Construction of linear and robust codes that is based on the scaling function coefficients of wavelet transforms

• Published in: Journal of applied and industrial mathematics Vol. 9; no. 4; pp. 540 - 546
• Main Authors: Levina, A. B., Taranov, S. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.10.2015; Springer Nature B.V
• Subjects: Algorithms; Codes; Coding theory; Computer programming; Construction; Construction industry; Data compression; Decomposition; Distortion; Error correction & detection; Error detection; Errors; Linear codes; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Probability; Studies; Wavelet transforms; robust code; wavelet decomposition; scaling function; linear code; probability of error detection
• ISSN: 1990-4789; 1990-4797
• DOI: 10.1134/S1990478915040109

Wavelet transforms are used in many areas such as computer graphics, image and signal processing, and speech recognition. We propose a way of applying the wavelet transform in coding theory. Wavelet analysis is a special type of linear transformation of signals and physical data on the basis of which it is possible to construct a linear code. The error protection schemes, based on linear codes, do not provide the same level of protection against all possible errors, but concentrate their detecting abilities on a specific set of errors. This dependence of the abilities of a linear code on the distribution of errors may distort the data to be protected in the case when the error does not belong to the set of undetectable errors. To reduce the probability of error masking, the robust codes are used. Robust codes are nonlinear codes independent of the type and dimension of the error. Some methods are suggested for constructing the linear and robust codes that is based on wavelet transforms.