Limit results on pattern entropy

Alon Orlitsky, Narayana Santhanam, Krishnamurthy Viswanathan and Junan Zhang
December 27, 2004

We determine the entropy rate of patterns of certain random processes, bound the speed at which the per-symbol pattern entropy converges to this rate, and show that patterns satisfy an asymptotic equipartition property. To derive some of these results we upper bound the probability that the $n'$th variable in a random process differs from all preceding ones.

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