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 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     

Optimal Universal Coding with Respect to the Maximal Individual Relative Redundancy Criterion

Advantages of the relative redundancy criterion are discussed. Two types of universal (with respect to this criterion) codes are proposed. It is proved that, for the set of binary memoryless sources, variable-to-fixed length codes are more efficient than fixed-to-variable length codes if the number of encoded messages is the same.     

Joint Matrix Universal Coding of Sequences of Independent Symbols

Coding divergences of probability distributions are introduced. A method of joint matrix universal coding for a set of sequences of independent symbols with different statistics is proposed and studied. Two methods of multialphabet matrix coding are considered. The method proposed is compared with the PPM algorithm, and ways for integrating them are discussed.     

Universal coding algorithm for a family of context Markov sources

Often, for a source to be encoded it is only known (or assumed) that its model belongs to some known family; parameters of models are unknown. The number of context Markov models in a family can be enormous, and methods for finding the best of them to describe a current block (message fragment of length n) have not been discussed previously. We propose a way to solve this problem and describe a coding algorithm.     

Individual redundancy of adaptive and weighted source coding

We define individual redundancy of adaptive codes. We propose a method of weighted coding asymptotically optimal with respect to the maximal average and maximal individual redundancy criteria for universal and adaptive codes.     

Context weighting for general finite-context sources

Context weighting procedures are presented for sources with models (structures) in four different classes. Although the procedures are designed for universal data compression purposes, their generality allows application in the area of classification