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Pseudocodeword-free criterion for codes with cycle-free Tanner graph

  • Wittawat Kositwattanarerk
Article
  • 26 Downloads

Abstract

Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.

Keywords

Iterative decoding Linear programming decoding Low-density parity-check (LDPC) code Tanner graphs Pseudocodewords 

Mathematics Subject Classification

94B05 

Notes

Acknowledgements

The author wishes to thank Gretchen L. Matthews for her support while the author is at Clemson University, Patanee Udomkavanich for her advice, and the anonymous reviewers for their helpful suggestions and comments. This work is supported by the Thailand Research Fund under Grant TRG5880116 and the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceMahidol UniversityBangkokThailand
  2. 2.Centre of Excellence in MathematicsThe Commission on Higher EducationBangkokThailand

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