I-Measure. Recall Shannon’s Information measures.

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Presentation transcript:

I-Measure

Recall Shannon’s Information measures

The Chain Rules

Markov Chains

A Signed measure function and its properties.

I-measure and Signed measure

The I-measure and Signed measure Hence we can clearly see the one to one correspondence between Shannon’s information measure and set theory in general.

Applications of the I- measure

Information diagram The one to one relations between Shannon’s information measure and set theory suggest that we should be able to display Shannon’s information measures in an information diagram using Venn diagram. But actually for n random variable we need a n-1 dimension to completely display all of them. On the other hand when the random variable that we are dealing with form a markov Chain, 2 dimensions is enough to

Information diagram

References Book: Fundamentals of Real Analysis Sterling K, Berberian Book : A first course in Information Theory Raymond W, Yeung. The Chinese University of Hong Kong