codes. Previous works have proposed complexity-reducing algorithms that either relax the problem or modify the number of constraints; however, little work is done in optimizing solver implementation. We show that popular LP solvers like LIPSOL may not be efficient for LP decoding (LPD), and that an equivalent dual LP problem can be solved with equal accuracy but much more quickly. We propose an improved primal-dual method (iPD-MPC) whose overall runtime for both problem formulations outpreform LIPSOL. Additionally, as an alternative for memory-limited systems, we propose an improved hybrid gradient descent and Newton's method (iGD-NM) that further decreases overall runtime. In this way, we make LPD more feasible for channel codes of practical lengths.
In this paper, an efficient implementation of the interior point algorithm recently proposed by Wadayama for linear programming (LP) decoding of low-density parity-check (LDPC) codes is presented. The main idea behind the modification is to approximate the barrier function for the fundamental polytope defining the code so that it contains only one linear constraint for each of the parity-check constraints. Simulation results show that the approximations introduced do not result in any performance degradation, while considerably reducing the decoding complexity and latency.
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