A separation algorithm for improved LP-decoding of linear block codes

Authors:
Akin Tanatmis;Stefan Ruzika;Horst W. Hamacher;Mayur Punekar;Frank Kienle;Norbert Wehn
Affiliations:
Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany;Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany;Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany;Department of Electronic and Electrical Engineering, University College Dublin, Belfield, Dublin-4, Ireland;Microelectronic Systems Design Research Group, University of Kaiserslautern, Kaiserslautern, Germany;Microelectronic Systems Design Research Group, University of Kaiserslautern, Kaiserslautern, Germany
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

Maximum likelihood (ML) decoding is the optimal decoding algorithm for arbitrary linear block codes and can be written as an integer programming (IP) problem. Feldman et al. relaxed this IP problem and presented linear programming (LP) based decoding. In this paper, we propose a new separation algorithm to improve the error-correcting performance of LP decoding for binary linear block codes. We use an IP formulation with indicator variables that help in detecting the violated parity checks. We derive Gomory cuts from the IP and use them in our separation algorithm. An efficient method of finding cuts induced by redundant parity checks (RPC) is also proposed. Under certain circumstances we can guarantee that these RPC cuts are valid and cut off the fractional optimal solutions of LP decoding. It is demonstrated on three LDPC codes and two BCH codes that our separation algorithm performs significantly better than LP decoding and belief propagation (BP) decoding.