Lossless Data Compression via Substring Enumeration for k-th Order Markov Sources with a Finite Alphabet

Dube and Beaudoin have proposed a technique of lossless data compression called compression via substring enumeration (CSE) for a binary source alphabet. Dube and Yokoo proved that CSE has a linear complexity both in time and in space worst-case performance for the length of string to be encoded. Dubé and Yokoo have specified appropriate predictors of the uniform and combinatorial prediction models for CSE, and proved that CSE has the asymptotic optimality for stationary binary ergodic sources. Our previous study evaluated the worst-case maximum redundancy of the modified CSE for an arbitrary binary string from the class of k-th order Markov sources. We propose a generalization of CSE for k-th order Markov sources with a finite alphabet X based on Ota and Morita in this study.