Geodesic
Construction of linear and robust codes based on wavelet decomposition
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 49-56

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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.
Keywords: robust code, linear code, scaling function, error masking probability.
Mots-clés : wavelet decomposition 
@article{SJIM_2015_18_3_a4,
     author = {A. B. Levina and S. V. Taranov},
     title = {Construction of linear and robust codes based on wavelet decomposition},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {49--56},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a4/}
}
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A. B. Levina; S. V. Taranov. Construction of linear and robust codes based on wavelet decomposition. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 49-56. http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a4/