Cybernetics And Systems Analysis logo
Editorial Board Announcements Abstracts Authors Archive
Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 519. 72
A.V. Anisimov1


1 Dr. of Sciences, professor, the dean of the faculty of the Taras Shevchenko National University of Kyiv

anatoly.v.anisimov@gmail.com

GENERATING (2,3)-CODES

Abstract. The (2,3)-representation of integers utilizes the mixed numeration base of the radix-2 and the auxillary radix-3. This representation yields a universal prefix-free binary encoding of all natural numbers with a variety of useful properties: robustness (self-synchronization), local error corrections, statistic regularities of code parameters, etc. The paper describes a procedure of monotonic generation of (2,3)-codewords in ascending order of their lengths.

Keywords: numeration system, radix, integer encoding, prefix encoding.



FULL TEXT

REFERENCES

  1. Elias P. Universal codewords sets and representations of integers. IEEE Transactions on Information Theory. 1975. Vol. 21, N 2. P. 194–203. https://doi.org/10.1109/TIT.1975.1055349.

  2. Levenshtein V.I. On the redundancy and deceleration of separable coding of natural numbers, Probl. Kibern. 1968. N 20. P. 173–179.

  3. Anisimov A.V. Two-base numeration systems. Cybernetics and Systems Analysis. 2013. Vol. 49, N 4. P. 501–510. https://doi.org/10.1007/s10559-013-9535-y.

  4. Fraenkel A.S. The use and usefulness of numeration systems. Information and Computation. 1989. Vol. 81, N 1. P. 46–61. https://doi.org/10.1016/0890-5401(89)90028-X.

  5. Apostolico A., Fraenkel A.S. Robust transmission of unbounded strings using Fibonacci representations. IEEE Transactions on Information Theory. 1987. Vol. 33, N 2. P. 238–245. https://doi.org/10.1109/TIT.1987.1057284.

  6. Anisimov A.V. Prefix encoding by means of (2,3)-representations of numbers. IEEE Transactions on Information Theory. 2013. Vol. 59, N. 4. P. 2359–2374. https://doi.org/10.1109/TIT.2012.2233544.

  7. Anisimov A.V., Zavadskyi I.A. Robust prefix encoding using lower (2,3) number representation. Cybernetics and Systems Analysis. 2014. Vol. 50, N 2. P. 163–175. https://doi.org/10.1007/s10559-014-9604-x.

  8. Butenko S., Pardalos P., Sergienko I., Shylo V., Stetsyuk P. Estimating the size of correcting codes using extremal graph problems. In: Optimization. Springer Optimization and Its Applications. Pearce C., Hunt E. (Eds). Vol. 32. New York: Springer, 2009. P. 227–243. https://doi.org/10. 1007/978-0-387-98096-6_12.
© 2020 Kibernetika.org. All rights reserved.