Universal Source Coding for Non - Stationary Processes

Universal source codes achieve the optimal performance without apriori knowledge of the source statistics. The problem of universal lossy source coding for general non-stationary processes is considered here. Fixed rate and fixed distortion lossy source codes derived from the Lempel-Ziv scheme are shown to be universal for non-stationary processes with abstract alphabets. We define the rate distortion function for non-stationary sources. We also prove the continuity and convexity properties of the distortion rate function.