On the Entropy Rate of Pattern Processes

DOI10.1109/TIT.2006.880044zbMATH Open1320.94034arXivcs/0504046MaRDI QIDQ3547946

George M. Gemelos, Tsachy Weissman

Publication date: 21 December 2008

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: We study the entropy rate of pattern sequences of stochastic processes, and its relationship to the entropy rate of the original process. We give a complete characterization of this relationship for i.i.d. processes over arbitrary alphabets, stationary ergodic processes over discrete alphabets, and a broad family of stationary ergodic processes over uncountable alphabets. For cases where the entropy rate of the pattern process is infinite, we characterize the possible growth rate of the block entropy.

Full work available at URL: https://arxiv.org/abs/cs/0504046

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Coding theorems (Shannon theory) (94A24)

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