Reducing the space complexity of a Bayes coding algorithm using an expanded context tree

The context tree models are widely used in a lot of research fields. Patricia like trees are applied to the context trees that are expanded according to the increase of the length of a source sequence in the previous researches of non-predictive source coding and model selection. The space complexity of the Patricia like context trees are O(t) where t is the length of a source sequence. On the other hand, the predictive Bayes source coding algorithm cannot use a Patricia like context tree, because it is difficult to hold and update the posterior probability parameters on a Patricia like tree. So the space complexity of the expanded trees in the predictive Bayes coding algorithm is O(t²). In this paper, we propose an efficient predictive Bayes coding algorithm using a new representation of the posterior probability parameters and the compact context tree holding the parameters whose space complexity is O(t).