Introduction to Linear Optimization
Introduction to Linear Optimization
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Decoding error-correcting codes via linear programming
Decoding error-correcting codes via linear programming
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
Adaptive Methods for Linear Programming Decoding
IEEE Transactions on Information Theory
Nonlinear programming approaches to decoding low-density parity-check codes
IEEE Journal on Selected Areas in Communications
Efficient Implementation of Linear Programming Decoding
IEEE Transactions on Information Theory
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In this paper, we focus on solving the linear programming (LP) problem that arises in the decoding of low-density parity-check (LDPC) codes by means of the revised simplex method. In order to take advantage of the structure of the LP problem, we reformulate the dual LP and apply the idea of Dantzig-Wolfe (D-W) decomposition method to solve the problem. Each subproblem in the D-W decomposition method is an LP over a convex polyhedral cone. We define the convex polyhedral cone as local parity-check cone and discuss its special structures. Then, we enumerate its extreme rays and use these extreme rays to design an efficient method for the general LP decoding problem. The proposed method exhibits advantages in reducing both the storage and computational requirements.