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Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing) [Englisch] [Gebundene Ausgabe]

Thomas M. Cover , Joy A. Thomas
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Kurzbeschreibung

8. September 2006 Wiley Series in Telecommunications and Signal Processing
The latest edition of this classic is updated with new problem sets and material
 

The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory.
 
All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points.
 
The Second Edition features:
* Chapters reorganized to improve teaching
* 200 new problems
* New material on source coding, portfolio theory, and feedback capacity
* Updated references
 
Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.

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"This book is recommended reading, both as a textbook and as a reference." (Computing Reviews.com, December 28, 2006)

Synopsis

The latest edition of this classic is updated with new problem sets and material. The second edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The second edition features: chapters reorganized to improve teaching 200 new problems; new material on source coding, portfolio theory, and feedback capacity; and, updated references. Now current and enhanced, the second edition of "Elements of Information Theory" remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.

An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.


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In diesem Buch (Mehr dazu)
Einleitungssatz
Information theory answers two fundamental questions in communication theory: What is the ultimate data compression (answer: the entropy H), and what is the ultimate transmission rate of communication (answer: the channel capacity C). Lesen Sie die erste Seite
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4.0 von 5 Sternen Information theory 28. März 2014
Format:Gebundene Ausgabe|Verifizierter Kauf
Leider hat sich die Informationstheorie so stark zu Theorie entwickelt, sodaß selbst ich, der ein Leben lang mit dieser Theorie gelebt hat es Schwierig finde das Buch zu lesen. Trotzdem zeigt es wie umfangreich sich diese Theorie entwickelt hat
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Amazon.com: 4.1 von 5 Sternen  21 Rezensionen
91 von 92 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen An Excellent Introduction to Information Theory 16. Mai 2008
Von A Reader - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Verifizierter Kauf
I am writing this review in response to some confusion and unfairness I see in other reviews. Cover and Thomas have written a unique and ambitious introduction to a fascinating and complex subject; their book must be judged fairly and not compared to other books that have entirely different goals.

Claude Shannon provided a working definition of "information" in his seminal 1948 paper, A Mathematical Theory of Communication. Shannon's interest in that and subsequent papers was the attainment of reliable communication in noisy channels. The definition of information that Shannon gave was perfectly fitted to this task; indeed, it is easily shown that in the context studied by Shannon, the only meaningful measure of information content that will apply to random variables with known distribution must be (up to a multiplicative constant) of the now-familiar form h(p) = log(1/p).

However, Shannon freely admitted that his definition of information was limited in scope and was never envisioned as being universal. Shannon deliberately avoided the "murkier" aspects of human communication in framing his definitions; problematic themes such as knowledge, semantics, motivations and intentions of the sender and/or receiver, etc., were avoided altogether.

For several decades, Information Theory continued to exist as a subset of the theory of reliable communication. Some classical and highly regarded texts on the subject are Gallager, Ash, Viterbi and Omura, and McEliece. For those whose interest in Information Theory is motivated largely by questions from the field of digital communications, these texts remain unrivalled standards; Gallager, in particular, is so highly regarded by those who learned from it that it is still described as superior to many of its more recent, up-to-date successors.

In recent decades, Information Theory has been applied to problems from across a wide array of academic disciplines. Physicists have been forced to clarify the extent to which information is conserved in order to completely understand black hole dynamics; biologists have found extensive use of Information Theoretic concepts in understanding the human genome; computer scientists have applied Information Theory to complex issues in computational vs. descriptive complexity (the Mandelbrot set, which has been called the most complex set in all of mathematics, is actually extremely simple from the point of view of Kolmogorov complexity); and John von Neumann's brilliant creation, game theory, which has been called "a universal language for the unification of the behavioral sciences," is intimately coupled to Information Theory, perhaps in ways that have not yet been fully appreciated or explored.

Cover and Thomas' book "Elements of Information Theory" is written for the reader who is interested in these eclectic and exciting applications of Information Theory. This book does NOT treat Information Theory as a subset of reliable communication theory; therefore, the book is NOT written as a competitor for Gallager's classic text. Critics who ask
for a more thorough treatment of rate distortion theory or convolutional codes are criticizing the authors for failing to include topics that are not even central to their goals for the text!

A very selective list of some of the more interesting topics that Cover and Thomas study includes: (1) the Asymptotic Equipartition Property and its consequences for data compression; (2) Information Theory and gambling; (3) Kolmogorov complexity and Chaitin's Omega; (4) Information Theory and statistics; and (5) Information Theory and the stock market. Item (4) on this list is only briefly introduced in Cover and Thomas's book, and appropriately so; however, readers who wish to pursue the fascinating subject of Fischer Information further should consider B. Roy Frieden's book Physics from Fisher Information: A Unification. Frieden identifies a principle of "extreme physical information" as a unifying theme across all of physics, deriving such classic equations as the Klein-Gordon equation, Maxwell's equations, and Einstein's field equations for general relativity from this information-theoretic principle.

This last point is quite typical of Cover and Thomas's book. I participated in a faculty seminar on Information Thoery at my university a few years ago, in which we studied Cover and Thomas as our primary source. We were a diverse group, drawn from five different academic disciplines, and we all found that Cover and Thomas repeatedly introduced us to exciting and unexpected applications of Information Theory, always sending us to the journals for further, more in-depth study.

Cover and Thomas' book has become an established favorite in university courses on information theory. In truth, the book has few competitors. Interested readers looking for additional references might also consider David MacKay's book Information Theory, Inference, and Learning Algorithms, which has as a primary goal the use of information theory in the study of Neural Networks and learning algorithms. George Klir's book Uncertainty and Information considers many alternative measures of information/uncertainty, moving far beyond the classical log(1/p) measure of Shannon and the context in which it arose. Jan Kahre's iconoclastic book The Mathematical Theory of Information is an intriguing alternative in which the so-called Law of Diminishing Information is elevated to primary axiomatic status in deriving measures of information content. I alluded to some of the "murkier" issues of human communication earlier; readers who wish to study some of those issues will find Yehoshua Bar-Hillel's book Language and Information a useful source.

In conclusion, I highly recommend Cover and Thomas' book on Information Theory. It is currently unrivalled as a rigorous introduction to applications of Information Theory across the curriculum. As a person who used to work in the general area of signals analysis, I resist all comparisons of Cover and Thomas' book with the classic text of Gallager; the books have vastly different goals and very little overlap.
10 von 10 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Updated, reorganized, expanded Second Edition 24. März 2007
Von John Matlock - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
The preface of this book says, 'This is intended to be a simple and accessible book on information theory.' That's true, but it is aimed at the senior year or early graduate level where a theoretical background is needed for computer science, communications engineering, applied mathematics or similar fields. The mathematical nature of the book says that the student should at least have a background through calculus and a couple of upper level courses in statistics/probability. After all, Information Theory is generally considered to be a branch of applied mathematics.

On the whole, the writing style of the book (other than the equasions) is rather light and entertaining. For instance his discussion on the similarities between gambling and data compression brings a rather complex notion down something we can identify - that's before he gets into the math of course.

One complaint about the first edition of the book was that it didn't have enough problems for the student. This has been solved by the addition of a couple of hundred additional problems. There is also a dedicated web site for this book with more material, including solutions to selected problems.
14 von 16 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen A good survey of Information Theory 8. Februar 2007
Von Desperate Scholar - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
Elements of Information Theory was the book I used in graduate school. It takes a topical approach to the subject from standard topics like source and channel coding, esoteric concepts like Kolmogorov complexity, to applied topics like how to get rich by applying Information theory to horse racing and the stock market. Overall I thought it was a good book. It is well written and exposes the grandure of subject. However what it provides in bredth it takes away in depth. Several topics, including fundemental ones like entropy, while well illustrated are not at all motivated - they are just given as definitions. In this I feel Galleghers book is superior. Also there is a real dearth of problems, its unusual to do all the problems in a book and feel you have not done enough to understand the material. Many a time I found myself scouring the web for more problems to augment the ones provided. So if you are looking for a broad view of the subject of information theory, this is the book to buy. If you are looking for a deeper understanding of the fundamental topics get Gallegher.
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5.0 von 5 Sternen Very solid introductory book on information theory 21. April 2008
Von Alexander C. Zorach - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Verifizierter Kauf
I give this book five stars for its outstanding clarity, thoroughness, and choice of topics. The writing is excellent, and most topics are easy to understand, although I have a few isolated quibbles about how certain topics are presented.

I feel like the chapters on continuous channels are much tougher to understand and less intuitive than the chapters on discrete channels.

The exercises are very useful, but in my opinion, a bit too easy. There are lots of exercises at the end of each chapter, but there are very few that require deep thinking or creative insight. Most of the exercises are fairly routine. I think a few more involved ones would be welcome.

The one thing that is most lacking in this book are examples. The bulk of the text is made up in exposition of new ideas and proofs of theorems. While the exercises give lots of examples, I still feel that something is missing--especially in the chapters on continuous channels.

As a supplement, I would recommend "Information Theory, Inference, and Learning Algorithms" by MacKay. The two books are very different from each other and have less overlap than one might expect; I think everyone would do well to study both books. That book is much more suitable for self-study, has more concrete examples, and is in my opinion more fun and interesting (which says a lot, because this book is itself quite fun and interesting). It also has some more involved exercises. Also, it covers coding theory in more depth than this book (something that one might not realize from its name), and it integrates a Bayesian perspective into things more deeply.
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5.0 von 5 Sternen Inspiring Introduction to an Inspiring Subject 23. März 2012
Von const - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
This classic text on Information Theory is one of the best scientific book I have read to date. If I have to be completely honest, part of the book's success is well due to the inherent beauty of the subject it deals with, Information Theory.

Studying Information Theory, something this book is ideal for, will give you a greater understanding and appreciation of all fields actively related to probability/statistics. And that as Information theory is not necessarily viewed --and this book does not view it-- in the narrow perspective of transmission channels and communication systems (although things come in place naturally there). The presentation found here is sufficiently devoid of such restrictive connections, thus allowing the reader to easily reflect information theoretic ideas on his field of interest.

The clarity of the presentation is remarkable. The various notions of information theory are presented intuitively and yet succinctly. The breadth of the subjects the book deals with is extensive enough to at least introduce you to most Information Theoretic subjects one might ever encounter. There are chapters about Entropy Rates of Stochastic Processes (Random Walks, Markov Chains), Data Compression, Channel Capacity, Rate Distortion Theory and Kolmogorov Complexity. There are also chapters studying the connections of Information Theory and its implications to Gambling (not enough to get you addicted), Portfolio Theory and Statistics. There is also a separate chapter containing a collection of some useful inequalities for Information Theory.

Most fundamental theorems have proofs, or proof sketches. Proofs are all concise and very very accessible. Each non-trivial step in an equation is explained, but not in a frustrating way. Actually that is one of the most brilliant features of the book, the proofs and their explanations sort of replace the need for informal, lengthy verbal explanations. In a sense, they sort of urge you to read the proofs, even if you are lazy. And it pays off.

Now, provided all can never be satisfied, mathematicians and people obsessed with rigour --in the good sense-- will certainly not find what they are looking for here. Although I strongly believe that a first introduction to Information Theory should be more intuitive and less formal, it is true that some unclear or demanding and complex portions of the book could be traced down to the lack of rigour. And although the authors brilliantly conceal them and sort of let you take their word for it, the only way to really address the issues is by reintroducing the entire theory in a Measure Theoretic context. That is not for the faint of the heart though, as Measure Theory is a very abstracted mathematical theory and would inevitably destroy the beauty of the subject by making it more dry and formal.
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