Abstract

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

Keywords

Upper and lower boundsBinary treeMinimum description lengthMathematicsWeightingAlgorithmRedundancy (engineering)Bounded functionTree (set theory)Kolmogorov complexityBinary numberComputer scienceTheoretical computer scienceCombinatoricsArithmetic

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Publication Info

Year
1995
Type
article
Volume
41
Issue
3
Pages
653-664
Citations
911
Access
Closed

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Cite This

F.M.J. Willems, Yuri M. Shtarkov, T.J. Tjalkens (1995). The context-tree weighting method: basic properties. IEEE Transactions on Information Theory , 41 (3) , 653-664. https://doi.org/10.1109/18.382012

Identifiers

DOI
10.1109/18.382012