Information Theory

Download e-book for iPad: Elements of Information Theory (2nd Edition) (Wiley Series by Thomas M. Cover, Joy A. Thomas

By Thomas M. Cover, Joy A. Thomas

ISBN-10: 0471241954

ISBN-13: 9780471241959

The most recent version of this vintage is up to date with new challenge units and material

the second one variation of this primary textbook continues the book's culture of transparent, thought-provoking guide. Readers are supplied once more with an instructive mixture of arithmetic, physics, facts, and knowledge theory.

all of the crucial subject matters in info concept are coated intimately, together with entropy, info compression, channel ability, cost distortion, community info conception, and speculation checking out. The authors supply readers with an excellent knowing of the underlying concept and purposes. challenge units and a telegraphic precis on the finish of every bankruptcy additional support readers. The ancient notes that stick with every one bankruptcy recap the most points.

the second one version features:
* Chapters reorganized to enhance teaching
* 2 hundred new problems
* New fabric on resource coding, portfolio idea, and suggestions capacity
* up to date references

Now present and improved, the second one version of components of data conception continues to be the appropriate textbook for upper-level undergraduate and graduate classes in electric engineering, information, and telecommunications.
An Instructor's handbook proposing exact strategies to all of the difficulties within the publication is offered from the Wiley editorial division.

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Extra resources for Elements of Information Theory (2nd Edition) (Wiley Series in Telecommunications and Signal Processing)

Sample text

A function is convex if it always lies below any chord. A function is concave if it always lies above any chord. Examples of convex functions include x 2 , |x|, ex , x log x (for √ x≥ 0), and so on. Examples of concave functions include log x and x for x ≥ 0. 3 shows some examples of convex and concave functions. Note that linear functions ax + b are both convex and concave. Convexity underlies many of the basic properties of information-theoretic quantities such as entropy and mutual information.

Then I (X; Y ) = 0, but I (X; Y |Z) = H (X|Z) − H (X|Y, Z) = H (X|Z) = P (Z = 1)H (X|Z = 1) = 12 bit. 9 SUFFICIENT STATISTICS This section is a sidelight showing the power of the data-processing inequality in clarifying an important idea in statistics. Suppose that we have a family of probability mass functions {fθ (x)} indexed by θ , and let X be a sample from a distribution in this family. Let T (X) be any statistic (function of the sample) like the sample mean or sample variance. 123) for any distribution on θ .

Other sufficient statistics may contain additional irrelevant information. For example, for a normal distribution with mean θ , the pair of functions giving the mean of all odd samples and the mean of all even samples is a sufficient statistic, but not a minimal sufficient statistic. In the preceding examples, the sufficient statistics are also minimal. 10 FANO’S INEQUALITY Suppose that we know a random variable Y and we wish to guess the value of a correlated random variable X. Fano’s inequality relates the probability of error in guessing the random variable X to its conditional entropy H (X|Y ).

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Elements of Information Theory (2nd Edition) (Wiley Series in Telecommunications and Signal Processing) by Thomas M. Cover, Joy A. Thomas

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