A cutting-plane method based on redundant rows for improving fractional distance

  • Authors:

  • Makoto Miwa;Tadashi Wadayama;Ichi Takumi

  • Affiliations:

  • Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Japan;Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Japan;Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Japan

  • Venue:
  • IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
  • Year:
  • 2009

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Abstract

Decoding performance of linear programming (LP) decoding is closely related to geometrical properties of a fundamental polytope: fractional distance, pseudo codeword, etc. In this paper, an idea of the cutting-plane method is employed to improve the fractional distance of a given binary parity-check matrix. The fractional distance is the minimum weight (with respect to l1-distance) of nonzero vertices of the fundamental polytope. The cutting polytope is defined based on redundant rows of the parity-check matrix. The redundant rows are codewords of the dual code not yet appearing as rows in the parity-check matrix. The cutting polytope plays a key role to eliminate unnecessary fractional vertices in the fundamental polytope. We propose a greedy algorithm and its efficient implementation based on the cutting-plane method. It has been confirmed that the fractional distance of some parity-check matrices are actually improved by using the algorithm.