On the relationship between process and pattern entropy rate

George M. Gemelos, Tsachy Weissman

Abstract: The recent study of pattern sequences and their compressibility properties has led to interest in the entropy rate of pattern sequences of stochastic processes, and its relationship to the entropy rate of the original process. In this work we give a complete characterization of this relationship for general discrete Markov processes as well as for a broad family of Markov and additive noise processes over a continuous alphabet