The Context-Tree Weighting Method : Extensions

First we modify the basic (binary) context-tree weighting method such that the past symbols x1 D; x2 D; ; x0 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 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.