Coding for Discrete Markov Sources

Abstract

Consider a finite Markov chain φ having K states ${J_1},{J_2}, \ldots ,{J_k}$ and defined by the initial probability distribution

$${\Pi _0} = {\left[ {{P_1} \cdots {P_k}} \right]^{\left. + \right)}}$$

(3.1)

and by the transition probability matrix

$$\Pi = \left[ {\begin{array}{*{20}{c}} {{{\text{P}}_{{\text{11}}}}{{\text{P}}_{{\text{12}}}} \cdots {{\text{P}}_{{\text{1k}}}}} \\ {{{\text{p}}_{{\text{k1}}}}{{\text{p}}_{{\text{k}}2}} \cdots {{\text{p}}_{{\text{kk}}}}} \end{array}} \right].$$

(3.2)