Titlebook: Entropy and Information Theory; Robert M. Gray Book 19901st edition Springer-Verlag New York 1990 Normal.Random variable.Shannon.behavior.

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Entropy and Information,dern age of ergodic theory. We shall see that entropy and related information measures provide useful descriptions of the long term behavior of random processes and that this behavior is a key factor in developing the coding theorems of information theory. We now introduce the various notions of ent

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The Entropy Ergodic Theorem,odic theorem of information theory or the asymptotic equipartion theorem, but it is best known as the Shannon-McMillan-Breiman theorem. It provides a common foundation to many of the results of both ergodic theory and information theory. Shannon [129] first developed the result for convergence in pr

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Information Rates I,perties of information and entropy rates of finite alphabet processes. We show that codes that produce similar outputs with high probability yield similar rates and that entropy and information rate, like ordinary entropy and information, are reduced by coding. The discussion introduces a basic tool

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Relative Entropy Rates,f entropy rates are proved and a mean ergodic theorem for relative entropy densities is given. The principal ergodic theorems for relative entropy and information densities in the general case are given in the next chapter.

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