Elements of Information Theory (2nd Edition) (Wiley Series by Thomas M. Cover, Joy A. Thomas

By Thomas M. Cover, Joy A. Thomas

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

the second one variation of this primary textbook keeps the book's culture of transparent, thought-provoking guideline. Readers are supplied once more with an instructive mixture of arithmetic, physics, information, and data theory.

the entire crucial issues in info conception are coated intimately, together with entropy, info compression, channel means, expense distortion, community details concept, and speculation checking out. The authors supply readers with a high-quality figuring out of the underlying concept and purposes. challenge units and a telegraphic precis on the finish of every bankruptcy extra help readers. The old notes that stick to 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 thought, and suggestions capacity
* up-to-date references

Now present and superior, the second one variation of components of knowledge idea continues to be the proper textbook for upper-level undergraduate and graduate classes in electric engineering, records, and telecommunications.
An Instructor's guide featuring distinctive options to the entire difficulties within the booklet is obtainable from the Wiley editorial division.

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

Example text

5) In particular, H (X) = 1 bit when p = 12 . 1. The figure illustrates some of the basic properties of entropy: It is a concave function of the distribution and equals 0 when p = 0 or 1. This makes sense, because when p = 0 or 1, the variable is not random and there is no uncertainty. Similarly, the uncertainty is maximum when p = 12 , which also corresponds to the maximum value of the entropy. 2 Let  a     b X=  c    d with with with with probability 12 , probability 14 , probability 18 , probability 18 .

Hence, we have D(p||q) = 0 if and only if p(x) = q(x) for all x. 90) with equality if and only if X and Y are independent. , X and Y are independent). 91) with equality if and only if p(y|x) = q(y|x) for all y and x such that p(x) > 0. 92) with equality if and only if X and Y are conditionally independent given Z. We now show that the uniform distribution over the range X is the maximum entropy distribution over this range. It follows that any random variable with this range has an entropy no greater than log |X|.

We observe a random variable Y that is related to X by the conditional distribution p(y|x). From Y , we 38 ENTROPY, RELATIVE ENTROPY, AND MUTUAL INFORMATION ˆ where Xˆ is an estimate of X and takes on calculate a function g(Y ) = X, ˆ to be equal to X, and we ˆ . We will not restrict the alphabet X values in X will also allow the function g(Y ) to be random. We wish to bound the probability that Xˆ = X. We observe that X → Y → Xˆ forms a Markov chain. Define the probability of error Pe = Pr Xˆ = X .

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