The context-tree weighting method: basic properties

Describes a sequential universal data compression procedure for binary tree sources that performs the "double mixture." Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirabl...

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Vydáno v:IEEE transactions on information theory Ročník 41; číslo 3; s. 653 - 664
Hlavní autoři: Willems, F.M.J., Shtarkov, Y.M., Tjalkens, T.J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.05.1995
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Applied sciences
Arithmetic
Binary trees
Coding, codes
Context modeling
Data compression
Decoding
Exact sciences and technology
Information technology
Information theory
Information, signal and communications theory
Redundancy
Signal and communications theory
Source coding
State estimation
Telecommunications and information theory
Upper bound
Arithmetic code
Signal processing
Binary tree
Coding
Sequential method
Data compression
ISSN:0018-9448, 1557-9654
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Shrnutí:Describes a sequential universal data compression procedure for binary tree sources that performs the "double mixture." Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirable coding distribution for tree sources with an unknown model and unknown parameters. Computational and storage complexity of the proposed procedure are both linear in the source sequence length. The authors derive a natural upper bound on the cumulative redundancy of the method for individual sequences. The three terms in this bound can be identified as coding, parameter, and model redundancy, The bound holds for all source sequence lengths, not only for asymptotically large lengths. The analysis that leads to this bound is based on standard techniques and turns out to be extremely simple. The upper bound on the redundancy shows that the proposed context-tree weighting procedure is optimal in the sense that it achieves the Rissanen (1984) lower bound.< >
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.382012