A note on the branch-and-cut approach to decoding linear block codes

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Maximum likelihood (ML) decoding of linear block codes can be considered as an integer linear programming (ILP). Since it is an NPhard problem in general, there are many researches about the algorithms to approximately solve the problem. One of the most popular algorithms is linear programming (LP) decoding proposed by Feldman et al. LP decoding is based on the LP relaxation, which is a method to approximately solve the ILP corresponding to the ML decoding problem. Advanced algorithms for solving ILP (approximately or exactly) include cutting-plane method and branch-and-bound method. As applications of these methods, adaptive LP decoding and branch-and-bound decoding have been proposed by Taghavi et al. and Yang et al., respectively. Another method for solving ILP is the branch-and-cut method, which is a hybrid of cutting-plane and branch-and-bound methods. The branch-and-cut method is widely used to solve ILP, however, it is unobvious that the method works well for the ML decoding problem. In this paper, we show that the branch-and-cut method is certainly effective for the ML decoding problem. Furthermore the branch-and-cut method consists of some technical components and the performance of the algorithm depends on the selection of these components. It is important to consider how to select the technical components in the branch-and-cut method. We see the differences caused by the selection of those technical components and consider which scheme is most effective for the ML decoding problem through numerical simulations.

Original languageEnglish
Pages (from-to)1912-1917
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE93-A
Issue number11
DOIs
Publication statusPublished - 2010 Nov

Fingerprint

Branch-and-cut
Block Codes
Block codes
Linear Codes
Linear programming
Decoding
Integer Linear Programming
Maximum likelihood
Maximum Likelihood
Branch and bound method
Branch and Bound Method
Cutting Plane Method
Cutting Planes
Linear Programming Relaxation
Adaptive Method
Branch-and-bound
NP-complete problem
Numerical Simulation

Keywords

  • Branch-and-cut method
  • Linear programming decoding
  • Lowdensity-parity-check code

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics
  • Signal Processing

Cite this

@article{78c1d69f621846639be87ffada295cae,
title = "A note on the branch-and-cut approach to decoding linear block codes",
abstract = "Maximum likelihood (ML) decoding of linear block codes can be considered as an integer linear programming (ILP). Since it is an NPhard problem in general, there are many researches about the algorithms to approximately solve the problem. One of the most popular algorithms is linear programming (LP) decoding proposed by Feldman et al. LP decoding is based on the LP relaxation, which is a method to approximately solve the ILP corresponding to the ML decoding problem. Advanced algorithms for solving ILP (approximately or exactly) include cutting-plane method and branch-and-bound method. As applications of these methods, adaptive LP decoding and branch-and-bound decoding have been proposed by Taghavi et al. and Yang et al., respectively. Another method for solving ILP is the branch-and-cut method, which is a hybrid of cutting-plane and branch-and-bound methods. The branch-and-cut method is widely used to solve ILP, however, it is unobvious that the method works well for the ML decoding problem. In this paper, we show that the branch-and-cut method is certainly effective for the ML decoding problem. Furthermore the branch-and-cut method consists of some technical components and the performance of the algorithm depends on the selection of these components. It is important to consider how to select the technical components in the branch-and-cut method. We see the differences caused by the selection of those technical components and consider which scheme is most effective for the ML decoding problem through numerical simulations.",
keywords = "Branch-and-cut method, Linear programming decoding, Lowdensity-parity-check code",
author = "Shunsuke Horii and Toshiyasu Matsushima and Shigeichi Hirasawa",
year = "2010",
month = "11",
doi = "10.1587/transfun.E93.A.1912",
language = "English",
volume = "E93-A",
pages = "1912--1917",
journal = "IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences",
issn = "0916-8508",
publisher = "Maruzen Co., Ltd/Maruzen Kabushikikaisha",
number = "11",

}

TY - JOUR

T1 - A note on the branch-and-cut approach to decoding linear block codes

AU - Horii, Shunsuke

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 2010/11

Y1 - 2010/11

N2 - Maximum likelihood (ML) decoding of linear block codes can be considered as an integer linear programming (ILP). Since it is an NPhard problem in general, there are many researches about the algorithms to approximately solve the problem. One of the most popular algorithms is linear programming (LP) decoding proposed by Feldman et al. LP decoding is based on the LP relaxation, which is a method to approximately solve the ILP corresponding to the ML decoding problem. Advanced algorithms for solving ILP (approximately or exactly) include cutting-plane method and branch-and-bound method. As applications of these methods, adaptive LP decoding and branch-and-bound decoding have been proposed by Taghavi et al. and Yang et al., respectively. Another method for solving ILP is the branch-and-cut method, which is a hybrid of cutting-plane and branch-and-bound methods. The branch-and-cut method is widely used to solve ILP, however, it is unobvious that the method works well for the ML decoding problem. In this paper, we show that the branch-and-cut method is certainly effective for the ML decoding problem. Furthermore the branch-and-cut method consists of some technical components and the performance of the algorithm depends on the selection of these components. It is important to consider how to select the technical components in the branch-and-cut method. We see the differences caused by the selection of those technical components and consider which scheme is most effective for the ML decoding problem through numerical simulations.

AB - Maximum likelihood (ML) decoding of linear block codes can be considered as an integer linear programming (ILP). Since it is an NPhard problem in general, there are many researches about the algorithms to approximately solve the problem. One of the most popular algorithms is linear programming (LP) decoding proposed by Feldman et al. LP decoding is based on the LP relaxation, which is a method to approximately solve the ILP corresponding to the ML decoding problem. Advanced algorithms for solving ILP (approximately or exactly) include cutting-plane method and branch-and-bound method. As applications of these methods, adaptive LP decoding and branch-and-bound decoding have been proposed by Taghavi et al. and Yang et al., respectively. Another method for solving ILP is the branch-and-cut method, which is a hybrid of cutting-plane and branch-and-bound methods. The branch-and-cut method is widely used to solve ILP, however, it is unobvious that the method works well for the ML decoding problem. In this paper, we show that the branch-and-cut method is certainly effective for the ML decoding problem. Furthermore the branch-and-cut method consists of some technical components and the performance of the algorithm depends on the selection of these components. It is important to consider how to select the technical components in the branch-and-cut method. We see the differences caused by the selection of those technical components and consider which scheme is most effective for the ML decoding problem through numerical simulations.

KW - Branch-and-cut method

KW - Linear programming decoding

KW - Lowdensity-parity-check code

UR - http://www.scopus.com/inward/record.url?scp=78049494459&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78049494459&partnerID=8YFLogxK

U2 - 10.1587/transfun.E93.A.1912

DO - 10.1587/transfun.E93.A.1912

M3 - Article

AN - SCOPUS:78049494459

VL - E93-A

SP - 1912

EP - 1917

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 11

ER -