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Coding in a Z-Channel in Case of Many Errors

  • CODING THEORY
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Abstract

We prove that the maximum number of words in a code that corrects a fraction of \(1/4+\varepsilon\) of asymmetric errors in a Z-channel is \(\Theta(\varepsilon^{-3/2})\) as \(\varepsilon\to 0\).

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References

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Funding

The research of V.S. Lebedev was supported in part by the Russian Foundation for Basic Research, project nos. 19-01-00364 and 20-51-50007). The research of N.A. Polyanskii was carried out at the Technische Universität München and Skolkovo Institute of Science and Technology under partial support of the DFG grant, project no. WA3907/1-1.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. S. Lebedev

  2. Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia

    N. A. Polyanskii

  3. Technische Universität München, Munich, Germany

    N. A. Polyanskii

Authors
  1. V. S. Lebedev
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  2. N. A. Polyanskii
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Additional information

Translated from Problemy Peredachi Informatsii, 2021, Vol. 57, No. 2, pp. 36–43 https://doi.org/10.31857/S0555292321020029.

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Lebedev, V., Polyanskii, N. Coding in a Z-Channel in Case of Many Errors. Probl Inf Transm 57, 129–135 (2021). https://doi.org/10.1134/S0032946021020022

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  • DOI: https://doi.org/10.1134/S0032946021020022

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