Length of minimal forbidden words on a stationary ergodic source

Authors:
Takahiro Ota;Hiroyoshi Morita
Affiliations:
Department of Electronic Engineering, Nagano Prefectural Institute of Technology, Ueda, Nagano, Japan;Graduate School of Information Systems, University of Electro-Communications, Chofu, Tokyo, Japan
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Year:
2009

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Abstract

An antidictionary is in particular useful for data compression, and it consists of minimal forbidden words for a given string. We derive the average length Mn of minimal forbidden words in strings of length n under a stationary ergodic source with entropy H which takes values on a finite alphabet. For the string length n, we prove, log n/Mn = H, in probability, as n → ∞. We use the Wyner-Ziv result, with respect to connection between entropy and recurrence-time for ergodic processes, to prove the theorem. Its validity is shown by simulation results on a memoryless binary information source.