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An Overview of the Isoperimetric Method in Coding Theory (Extended Abstract) [Invited Paper]

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Cryptography and Coding (Cryptography and Coding 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1746))

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Abstract

When decoding a threshold phenomenon is often observed: decoding deteriorates very suddenly around some critical value of the channel parameter. Threshold behaviour has been studied in many situations outside coding theory and a number of tools have been developped. One of those turns out to be particularly relevant to coding, namely the derivation of isoperimetric inequalities for product measures on Hamming spaces. we discuss this approach and derive consequences.

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References

  1. Bobkov, S., Goetze, F. (1996) Discrete Isoperimetric and Poincaré-type inequalities. Technical report SFB 343 University of Bielefeld 96–086. ftp://ftp.mathematik.uni-bielefeld.de/pub/papers/sfb343/pr96086.ps.gz

  2. Margulis, G. (1974) Probabilistic characteristics of graphs with large connectivity. Problemy Peredachi Informatsii. 10, 101–108

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  3. Talagrand, M. (1993) Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis’ graph connectivity theorem. Geometric and Functional Analysis. 3, 295–314.

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  4. Tillich, J-P., Zémor, G. (1999) Discrete inequalities and the probability of a decoding error. Submitted to Combinatorics, Probability & Computing. http://www.infres.enst.fr/zemor/isoperimetric.ps

  5. Zémor, G. (1994) Threshold effects in codes. In Algebraic coding, Springer-Verlag, LNCS 781 278–286.

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Author information

Authors and Affiliations

  1. Université Paris-Sud, bâtiment 490, 91405, Orsay, France

    Jean-Pierre Tillich

  2. École Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634, Paris 13, France

    Gilles Zémor

Authors
  1. Jean-Pierre Tillich
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  2. Gilles Zémor
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Editor information

Editors and Affiliations

  1. Vodafone Limited, The Courtyard, 2-4 London Road Newbury, Berkshire, RG14 1JX, UK

    Michael Walker

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© 1999 Springer-Verlag Berlin Heidelberg

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Tillich, JP., Zémor, G. (1999). An Overview of the Isoperimetric Method in Coding Theory (Extended Abstract) [Invited Paper]. In: Walker, M. (eds) Cryptography and Coding. Cryptography and Coding 1999. Lecture Notes in Computer Science, vol 1746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46665-7_14

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  • DOI: https://doi.org/10.1007/3-540-46665-7_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66887-9

  • Online ISBN: 978-3-540-46665-9

  • eBook Packages: Springer Book Archive

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