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

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3 Author(s)
Makoto Miwa ; Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555 Japan (e-mail:, {wadayama, takumi} ; Tadashi Wadayama ; Ichi Takumi

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 lscr1-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.

Published in:

IEEE Journal on Selected Areas in Communications  (Volume:27 ,  Issue: 6 )