Nonlinear programming approaches to decoding low-density parity-check codes

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...

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Vydáno v:	IEEE journal on selected areas in communications Ročník 24; číslo 8; s. 1603 - 1613
Hlavní autoři:	Kai Yang, Feldman, J., Xiaodong Wang
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.08.2006 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithm design and analysis Algorithms Belief propagation Block codes Branch-and-bound Codes Computational complexity Convergence Decoders Decoding integer programming Iterative algorithms Iterative decoding linear codes Linear programming linear programming (LP) decoding low-density parity-check (LDPC) codes Maximum likelihood decoding Multistage Nonlinear programming Parity check codes Quadratic programming Serials Studies
ISSN:	0733-8716, 1558-0008
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Abstract	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
AbstractList	[...] we transform the original LP decoding formulation into a box-constrained quadratic programming form. 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
Author	Kai Yang Xiaodong Wang Feldman, J.
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Cites_doi	10.1109/TIT.1962.1057683 10.1109/18.651072 10.1109/TCOMM.2004.841982 10.1109/TIT.2004.842696 10.1109/18.910577 10.1109/LCOMM.2004.825737 10.1109/26.539767 10.1109/TIT.2005.856938 10.1109/26.939851 10.1109/18.910572 10.1109/18.910578 10.1109/ISIT.2004.1365380
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SubjectTerms	Algorithm design and analysis Algorithms Belief propagation Block codes Branch-and-bound Codes Computational complexity Convergence Decoders Decoding integer programming Iterative algorithms Iterative decoding linear codes Linear programming linear programming (LP) decoding low-density parity-check (LDPC) codes Maximum likelihood decoding Multistage Nonlinear programming Parity check codes Quadratic programming Serials Studies
Title	Nonlinear programming approaches to decoding low-density parity-check codes
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