Guessing facets: polytope structure and improved LP decoder
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
Improving the performance of LP decoders for cyclic codes
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
A separation algorithm for improved LP-decoding of linear block codes
IEEE Transactions on Information Theory
On the decomposition method for linear programming decoding of LDPC codes
IEEE Transactions on Communications
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We consider the decoding problem for low-density parity-check codes, and apply nonlinear programming methods. This extends previous work using linear programming (LP) to decode linear block codes. First, a multistage LP decoder based on the branch-and-bound method is proposed. This decoder makes use of the maximum-likelihood-certificate property of the LP decoder to refine the results when an error is reported. Second, we transform the original LP decoding formulation into a box-constrained quadratic programming form. Efficient linear-time parallel and serial decoding algorithms are proposed and their convergence properties are investigated. Extensive simulation studies are performed to assess the performance of the proposed decoders. It is seen that the proposed multistage LP decoder outperforms the conventional sum-product (SP) decoder considerably for low-density parity-check (LDPC) codes with short to medium block length. The proposed box-constrained quadratic programming decoder has less complexity than the SP decoder and yields much better performance for LDPC codes with regular structure