Fractal functions and their application to source data coding

Zamrii I.; Sobchuk V.; Laptiev O.; Savchenko V.; Shkapa V.; Kovalenko V.; Kotok V.

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Fractal functions and their application to source data coding

Author(s)

Zamrii I. Department of Higher Mathematics, Mathematical Modeling and Physics, State University of Telecommunications,Solomianska St, Kyiv,Ukraine

Sobchuk V. Department of Integral and Differential Equations, Taras Shevchenko National University of Kyiv,Kyiv,Ukraine

Laptiev O. Department of Cyber Security and Information Protection, Taras Shevchenko National University of Kyiv,Kyiv,Ukraine

Savchenko V. Educational and Scientific Institute of Information Protection, State University of Telecommunications,Solomianska St, Kyiv,Ukraine

Shkapa V. Department of Higher Mathematics, Mathematical Modeling and Physics, State University of Telecommunications,Solomianska St, Kyiv,Ukraine

Kovalenko V. Department of Analytical Chemistry and Chemical Technology of Food Additives and Cosmetics, Ukrainian State University of Chemical Technology,Gagarin Ave, Dnipro,Ukraine

Kotok V. Department of Processes, Apparatus and General Chemical Technology, Ukrainian State University of Chemical Technology,Gagarin Ave, Dnipro,Ukraine

Abstract

Building effective systems for information exchange, compression and storage of information requires the use of reliable codes with certain properties that can be easily implemented in information systems. The paper considers a mathematical model based on a class of continuous functions with fractal properties defined by a three-character representation (coding). This mathematical model is used for encoding of digital data source. For the mathematical apparatus, the theorem that proove the uniqueness of the functional equation solution under initial conditions is offered, which in turn allows to construct an algorithm for encoding and decoding information. There are also examples of applications of this apparatus, which in particular have the property of decoding uniformity. The proposed model allows to develop a new fractal coding technology for efficient transmission and processing of data over communication channels in geographic information systems.

Publication Details

Page(s) 424-435

DOI DOI not available

Published Journal: ARPN Journal of Engineering and Applied Sciences, Volume: 17, Issue: 4, Year: 2022

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Keywords

code property, coding, self-similarity, iterated function system, fractal geometry, fractal function

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