1. Universal lossless data compression

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1851)

Abstract

  • 1.1. A link between coding and estimation
    • 1.1.1. Coding and Shannon entropy

    • 1.1.2. Instantaneous codes

  • 1.2. Universal coding and mixture codes
    • 1.2.1. The Bayesian approach

    • 1.2.2. The minimax approach

    • 1.2.3. Oracle inequalities

  • 1.3. Lower bounds for the minimax compression rate

  • 1.4. Mixtures of i.i.d. coding distributions

  • 1.5. Double mixtures and adaptive compression
    • 1.5.1. General principle

    • 1.5.2. The context tree weighting coding distribution

    • 1.5.3. Context tree weighting without initial context

    • 1.5.4. Weighting of trees of arbitrary depth

Mathematics Subject Classification (2000):

62B10 68T05 62C05 62E17 62G05 62G07 62G08 62H30 62J02 94A15 94A17 94A24 68Q32 60F10 60J10 60J20 65C05 68W20 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles Aléatoires, UMR CNRS 7599, Case 188Université Paris 6Paris Cedex 05France

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