RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. IMI UdGU:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. IMI UdGU, 2019, Volume 53, Pages 115–126 (Mi iimi375)  

List decoding of wavelet codes

D. V. Litichevskii

Chelyabinsk State University, ul. Brat’ev Kashirinykh, 129, Chelyabinsk, 454001, Russia

Abstract: This paper discusses the possibility of list decoding of wavelet codes and states that wavelet codes over the field $GF(q)$ of an odd characteristic with the length of the code and information words $n=q-1$ and $\frac{n}{2} $, respectively, as well as over the field of an even characteristic with the length of the code and information words $n=q-1$ and $\frac{n-1}{2}$, respectively, allow list decoding if among the coefficients of the spectral representation of the polynomials generating them there are $d + 1$ consecutive zeros, $0 <d <\frac{n}{2}$ for fields of the odd characteristic and $0 <d < \frac{n-3}{2}$ for fields of the even characteristic. Also, a description is given of an algorithm that allows one to perform list decoding of wavelet codes subject to the listed conditions. As a demonstration of the operation of this algorithm, step-by-step solutions for model problems of list decoding of noisy wavelet code words over fields of even and odd characteristics are given. In addition, a wavelet version of Golay's quasi-perfect ternary code is constructed. The lengths of its code and information words are $8$ and $4$, respectively, the code distance is $4$, the minimum radius of balls with centers in code words covering the space of words of length $8$ is $3$.

Keywords: wavelet codes, polyphase coding, list decoding.

DOI: https://doi.org/10.20537/2226-3594-2019-53-10

Full text: PDF file (159 kB)
References: PDF file   HTML file

UDC: 519.725
MSC: 12Y05, 94B05, 94B60, 94B35
Received: 07.04.2019

Citation: D. V. Litichevskii, “List decoding of wavelet codes”, Izv. IMI UdGU, 53 (2019), 115–126

Citation in format AMSBIB
\Bibitem{Lit19}
\by D.~V.~Litichevskii
\paper List decoding of wavelet codes
\jour Izv. IMI UdGU
\yr 2019
\vol 53
\pages 115--126
\mathnet{http://mi.mathnet.ru/iimi375}
\crossref{https://doi.org/10.20537/2226-3594-2019-53-10}
\elib{http://elibrary.ru/item.asp?id=38503203}


Linking options:
  • http://mi.mathnet.ru/eng/iimi375
  • http://mi.mathnet.ru/eng/iimi/v53/p115

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
    Number of views:
    This page:25
    Full text:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019