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Paper:

TR06-077 | 12th June 2006 00:00

Lempel-Ziv Dimension for Lempel-Ziv Compression

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TR06-077
Authors: Maria Lopez-Valdes
Publication: 21st June 2006 19:50
Downloads: 1501
Keywords: 


Abstract:

This paper describes the Lempel-Ziv dimension (Hausdorff like
dimension inspired in the LZ78 parsing), its fundamental properties
and relation with Hausdorff dimension.

It is shown that in the case of individual infinite sequences, the
Lempel-Ziv dimension matches with the asymptotical Lempel-Ziv
compression ratio.

This fact is used to describe results on Lempel-Ziv compression in
terms of dimension of complexity classes and vice versa.



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