By Raymond W. Yeung (auth.)

ISBN-10: 1441986081

ISBN-13: 9781441986085

ISBN-10: 1461346452

ISBN-13: 9781461346456

A First path in info idea is an updated creation to info thought. as well as the classical subject matters mentioned, it presents the 1st accomplished remedy of the idea of I-Measure, community coding idea, Shannon and non-Shannon style info inequalities, and a relation among entropy and team thought. ITIP, a software program package deal for proving details inequalities, can be integrated. With quite a few examples, illustrations, and unique difficulties, this booklet is great as a textbook or reference e-book for a senior or graduate point direction at the topic, in addition to a reference for researchers in similar fields.

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**Extra resources for A First Course in Information Theory**

**Example text**

For brevity, a prefix-free code will be referred to as a prefix code. 3 is not a prefix code because the codeword 0 is a prefix of the codeword 01, and the codeword 1 is a prefix of the codeword 10. It can easily be checked that the follow ing code C' is a prefix code. EXAMPLE X C'(x ) A B 0 JO llO IllI C D A D-ary tree is a graphical representation of a collection of finite sequences of D-ary symbols. In a D-ary tree, each node has at most D children. If a node has at least one child, it is called an internal node, otherwise it is called a leaf The children of an internal node are labeled by the D symbols in the code alphabet.

5 INFORMATIONAL DIVERGENCE Let p and q be two probability distributions on a common alphabet X . We very often want to measure how much p is different from q, and vice versa. In order to be useful, this measure must satisfy the requirements that it is always nonnegative and it takes the zero value if and only if p = q. We denote the support of p and q by Sp and Sq, respectively. The informational divergence defined below serves this purpose. 87) where E p denotes expectation with respect to p. In the above definition, in addition to the convention that the summation is taken over Sp, we further adopt the convention p(x) log ~ = 00 if q(x) = O.

As Pe ~ O. 159) tends to 0, which implies H(XIX) also tends to O. However. this is not necessarily the case if X is infinite, which is shown in the next example. 49 Let X take the value 0 with probability 1. Let Z be an independent binary random variable taking values in {O, I}. 46 whose entropy is infinity. Let P; = Pr{X =I X} = Pr{Z = I}. 177) (1 - Pe) · 0 + P, . 179) > O. Therefore, H(X JX) does not tend to 0 as P, ~ O. ENTROPY RATE OF STATIONARY SOURCE In the previous sections, we have discussed various properties of the entropy of a finite collection of random variables.

### A First Course in Information Theory by Raymond W. Yeung (auth.)

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