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Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Gallager Published Mathematics. Communication Systems and Information Theory.

All rights reserved. Reproduction or translation of any part of this work beyond that permitted by Sections or of the United States Copyright Act without the permission of the copyright owner is unlawful. This book is designed primarily for use as a first-year graduate text in information theory, suitable for both engineers and mathematicians. It is assumed that the reader has some understanding of freshman calculus and elementary probability, and in the later chapters some introductory random process theory.

Unfortunately there is one more requirement that is harder to meet. The reader must have a reasonable level of mathematical maturity and capability for abstract thought. The major results of the theory are quite subtle and abstract and must sometimes be arrived at by what appears to be rather devious routes. Fortunately, recent simplifications in the theory have made the major results more accessible than in the past.

Because of the subtlety and abstractness of the subject, it is necessary to be more rigorous than is usual in engineering.

I have attempted to soften this wherever possible by preceding the proof of difficult theorems both with some explanation of why the theorem is important and with an intuitive explanation of why it is true.

An attempt has also been made to provide the simplest and most elementary proof of each theorem, and many of the proofs here are new. I have carefully avoided the rather obnoxious practice in many elementary textbooks of quoting obscure mathematical theorems in the middle of a proof to make it come out right.

There are a number of reasons for the stress on proving theorems here. One of the main reasons is that the engineer who attempts to apply the theory will rapidly find that engineering problems are rarely solved by applying theorems to them. The theorems seldom apply exactly and one must understand the proofs to see whether the theorems provide any insight into the problem.

Another reason for the stress on proofs is that the techniques used in the proofs are often more useful in doing new research in the area than the theorems themselves.

A final reason for emphasizing the precise statement of results and careful proofs is that the text has been designed as an integral part of a course in information theory rather than as the whole course. Philosophy, intuitive understanding, examples, and applications, for example, are better developed in the give and take of a classroom, whereas precise statements and details are better presented in the permanent record v.

Enough of the intuition has been presented here for the instructor and the independent student, but added classroom stress is needed for the beginning graduate student. A large number of exercises and problems are given at the end of the text. These range from simple numerical examples to significant generalizations of the theory. There are relatively few examples worked out in the text, and the student who needs examples should pause frequently in his reading to work out some of the simpler exercises at the end of the book.

There are a number of ways to organize the material here into a onesemester course. Chapter I should always be read first and probably last also.

After this, my own preference is to cover the following sections in order: 2. Another possibility, for students who have some background in random processes, is to start with Sections 8. Another possibility, for students with a strong practical motivation, is to start with Chapter 6 omitting Section 6. Other possible course outlines can be made up with the help of the following table of prerequisites.

Table of Prerequisites Sections 2. As a general rule, the latter topics in each chapter are more difficult and are presented in a more terse manner than the earlier topics. They are included primarily for the benefit of advanced students and workers in the field, although most of them can be covered in a second semester. Instructors are. The material in Sections 4. I apologize to the many authors of significant papers in information theory whom I neglected to cite.

I tried to list the references that I found useful in the preparation of this book along with references for selected advanced material. Many papers of historical significance were neglected, and the authors cited are not necessarily the ones who have made the greatest contributions to the field.

Robert G. I am particularly grateful to R. Fano who stimulated my early interest in information theory and to whom lowe much of my conceptual understanding of the subject. This text was started over four years ago with the original idea of making it a revision, under joint authorship, of The Transmission of Information by R.

As the years passed and the text grew and changed, it became obvious that it was a totally different book. However, my debt to The Transmission of Information is obvious to anyone familiar with both books. I am also very grateful to P. Elias, J. Wozencraft, and C. Shannon for their ideas and teachings, which I have used liberally here. Another debt is owed to the many students who have taken the information theory course at MIT and who have made candid comments about the many experiments in different ways of presenting the material here.

Finally I am indebted to the many colleagues who have been very generous in providing detailed criticisms of different parts of the manuscript.

Massey has been particularly helpful in this respect. Also, G. Forney, H. Yudkin, A. Wyner, P. Elias, R. Kahn, R. Kennedy, J. Max, J. Pinkston, E. Berlekamp, A. Kohlenberg, 1. Jacobs, D. Sakrison, T. Kailath, L. Seidman, and F. Preparata have all made a number of criticisms that significantly improved the manuscript.

Group Theory Subgroups Cyclic Subgroups 6. Memoryless Channels with Discrete Time 7. Communication theory deals primarily with systems for transmitting information or data from one point to another. A rather general block diagram for visualizing the behavior of such systems is given in Figure 1. The source output in Figure 1. The channel might represent, for example, a telephone line, a high frequency radio link, a space communication link, a storage medium, or a biological organism for the case where the source output is a sensory input to that organism.

The channel is usually subject to various types of noise disturbances, which on a telephone line, for example, might take the form of a time-varying frequency response, crosstalk from other lines, thermal noise, and impulsive switching noise. The encoder in Figure 1. The processing might include, for example, any combination of modulation, data reduction, and insertion of redundancy to combat the channel noise.

The decoder represents the processing of the channel output with the objective of producing at the destination an acceptable replica of or response to the source output.

In the early 's, C. Shannon developed a mathematical theory, called information theory, for dealing with the more fundamental aspects of communication systems. The distinguishing characteristics of this theory are, first, a great emphasis on probability theory and, second, a primary concern with the encoder and decoder, both in terms of their functional roles and in terms of the existence or nonexistence of encoders and decoders that achieve a given level of performance.

In the past 20 years; information theory has been made more precise, has been extended, and has 1. Our purpose in this book is to present this theory, both bringing out its logical cohesion and indicating where and how it can be applied.

As in any mathematical theory, the theory deals only with mathematical models and not with physical sources and physical channels.

One would think, therefore, that the appropriate way to begin the development of the theory would be with a discussion of how to construct appropriate mathematical models for physical sources and channels.

This, however, is not the way that theories are constructed, primarily because physical reality is rarely simple enough to be precisely modeled by mathematically tractable Noise. Our procedure here will be rather to start by studying the simplest classes of mathematical models of sources and channels, using the insight and the results gained to study progressively more complicated classes of models. Naturally, the choice of classes of models to study will be influenced and motivated by the more important aspects of real sources and channels, but our view of what aspects are important will be modified by the theoretical results.

Finally, after understanding the theory, we shall find it useful in the study of real communication systems in two ways. First, it will provide a framework within which to construct detailed models of real sources and channels. Second, and more important, the relationships established by the theory provide an indication of the types of tradeoffs that exist in constructing encoders and decoders for given systems.

While the above comments apply to almost any mathematical theory, they are particularly necessary here because quite an extensive theory must be developed before the more important implications for the design of communication systems will become apparent.

In order to further simplify our study of source models and channel models, it is helpful to partly isolate the effect of the source in a communication system from that of the channel.

This can be done by breaking the encoder and decoder of Figure 1. The purpose of the source encoder is to represent the source output by a sequence of binary digits and one of the major questions of concern is to determine how many binary digits per unit time are required to represent the output of any given source model.

The purpose of the channel encoder. It is not obvious, of course, whether restricting the encoder and decoder to the form of Figure 1. One of the most important results of-tt. Figure 1. From a practical standpoint, the splitting of encoder and decoder in Figure 1.

This, of course, facilitates the use of different sources on the same channel. In the next two sections, we shall briefly describe the classes of source models and channel models to be studied in later chapters and the encoding and decoding of these sources and channels.

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Robert G. Download book Information Theory and Reliable communication. Click on a thumbnail to go to Google Books. Get this from a library! Information theory and reliable communication. This file is hosted at fileserve. The book is.

INFORMATION THEORY AND. RELIABLE COMMUNICATION. Robert G. Gallager. Massachusetts Institute of Technology. JOHN WILEY & SONS. New York.

Course Pre-requisites: EE and familiarity with basic concepts of probability. Course Outline: This course will serve as the first among the sequence of two courses in the area of Information Theory. The first part of the first course will introduce the ideal of uncertainty, which is a useful measure in studying the data compression and deriving the results related to compression. Compressing data naturally leads to the need for coding strategies that can represent the data in the most efficient way. This problem is studied in the context of optimal coding and the notion of optimality is introduced.

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*Robert G. From to , he was at Bell Telephone Laboratories and then the U.*

Robert Gray Gallager is an American electrical engineer known for his work on information theory and communications networks. He received the Claude E. Information Theory and Reliable Communication Guide books.

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ГЛАВА 106 К окну комнаты заседаний при кабинете директора, расположенной высоко над куполом шифровалки, прильнули три головы. От раздавшегося взрыва содрогнулся весь комплекс Агентства национальной безопасности. Лиланд Фонтейн, Чед Бринкерхофф и Мидж Милкен в безмолвном ужасе смотрели на открывшуюся их глазам картину. Тридцатью метрами ниже горел купол шифровалки. Поликарбонатная крыша еще была цела, но под ее прозрачной оболочкой бушевало пламя. Внутри клубились тучи черного дыма.

Course held at the Department for Automation and Information July Authors; (view affiliations). Robert Gallager Download book PDF Book Title Information Theory and Reliable Communication; Book Subtitle Course held at the.