On the guaranteed error-correction of decimation-enhanced iterative decoders

Shiva Kumar Planjery, David Declercq, Madiagne Diouf, Bane Vasic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Finite alphabet iterative decoders (FAIDs) proposed for LDPC codes on the binary symmetric channel are capable of surpassing the belief propagation (BP) decoder in the error floor region with lower complexity and precision, but these decoders are difficult to analyze for finite-length codes. Recently, decimation-enhanced FAIDs (DFAIDs) were proposed for column-weight-three codes. Decimation involves fixing the bit values of certain variable nodes during message-passing based on the messages they receive after some number of iterations. In this paper, we address the problem of proving the guaranteed error-correction capability of DFAIDs for column-weight-three LDPC codes. We present the methodology of the proof to derive sufficient conditions on the Tanner graph that guarantee the correction of a given error pattern in a finite number of iterations. These sufficient conditions are described as a list of forbidden graphs that must not be contained in the Tanner graph of the code. As a test case, we consider the problem of guaranteeing the correction of four errors. We illustrate the analysis for a specific 4-error pattern and provide the sufficient conditions for its correction. We also present results on the design of codes satisfying those sufficient conditions and their impact on the achievable code rate.

Original languageEnglish (US)
Title of host publicationInternational Symposium on Turbo Codes and Iterative Information Processing, ISTC
PublisherIEEE Computer Society
Pages57-61
Number of pages5
ISBN (Electronic)9781479959853
DOIs
StatePublished - Nov 12 2014
Event2014 8th International Symposium on Turbo Codes and Iterative Information Processing, ISTC 2014 - Bremen, Germany
Duration: Aug 18 2014Aug 22 2014

Publication series

NameInternational Symposium on Turbo Codes and Iterative Information Processing, ISTC
ISSN (Print)2165-4700
ISSN (Electronic)2165-4719

Other

Other2014 8th International Symposium on Turbo Codes and Iterative Information Processing, ISTC 2014
CountryGermany
CityBremen
Period8/18/148/22/14

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Information Systems
  • Theoretical Computer Science

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    Planjery, S. K., Declercq, D., Diouf, M., & Vasic, B. (2014). On the guaranteed error-correction of decimation-enhanced iterative decoders. In International Symposium on Turbo Codes and Iterative Information Processing, ISTC (pp. 57-61). [6955085] (International Symposium on Turbo Codes and Iterative Information Processing, ISTC). IEEE Computer Society. https://doi.org/10.1109/ISTC.2014.6955085