信息论基础第二版：电子信息工程权威教材

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《信息论基础第二版》是一本专为电子信息工程专业学生编写的原版英文教材，由Thomas Cover和Joy Thomas合著，由John Wiley & Sons, Inc. 出版。该书在2006年首次发行，并受到版权保护。本书旨在深入介绍信息论的基本概念、理论和应用，是理解和研究通信系统、数据压缩、密码学等领域不可或缺的参考资料。信息论是通信科学与电子工程的核心分支，它探讨了信息的量化、编码、传输和处理的基本原理。《信息论基础第二版》涵盖了以下几个关键知识点： 1. **概率论基础**：作为信息论的基石，章节会介绍概率论的概念，如随机变量、概率分布、期望值和方差，这些是理解信源和信道特性的前提。 2. **信源编码**：作者会讲解如何将随机信号转换为数字形式，包括无失真编码（如香农编码）、有损编码（如哈夫曼编码），以及熵和信息率等概念。 3. **信道模型与容量**：书中会讨论各种信道模型（如加性白噪声信道、多径衰落信道），重点介绍信道容量的计算方法，即在给定信噪比下，最大可能的信息传输速率。 4. **错误控制编码**：这部分内容涉及纠错码的设计，如线性分组码、卷积码、 turbo码等，以及它们在实际通信系统中的应用。 5. **数据压缩**：作者会阐述熵编码（如霍夫曼编码）和源编码的联合，以及熵编码在数据压缩中的重要性，如Lempel-Ziv算法。 6. **信息理论在其他领域的应用**：除了通信技术，信息论也广泛应用于密码学（如密码分析和密码设计）、信号处理（如信号检测）以及计算机科学（如算法复杂度）等领域。 7. **版权和法律问题**：在版权页的最后，提到了出版商对复制、存储和传播该书内容的规定，强调了遵循版权法的重要性。《信息论基础第二版》是一本详尽且深入的教科书，适合对信息技术感兴趣的读者进行系统学习，无论是作为课堂教材还是自我研习，都能帮助读者掌握信息论这一核心领域的基本理论和技术。

PREFACE TO THE

SECOND EDITION

In the years since the publication of the ﬁrst edition, there were many

aspects of the book that we wished to improve, to rearrange, or to expand,

but the constraints of reprinting would not allow us to make those changes

between printings. In the new edition, we now get a chance to make some

of these changes, to add problems, and to discuss some topics that we had

omitted from the ﬁrst edition.

The key changes include a reorganization of the chapters to make

the book easier to teach, and the addition of more than two hundred

new problems. We have added material on universal portfolios, universal

source coding, Gaussian feedback capacity, network information theory,

and developed the duality of data compression and channel capacity. A

new chapter has been added and many proofs have been simpliﬁed. We

have also updated the references and historical notes.

The material in this book can be taught in a two-quarter sequence. The

ﬁrst quarter might cover Chapters 1 to 9, which includes the asymptotic

equipartition property, data compression, and channel capacity, culminat-

ing in the capacity of the Gaussian channel. The second quarter could

cover the remaining chapters, including rate distortion, the method of

types, Kolmogorov complexity, network information theory, universal

source coding, and portfolio theory. If only one semester is available, we

would add rate distortion and a single lecture each on Kolmogorov com-

plexity and network information theory to the ﬁrst semester. A web site,

http://www.elementsoﬁnformationtheory.com, provides links to additional

material and solutions to selected problems.

In the years since the ﬁrst edition of the book, information theory

celebrated its 50th birthday (the 50th anniversary of Shannon’s original

paper that started the ﬁeld), and ideas from information theory have been

applied to many problems of science and technology, including bioin-

formatics, web search, wireless communication, video compression, and

PREFACE TO THE

FIRST EDITION

This is intended to be a simple and accessible book on information theory.

As Einstein said, “Everything should be made as simple as possible, but no

simpler.” Although we have not veriﬁed the quote (ﬁrst found in a fortune

cookie), this point of view drives our development throughout the book.

There are a few key ideas and techniques that, when mastered, make the

subject appear simple and provide great intuition on new questions.

This book has arisen from over ten years of lectures in a two-quarter

sequence of a senior and ﬁrst-year graduate-level course in information

theory, and is intended as an introduction to information theory for stu-

dents of communication theory, computer science, and statistics.

There are two points to be made about the simplicities inherent in infor-

mation theory. First, certain quantities like entropy and mutual information

arise as the answers to fundamental questions. For example, entropy is

the minimum descriptive complexity of a random variable, and mutual

information is the communication rate in the presence of noise. Also,

as we shall point out, mutual information corresponds to the increase in

the doubling rate of wealth given side information. Second, the answers

to information theoretic questions have a natural algebraic structure. For

example, there is a chain rule for entropies, and entropy and mutual infor-

mation are related. Thus the answers to problems in data compression

and communication admit extensive interpretation. We all know the feel-

ing that follows when one investigates a problem, goes through a large

amount of algebra, and ﬁnally investigates the answer to ﬁnd that the

entire problem is illuminated not by the analysis but by the inspection of

the answer. Perhaps the outstanding examples of this in physics are New-

ton’s laws and Schr

odinger’s wave equation. Who could have foreseen the

awesome philosophical interpretations of Schr

odinger’s wave equation?

In the text we often investigate properties of the answer before we look

at the question. For example, in Chapter 2, we deﬁne entropy, relative

entropy, and mutual information and study the relationships and a few

xvii

xviii PREFACE TO THE FIRST EDITION

interpretations of them, showing how the answers ﬁt together in various

ways. Along the way we speculate on the meaning of the second law of

thermodynamics. Does entropy always increase? The answer is yes and

no. This is the sort of result that should please experts in the area but

might be overlooked as standard by the novice.

In fact, that brings up a point that often occurs in teaching. It is fun

to ﬁnd new proofs or slightly new results that no one else knows. When

one presents these ideas along with the established material in class, the

response is “sure, sure, sure.” But the excitement of teaching the material

is greatly enhanced. Thus we have derived great pleasure from investigat-

ing a number of new ideas in this textbook.

Examples of some of the new material in this text include the chapter

on the relationship of information theory to gambling, the work on the uni-

versality of the second law of thermodynamics in the context of Markov

chains, the joint typicality proofs of the channel capacity theorem, the

competitive optimality of Huffman codes, and the proof of Burg’s theorem

on maximum entropy spectral density estimation. Also, the chapter on

Kolmogorov complexity has no counterpart in other information theory

texts. We have also taken delight in relating Fisher information, mutual

information, the central limit theorem, and the Brunn–Minkowski and

entropy power inequalities. To our surprise, many of the classical results

on determinant inequalities are most easily proved using information the-

oretic inequalities.

Even though the ﬁeld of information theory has grown considerably

since Shannon’s original paper, we have strived to emphasize its coher-

ence. While it is clear that Shannon was motivated by problems in commu-

nication theory when he developed information theory, we treat informa-

tion theory as a ﬁeld of its own with applications to communication theory

and statistics. We were drawn to the ﬁeld of information theory from

backgrounds in communication theory, probability theory, and statistics,

because of the apparent impossibility of capturing the intangible concept

of information.

Since most of the results in the book are given as theorems and proofs,

we expect the elegance of the results to speak for themselves. In many

cases we actually describe the properties of the solutions before the prob-

lems. Again, the properties are interesting in themselves and provide a

natural rhythm for the proofs that follow.

One innovation in the presentation is our use of long chains of inequal-

ities with no intervening text followed immediately by the explanations.

By the time the reader comes to many of these proofs, we expect that he

or she will be able to follow most of these steps without any explanation

and will be able to pick out the needed explanations. These chains of

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