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The structure of the I-measure of a Markov chain

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2 Author(s)
Kawabata, T. ; Dept. of Commun. & Syst. Eng., Electro-Commun. Univ., Chofu, Tokyo, Japan ; Yeung, R.W.

The underlying mathematical structure of Shannon's information measures was studied in a paper by R.W. Yeung (1991), and the I-Measure μ*, which is a signed measure defined on a proper σ-field F, was introduced. The I-Measure is a natural extension of Shannon's information measures and is uniquely defined by them. They also introduced as a consequence the I-Diagram as a geometric tool for visualizing the relationship among the information measures. In general, an I-Diagram for n random variables must be constructed in n-1 dimensions. It is shown that for any finite collection of random variables forming a Markov chain, μ* assumes a very simple structure which can be illustrated by an I-Diagram in two dimensions, and μ* is a nonnegative measure

Published in:

Information Theory, IEEE Transactions on  (Volume:38 ,  Issue: 3 )