Development of data compressing coding methods on basis of binary binomial numbers

• Main Authors: Igor Kulyk, Olga Berezhna, Marina Shevchenko
• Format: Article
• Language: English
• Published: PC Technology Center 2019-04-01
• Series: Tehnologìčnij Audit ta Rezervi Virobnictva
• Subjects: binary binomial numbers; binomial number systems; binary information compression
• Online Access: http://journals.uran.ua/tarp/article/view/169897

The object of research is the methods of compressive coding, which are used for economical presentation of data in information systems. Compression methods can be used at various stages of data processing, in the transmission of messages and their storage. One of the most problematic places for the application of compression methods are high requirements for computing resources, significant hardware and software costs for their implementation and low coding/decoding speed. In this case, of particular interest are methods, on the results of compression of which computational operations are possible without reversing them. Within the framework of the approach, when at the basis of any code it is possible to detect a structural number system, mathematical models of compression based on binary binomial numbers are developed. In the structure of sequences, the corresponding binomial numbers are determined on the basis of systems of code-forming constraints. As a result, each combination is assigned a binomial number, which is its compressed image. In the course of the study, theorems on a one-to-one correspondence between the initial sequences and binary binomial numbers are formulated, which demonstrate how to implement mappings based on simple analytical relations. The examples given confirm the simplicity of the transformations under compression coding and decoding. The models of the processes of compression and recovery are obtained, which are characterized by a small number of simple operations. As a result, the considered methods are characterized by high speed with good compression ratios. At the same time, the amount of hardware and software costs in practical implementation is small. An additional positive effect is that compressed images have the properties of numbers. The research results demonstrate the effectiveness of the use of compression based on binary binomial numbers in information systems in order to increase their productivity and reduce the cost of data processing. At the same time, compared with similar known methods, there are minimal costs for their implementation when achieving a high conversion rate and a good degree of compression of binary data of any kind.