Bayes coding algorithm for FSM sources

The optimal universal code for FSMX sources (Rissanen, 1981) with respect to Bayes redundancy criterion (Davison, 1973) is deduced under the condition that the model, the probabilistic parameters, and the initial state are unknown. The algorithm is not only Bayes optimal for FSMX sources but also asymptotically optimal for a stationary ergodic sources. Further, the algorithm is regarded as a generalization of the Ziv-Lempel algorithm. In the basic CTW algorithm, the algorithm needs an initial context, where a finite constant is the depth of the context tree, for calculating the coding probability. For the problems of the initial situation and the infinite depth tree, the extensions to the CTW algorithm have been proposed in a paper by Willems (1994). In this paper, an optimal algorithm is proposed that gives solution against these problems from new point of view. This proposed method is also regarded as a generalization of the Ziv-Lempel algorithm.