Universal Compression of a Piecewise Stationary Source Through Sequential Change Detection

Abstract

This paper focuses on universal compression of a piecewise stationary source using sequential change detection algorithms. The change detection algorithms that we have considered assume minimal knowledge of the source and make use of universal estimators of entropy. Here, data in each segment is characterized either by an I.I.D. random process or a first order Markov process. Simulation study of a modified sequential change detection test proposed by Jacob and Bansal [1] is carried out. Next, an algorithm to effectively compress a piece-wise stationary sequence using such change detection algorithms is proposed. Overall compression efficiency achieved with Page's Cumulative Sum (CUSUM) test and the modified change detection test proposed in [1] (JB-Page test) as part of the change detection schemes, are compared. Further, when JB-Page test is used for change detection, four different compression algorithms, namely, Lempel Ziv Welch (LZW), Lempel Ziv (LZ78), Burrows Wheeler Transform (BWT) and Context Tree Weighting (CTW) algorithms are compared based on their impact on overall compression.