A 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 stationary ergodic sources. Moreover the algorithm is regarded as a generalisation of the Ziv-Lempel algorithm. In the basic CTW algorithm, the algorithm needs the initial context x_1-dx_2-d…x₀ where: a finite constant d is the depth of the context tree, for calculating the coding probability of x₁. For the problem of the initial situation and the infinite depth tree, the extensions to the CTW algorithm have been proposed in Willems (1994). The optimal algorithm proposed in the present paper gives a solution against these problems from another new point of view