A cutting-plane method based on redundant rows for improving fractional distance
Miwa, M.
Wadayama, T.
Takumi, I.
Grad. Sch. of Eng., Nagoya Inst. of Technol., Nagoya, Japan;
This paper appears in: Selected Areas in Communications, IEEE Journal on
Publication Date: August 2009
Volume: 27,
Issue: 6
On page(s): 1005-1012
ISSN: 0733-8716
INSPEC Accession Number: 10794763
Digital Object Identifier: 10.1109/JSAC.2009.090818
Current Version Published: 2009-07-28
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 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.
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