IEEE Transactions on Information Theory
Multi-stage decoding of LDPC codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Iterative approximate linear programming decoding of LDPC codes with linear complexity
IEEE Transactions on Information Theory
A separation algorithm for improved LP-decoding of linear block codes
IEEE Transactions on Information Theory
Interior point decoding for linear vector channels based on convex optimization
IEEE Transactions on Information Theory
On the decomposition method for linear programming decoding of LDPC codes
IEEE Transactions on Communications
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Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we make a first step in studying this method, and show that by starting from a simple LP problem and adaptively adding the necessary constraints, the complexity of LP decoding can be significantly reduced. In particular, we observe that with adaptive LP decoding, the sizes of the LP problems that need to be solved become practically independent of the density of the parity-check matrix. We further show that adaptively adding extra constraints, such as constraints based on redundant parity checks, can provide large gains in the performance.