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Correlation function inadequacy in random-sequence entropy measures
O V Usatenko1, S S Melnyk1, G M Pritula1
1O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, 12 Proskura Street, 61805 Kharkiv, Ukraine.
Abstract:
Considering symbolic and numerical random sequences in the framework of the additive Markov chain approach, we establish a relation between their correlation functions and conditional entropies. We express the entropy by means of the two-point probability distribution functions and then evaluate the entropy for the numerical random chain in terms of the correlation function. We show that such approximation gives a satisfactory result only for special types of random sequences. In general case the conditional entropy of numerical sequences obtained in the two-point distribution function approach is lower. We derive the conditional entropy of the additive Markov chain as a sum of the Kullback-Leibler mutual information and give an example of random sequence with the exactly zero correlation function and the nonzero correlations.
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