Development and research of adaptive data compression methods based on linear fibonacci form

Authors

DOI:

https://doi.org/10.15587/1729-4061.2015.37026

Keywords:

adaptive compression, numerical model, data source, linear Fibonacci form, compression ratio

Abstract

A fundamentally new data compression approach, which is based on the optimizing properties of Fibonacci numbers lies in the fact that the figures are considered as positive whole numbers and presented by a linear Fibonacci form, was investigated. Formation features of the numerical data source model were examined. The effect of the length of data blocks of the compressed file on the compression ratio was studied. Changing the number of bytes in the block provides the formation of different data source models. Ability to change the data source model allows to choose a model that provides the greatest compression ratio for a given encoding rule. Analysis of the results has shown that the effect of the data block length on the compression ratio is different for different file types. For some types, the greatest compression ratio is achieved when the block length is 100 bytes, and the ratio decreases with the increased length. For other file types, the effect of the data block length has a "wave" pattern (the ratio repeatedly increases and decreases with the increased length), and for certain types of files, the dependence of the transformed data on the data source model used is negligible. Low compression ratios and no compression for certain file types are caused by the fact that the data modeling used does not ensure the formation of numbers that are compactly presented by the linear Fibonacci form. To eliminate this shortcoming, two adaptive data compression methods, based on the linear Fibonacci form, which involve using a set of numerical data source models were proposed and investigated. These models are based on the maximum value of the numerical equivalents of the ASCII codes of bytes that make up the block. Adaptation enhances the compression ratio compared to non-adaptive compression method based on the linear Fibonacci form.

Author Biographies

Володимир Андрійович Лужецький, Vinnitsia National Technical University Khmelnitske shose 95, Vinnitsia, Ukraine, 21021

Doctor of technical sciences, professor, head of the department

The department of information security

Людмила Анатоліївна Савицька, Vinnitsia National Technical University Khmelnitske shose 95, Vinnitsia, Ukraine, 21021

Assistant

The department of computer engineering

References

  1. Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27 (3), 379–423. doi: 10.1002/j.1538-7305.1948.tb01338.x
  2. Huffman, D. A. (1952). A Method for the Construction of Minimum-Redundancy Codes. Proceedings of the Institute of Electrical and Radio Engineers, 40, 9, 1098–1101. doi: 10.1109/jrproc.1952.273898
  3. Witten, I., Neal, R., Cleary, J. (1987). Arithmetic Coding for Data Compression. Communications of the ACM, 30 (6), 520–540. doi: 10.1145/214762.214771
  4. Ziv, J., Lempel, A. (1977). A universal algorithm for sequential data compression. IEEE Transactions on Information Theory, 23 (3), 337–343.
  5. Ziv, J., Lempel, A. (1978). Compression of individual sequences via variable-rate coding. IEEE Transactions on Information Theory, 24 (5), 530–535. doi: 10.1109/tit.1978.1055934
  6. Welch, T. A. (1984). A Technique for High Performance Data Compression. Computer, 17 (6), 176–189. doi: 10.1109/mc.1984.1659158
  7. Rissanen, J. J., Langdon, G. G. (1981). Universal modeling and coding. IEEE Transactions on Information Theory, 27 (1), 12–23. doi: 10.1109/tit.1981.1056282
  8. Storer, J. A., Szymanski, T. G. (1982). Data compression via textual substitution. Journal of the ACM, 29 (4), 928–951. doi: 10.1145/322344.322346
  9. Elias, P. (1975). Universal codeword sets and representations of the integers. IEEE Transactions on Information Theory, 21 (2), 194–203. doi: 10.1109/tit.1975.1055349
  10. Rice, R. F., Plaunt, J. R. (1971). Adaptive Variable-Length Coding for Efficient Compression of Spacecraft Television Data. IEEE Transactions on Communications, 16 (9), 889–897. doi: 10.1109/tcom.1971.1090789
  11. Levenstein, V. E. (1968). On the redundancy and delay of separable codes for the natural numbers. Problems of Cybernetics, 20, 173–179.
  12. Golomb, S. W. (1966). Run-length encodings. IEEE Transactions on Information Theory, 12 (3), 399–401. doi: 10.1109/tit.1966.1053907
  13. Even, S., Rodeh, M. (1978). Economical encoding of commas between strings. Communications of the ACM, 21 (4), 315–317. doi: 10.1145/359460.359480
  14. Klein, S. T., Kopel Ben-Nissan (2010). On the usefulness of fibonacci compression codes. The Computer Journal, 53 (6), 701–716. doi: 10.1093/comjnl/bxp046
  15. Bastys, R. (2010). Fibonacci Coding Within the Burrows-Wheeler Compression Scheme. Electronics and Electrical Engineering. Kaunas: Technologija, 1 (97), 28–32.
  16. Somasundaram, K., Sumitra, P. (2010). Compression of Image using Fibonacci Code (FC) in JPEG2000. International Journal of Engineering Science and Technology, 2 (12), 7311–7319.
  17. Kaloshin, D. B., Bashkirev, E. V., Burmin, V. Yu. (2008). Comparison of variable-length codes: Elias and Fibonacci codes as applied to problems of data compression. Seismic Instruments, 44 (3), 64–99.
  18. Anisimov, A. V. (1995). Linear Fibonacci forms and parallel algorithms for high dimension arithmetic. Cybernetics and Systems Analysis, 3, 106–115.
  19. Luzhetsky, V. A., Mohammad Al-Maita (1998). Method of presentation large integers. Measuring and computing equipment in industrial processes, 1, 156–162.
  20. Kshanovsky, O. D., Titarchuk, S. V., Luzhetsky, V. A. (1999). Arithmetic compression methods of digital information. Visnyk VPI, 5, 83–87.

Published

2015-02-25

How to Cite

Лужецький, В. А., & Савицька, Л. А. (2015). Development and research of adaptive data compression methods based on linear fibonacci form. Eastern-European Journal of Enterprise Technologies, 1(9(73), 16–22. https://doi.org/10.15587/1729-4061.2015.37026

Issue

Section

Information and controlling system