Abstract
The application of data compression methods is an effective means of improving the performance of information systems. At the same time, interest is aroused to the methods of compression without information loss which are distinguished by their versatility, low needs of costs during implementation, and the possibility of self-control. In this regard, the application of binomial numbering systems is promising. The numerical function of the binomial numbering system is used for compression. It makes it possible to put sequences in one-to-one compliance with their numbers. In this case, the transition from binary combinations to binomial numbers is used as an intermediate stage. During the study, theorems were formulated that indicate properties of compressing and restoring the mappings as well as the ways of their implementation. Models of compression processes were obtained on the basis of a numerical function, both for the case of compressible equilibrium combinations and the case when sequences of a general form are to be compressed. The compression models include coding steps based on binary binomials. The study results show the effectiveness of applying the compression based on the binomial numerical function. A 1.02 times increase in speed of information transmission through a communication channel was observed in the worst case and 18.29 times in the best case depending on the number of ones in 128-bit equilibrium combinations. The proposed methods are advantageous due to their high compression ratio (from 1.01 to 16 times for general 128-bit sequences) and versatility: combinations are compressed in which the number of ones is 75 % of their total variation range. The developed methods ensure control of errors during conversions. They are undemanding to computation resources and feature low implementation costs.
Highlights
Existing and newly developed information systems are of distributed nature and must transfer and store huge amounts of information and perform frequent and complex queries to databases [1,2,3]
The study results show the effectiveness of applying the compression based on the binomial numerical function
A mathematical model of the method of compressing equilibrium combinations based on a binomial numerical function has been constructed
Summary
Existing and newly developed information systems are of distributed nature and must transfer and store huge amounts of information and perform frequent and complex queries to databases [1,2,3]. Insufficient bandwidth of communication channels, low speed of information storage devices, and requirements to ensuring specified levels of fail-safety and error-free transmission are the factors that limit performance gain in such systems [3,4,5]. Development of compression methods and algorithms that would have the following properties and characteristics is of particular scientific and practical interest [1,2,3]:. – high performance when compressing and recovering information;. – the ability to control errors when compressing and recovering data. In this regard, the development and implementation of compression methods and algorithms with the above pro perties is an urgent problem of scientific and practical value One of the most effective measures taken to speed up information processing and reduce the cost of computer systems and the components that form the basis of present-day control systems and telecommunication consists in the application of methods and algorithms of data compression [1,2,3].
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