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Statistical Physics of Low Density Parity Check Error Correcting Codes

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Cryptography and Coding (Cryptography and Coding 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2260))

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Abstract

We study the performance of Low Density Parity Check (LDPC) error-correcting codes using the methods of statistical physics. LDPC codes are based on the generation of codewords using Boolean sums of the original message bits by employing two randomlyconstructed sparse matrices. These codes can be mapped onto Ising spin models and studied using common methods of statistical physics. We examine various regular constructions and obtain insight into their theoretical and practical limitations. We also briefly report on results obtained for irregular code constructions, for codes with non-binary alphabet, and on how a finite system size effects the error probability.

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Author information

Authors and Affiliations

  1. Neural Computing Research Group, Aston University, B4 7ET, Birmingham, UK

    David Saad

  2. Dept. of Comp. Intel. & Syst. Sci., Tokyo Institute of Technology, 2268502, Yokohama, Japan

    Yoshiyuki Kabashima & Tatsuto Murayama

  3. Dep. de Física Geral, Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo - SP, Brazil

    Renato Vicente

Authors
  1. David Saad
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  2. Yoshiyuki Kabashima
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  3. Tatsuto Murayama
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  4. Renato Vicente
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Editor information

Editors and Affiliations

  1. Faculty of Applied Sciences, Department of Communication Systems, Lancaster University, LA1 4YR, Lancaster, UK

    Bahram Honary

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© 2001 Springer-Verlag Berlin Heidelberg

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Saad, D., Kabashima, Y., Murayama, T., Vicente, R. (2001). Statistical Physics of Low Density Parity Check Error Correcting Codes. In: Honary, B. (eds) Cryptography and Coding. Cryptography and Coding 2001. Lecture Notes in Computer Science, vol 2260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45325-3_27

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  • DOI: https://doi.org/10.1007/3-540-45325-3_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43026-1

  • Online ISBN: 978-3-540-45325-3

  • eBook Packages: Springer Book Archive

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