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Weighted decoding of linear block codes by solving a system of implicit equations

  • Section II Information Theory, Decoding And Cryptography
  • Conference paper
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Book cover Coding Theory and Applications (Coding Theory 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 388))

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Abstract

Decoding a redundant code, when redefined as a means for estimating a posterior probability distribution given a prior one, has a simple output if one looks for the posterior distribution in a form separable with respect to the information symbols. The optimal distribution of this form results from minimizing its cross-entropy with respect to the prior distribution, which for a linear code leads to a system of implicit analog equations to be solved. This can be done by iteration, but the system has multiple solutions so that determining proper initial values becomes the main difficulty. We interpret any linear code as a kind of product of its parity checks whose successive decodings provide adequate initial values for solving the system, provided the received symbols are reordered by decreasing reliability (except for few inversions in order to keep the generator matrix in systematic form). Simulation results are presented.

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References

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Authors and Affiliations

  1. Département Communications et U.A. 820 du CNRS, Ecole Nationale Supérieure des Télécommunications, 46, rue Barrault, F - 75634, Paris Cedex 13, France

    G. Battail

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  1. G. Battail
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Editor information

Gérard Cohen Jacques Wolfmann

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© 1989 Springer-Verlag Berlin Heidelberg

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Battail, G. (1989). Weighted decoding of linear block codes by solving a system of implicit equations. In: Cohen, G., Wolfmann, J. (eds) Coding Theory and Applications. Coding Theory 1988. Lecture Notes in Computer Science, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019852

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  • DOI: https://doi.org/10.1007/BFb0019852

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51643-9

  • Online ISBN: 978-3-540-46726-7

  • eBook Packages: Springer Book Archive

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