V. S. Lebedev, N. A. Polyanskii, “Coding in a <nobr>$\mathrm{Z}$</nobr>-channel in case of many errors”, Probl. Peredachi Inf., 2021, Volume 57, Issue 2,Pages <nobr>36

Coding Theory

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

V. S. Lebedev^a, N. A. Polyanskii^bc

^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

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.

UDC: 621.391 : 519.724

Received: 14.12.2020
Revised: 25.03.2021
Accepted: 26.03.2021

DOI: 10.31857/S0555292321020029