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Prefix Encoding by Means of the (2,3) -Representation of Numbers

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1 Author(s)
Anatoly V. Anisimov ; Department of Mathematical Informatics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

A new family of universal self-synchronizable variable-length codes is introduced. This family is not a generalization or improvement of the existing prefix codes, but is based on a new method of integer representation in a mixed base using the radix-2 and the auxiliary radix-3. Upper length bounds for such codes are obtained. The asymptotic estimates for the (2,3)-encoding including the pointwise redundancy are also given. In particular, this implies that the average length of a (2,3)-codeword is shorter than that of Fibonacci code. Elias gamma and delta codes are adopted for the (2,3) -variant with asymptotically shorter codewords as against the original case. Improvement of gamma and delta encoding for all numbers is also presented. One of (2,3)-codes with high density is highlighted as a possible candidate for practical use in data compression. The (2,3) -codes are very simple to construct and they have evident features of strong robustness.

Published in:

IEEE Transactions on Information Theory  (Volume:59 ,  Issue: 4 )