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Estimating the fraction of erasure patterns correctable by linear codes

  • V. B. Afanassiev
  • A. A. Davydov
  • D. K. Zigangirov
Theory and Methods of Information Processing
  • 27 Downloads

Abstract

The conditional probability (fraction) of the successful decoding of erasure patterns of high (greater than the code distance) weights is investigated for linear codes with the partially known or unknown weight spectra of code words. The estimated conditional probabilities and the methods used to calculate them refer to arbitrary binary linear codes and binary Hamming, Panchenko, and Bose–Chaudhuri–Hocquenghem (BCH) codes, including their extended and shortened forms. Error detection probabilities are estimated under erasure-correction conditions. The product-code decoding algorithms involving the correction of high weight erasures by means of component Hamming, Panchenko, and BCH codes are proposed, and the upper estimate of decoding failure probability is presented.

Keywords

linear code erasure correction product code 

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Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  • V. B. Afanassiev
    • 1
  • A. A. Davydov
    • 1
  • D. K. Zigangirov
    • 1
  1. 1.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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