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5. Method for borders estimation of compression on basis of binary binomial numbers

#### Method for borders estimation of compression on basis of binary binomial numbers

I. Kulyk, A. Novhorodtsev, M. Shevchenko
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Description: In the paper the problem on searching the borders of the reasonable application for the compression method, using binomial numbers, is under review. The compression method would be used effectively for constant weight code, that is, when the amount of units is fixed. In case of the variable amount of units it is necessary to include the number of units by itself into the compressed form. As a result, the compression ratio is decreased, as well the hardware and program resources are spent to no effect. Therefore the searching of the reasonable application borders for the compression on basis of binary binomial numbers is a topical and useful task. The proposed method for the borders estimation allows us to separate out definitely and enough simply the areas of the efficient application of binary binomial numbers in order to compress arbitrary sequences, having the variable amount of units. The considered method for the borders estimation consist in seeking values of the units' amount and length of digits for the sequences to be compressed, when the resultant form is less than the initial sequence as to the quantity of digits. Taking into account the borders for the compression method, using binary binomial numbers, gives possibilities to improve its compression ratio and increase its compression and decompression speed. The formulated and proved theorems demonstrate the actuality and possibility to search the borders of the reasonable application for the compression method, as well they point to the minimal values of sequences length, at which the borders of the compression should be applied. The graphic and table of the found borders values, which demonstrate the areas for amounts of units to compress binary sequence, are given in the paper.

Keywords: binomial compression, binary binomial numbers, compression borders

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Reference:
﻿ Kulyk, Y.A., Novhorodtsev, A.Y. and Shevchenko, M.S. (2019), “Metod otsenky hranyts prymenenyia szhatyia na osnove dvoychnыkh bynomyalnыkh chysel” [Method for borders estimation of compression on basis of binary binomial numbers], Information Processing Systems, Vol. 2(157), pp. 57-62. https://doi.org/10.30748/soi.2019.157.07.