A factor-graph approach to the context-tree weighting method

Factor graphs (FG) are graphical models with origins in coding theory. The sum-product and the max-product algorithms (SPA/MPA), which operate by message passing in an FG, subsume a great variety of algorithms in coding, signal processing, and artificial intelligence. This paper aims at showing that it is possible to give an FG/SPA interpretation of one of the best data compression algorithms, namely the context-tree weighting (CTW) method. An arithmetic encoder/decoder needs the conditional probabilities of the next symbol can be obtained by performing the SPA on the FG which represents the joint pmf/pdf of all occuring random variables. Once the CTW algorithm is formulated in the FG/SPA-framework, new extensions of the algorithm become readily apparent.