Abstract:
Today wavelet transform is used in many fields such as computer graphics, image and signal processing, speech recognition. We want to provide method for the wavelet transform application in coding theory. Wavelet analysis is a special type of linear transformation of the signals and the physical data; therefore, it is possible to construct a linear code based on wavelets. Using coefficients of the wavelet decomposition scaling functions, we can derive generator and check matrix for the linear code. Linear codes are standard approach used in the schemes of error detection and correction. Compared to other codes, linear codes allow the implementation of more efficient encoding and decoding algorithms of information. However, error protection scheme based on linear codes do not provide the uniform level of protection against any possible errors, and concentrates their detect ability to certain errors set. This relationship between linear code opportunities and error distribution can cause an error if mistake belongs to undetectable error set. To reduce the error masking probability, it is necessary that error distribution was uniform. This distribution provides by robust codes. Robust codes are a nonlinear code that does not depend on type and dimension of errors. We provide method for constructing robust codes based on wavelets. Also characteristics of the proposed codes compares with each other.
Citation:
A. B. Levina, S. V. Taranov, “Construction of linear and robust codes based on wavelet decomposition”, Sib. Zh. Ind. Mat., 18:3 (2015), 49–56; J. Appl. Industr. Math., 9:4 (2015), 540–546
\Bibitem{LevTar15}
\by A.~B.~Levina, S.~V.~Taranov
\paper Construction of linear and robust codes based on wavelet decomposition
\jour Sib. Zh. Ind. Mat.
\yr 2015
\vol 18
\issue 3
\pages 49--56
\mathnet{http://mi.mathnet.ru/sjim893}
\crossref{https://doi.org/10.17377/sibjim.2015.18.305}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3549839}
\elib{https://elibrary.ru/item.asp?id=23877190}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 4
\pages 540--546
\crossref{https://doi.org/10.1134/S1990478915040109}
Linking options:
https://www.mathnet.ru/eng/sjim893
https://www.mathnet.ru/eng/sjim/v18/i3/p49
This publication is cited in the following 10 articles:
Levina Alla Borisovna, Panchenko Nikita Andreevich, 2023 12th Mediterranean Conference on Embedded Computing (MECO), 2023, 1
Alla Levina, Gleb Ryaskin, “Robust Code Constructions Based on Bent Functions and Spline Wavelet Decomposition”, Mathematics, 10:18 (2022), 3305
Vladmir Varuikhin, Alla Levina, 2022 11th Mediterranean Conference on Embedded Computing (MECO), 2022, 1
Varuikhin V., Levina A., “Continuous Wavelet Transform Applications in Steganography”, 14Th International Symposium Intelligent Systems, Procedia Computer Science, 186, eds. Zelinka I., Pereira F., Das S., Ilin A., Diveev A., Nikulchev E., Elsevier Science Bv, 2021, 580–587
V. A. Variukhin, A. B. Levina, “METHOD FOR STEGANOGRAPHIC HIDE OF INFORMATION BASED ON CONTINUOUS WAVELET TRANSFORM”, vkit, 2021, no. 204, 12
V. Varuikhin, A. Levina, “Steganographic information hiding method based on continuous wavelet transform”, 2020 9Th Mediterranean Conference on Embedded Computing (Meco), Mediterranean Conference on Embedded Computing, eds. R. Stojanovic, L. Jozwiak, V. Milutinovic, B. Lutovac, D. Jurisic, IEEE, 2020, 472–475
Vladmir Varuikhin, Alla Levina, 2020 9th Mediterranean Conference on Embedded Computing (MECO), 2020, 1
A. B. Levina, S. V. Taranov, D. I. Kaplun, P. Boyvalenkov, 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring), 2019, 3797
A. Levina, S. Taranov, “Creation of codes based on wavelet transformation and its application in ADV612 chips”, Int. J. Wavelets Multiresolut. Inf. Process., 15:2 (2017), 1750014
A. Ometov, A. Levina, P. Borisenko, R. Mostovoy, A. Orsino, S. Andreev, “Mobile social networking under side-channel attacks: practical security challenges”, IEEE Access, 5 (2017), 2591–2601
Citation in format AMSBIB
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