Valid inequalities for binary linear 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;Microelectronic Systems Design Research Group, University of Kaiserslautern, Kaiserslautern, Germany;Microelectronic Systems Design Research Group, University of Kaiserslautern, Kaiserslautern, Germany;Microelectronic Systems Design Research Group, University of Kaiserslautern, Kaiserslautern, Germany

  • Venue:
  • ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
  • Year:
  • 2009

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Abstract

We study an integer programming (IP) based separation approach to find the maximum likelihood (ML) codeword for binary linear codes. An algorithm introduced in Tanatmis et al. is extended and improved with respect to decoding performance without increasing the worst case complexity. This is demonstrated on the LDPC and the BCH code classes. Moreover, we propose an integer programming formulation to calculate the minimum distance of a binary linear code. We exemplarily compute the minimum distance of the (204, 102) LDPC code and the (576, 288) WIMAX code. Using the minimum distance of a code, a new class of valid inequalities is introduced.