Abstract

. First we modify the basic (binary) context-tree weighting method such that the past symbols x 1\GammaD ; x 2\GammaD ; \Delta \Delta \Delta ; x 0 are not needed by the encoder and the decoder. Then we describe how to make the context tree depth D infinite, which results in optimal redundancy behavior for all tree sources, while the number of records in the context tree is not larger than 2T \Gamma 1. Here T is the length of the source sequence. For this extended context-tree weighting algorithm we show that with probability one the compression ratio is not larger than the source entropy for source sequence length T ! 1 for stationary and ergodic sources. Keywords Sequential data compression, universal source coding, tree sources, modeling procedure, cumulative redundancy bounds, binary stationary and ergodic sources. 1. Introduction The context-tree weighting method, first presented at the San Antonio ISIT [7], appears to be an efficient implementation for weighting (mixing) the cod...

Citations

612	Compression of individual sequences via variable-rate coding - Ziv, Lempel - 1978
105	Trofimov, “The performance of universal encoding - Krichevsky, K - 1981
58	Entropy and data compression schemes - Ornstein, Weiss - 1993
52	Some asymptotic properties of the entropy of a stationary ergodic data source with applications to data compression - Wyner, Ziv - 1989
36	Asymptotic properties of data compression and suffix trees - Szpankowski - 1993
11	The ergodic and entropy theorems revisited - Shields - 1987
10	Linear size finite automata for the set of all subwords of a word: an outline of results - Blumer, Blumer, et al. - 1983
6	Context tree weighting: a sequential universal source coding procedure for FSMX sources - Willems, Shtarkov, et al. - 1993
2	Context tree weighting: Basic properties - Willems, Shtarkov, et al. - 1995
1	Combinatorial Method of Universal Cpding for Discrete Stationary Sources - Shtarkov, Babkin - 1971