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Logical Entropy of Information Sources
Peng Xu1, Yamin Sayyari2, Saad Ihsan Butt3
1School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Duyun, Guizhou 558000, China.
Abstract:
In this paper, we present the concept of the logical entropy of order m, logical mutual information, and the logical entropy for information sources. We found upper and lower bounds for the logical entropy of a random variable by using convex functions. We show that the logical entropy of the joint distributions X1 and X2 is always less than the sum of the logical entropy of the variables X1 and X2. We define the logical Shannon entropy and logical metric permutation entropy to an information system and examine the properties of this kind of entropy. Finally, we examine the amount of the logical metric entropy and permutation logical entropy for maps.
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