Lempel-Ziv Dimension for Lempel-Ziv Compression

  • Maria Lopez-Valdes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


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.


Compression Ratio Complexity Class Compression Algorithm Ergodic Measure Entropy Rate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Maria Lopez-Valdes
    • 1
  1. 1.Departamento de Informática e Ing. de SistemasUniversidad de ZaragozaZaragozaSpain

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