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Problemy Peredachi Informatsii, 2021, Volume 57, Issue 2, Pages 36–43
DOI: https://doi.org/10.31857/S0555292321020029 (Mi ppi2339) 		 
Coding Theory

Coding in a $\mathrm{Z}$-channel in case of many errors

V. S. Lebedeva, N. A. Polyanskiibc

a Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
b Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia
c Technische Universität München, Munich, Germany
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DOI: https://doi.org/10.31857/S0555292321020029
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 $\mathrm{Z}$-channel is $\Theta(\varepsilon^{-3/2})$ as $\varepsilon\to 0$.
Keywords: $\mathrm{Z}$-channel, minimum distance, constant-weight code.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00364
20-51-50007
Deutsche Forschungsgemeinschaft WA3907/1-1
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.
Received: 14.12.2020
Revised: 25.03.2021
Accepted: 26.03.2021
English version:
Problems of Information Transmission, 2021, Volume 57, Issue 2, Pages 129–135
DOI: https://doi.org/10.1134/S0032946021020022
Bibliographic databases:
Document Type: Article
UDC: 621.391 : 519.724
Language: Russian
Citation: V. S. Lebedev, N. A. Polyanskii, “Coding in a $\mathrm{Z}$-channel in case of many errors”, Probl. Peredachi Inf., 57:2 (2021), 36–43; Problems Inform. Transmission, 57:2 (2021), 129–135
Citation in format AMSBIB
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\paper Coding in a $\mathrm{Z}$-channel in case of many errors
\jour Probl. Peredachi Inf.
\yr 2021
\vol 57
\issue 2
\pages 36--43
\mathnet{http://mi.mathnet.ru/ppi2339}
\crossref{https://doi.org/10.31857/S0555292321020029}
\transl
\jour Problems Inform. Transmission
\yr 2021
\vol 57
\issue 2
\pages 129--135
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    		Проблемы передачи информации Problems of Information Transmission
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