On Coding a Stationary Process to Achieve a Given Marginal Distribution

Abstract

The problem of coding a stationary process $\{X_i\}^\infty_{i=-\infty}$ onto a stationary process $\{Y_i\}^\infty_{i=-\infty}$ so that for some positive integer $m, (Y_0, Y_1, \cdots, Y_{m-1})$ has a given marginal distribution is considered. The problem is solved for $\{X_i\}$ nonergodic as well as ergodic. The associated universal coding problem is also solved, where one seeks to find a coding function which yields the desired marginal distribution for each member of a class of possible distributions for $\{X_i\}$.