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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Bibliographic Details
Published in:IEEE journal on selected areas in communications Vol. 24; no. 8; pp. 1603 - 1613
Main Authors: Kai Yang, Feldman, J., Xiaodong Wang
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2006
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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
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ISSN:0733-8716
1558-0008
DOI:10.1109/JSAC.2006.879405