Development of Binary Information Compression Methods Based on the Binomial Numerical Function

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.

Keywords: binomial numbering systems, binomial numerical function, binomial numbers, compression of binary information