Thomas M. Cover与Joy A. Thomas的信息论基础第二版英文影印版概要

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"《信息论基础》第二版是Thomas M. Cover和Joy A. Thomas合著的一本经典著作，由John Wiley & Sons, Inc.出版。这本书是信息论领域的基石，是英文原版，对理解数据传输、编码理论、通信系统以及信息处理的基本原理有着至关重要的作用。作者以其深入浅出的方式阐述了诸如熵、信道容量、源编码、数据压缩、错误控制编码等核心概念，是学习和研究信息科学的必备参考书。本书的核心内容包括： 1. 基本概念：章节首先介绍了信息的基本概念，如信息量（熵）的定义和度量，以及如何量化不确定性。读者将理解熵与随机变量的概率分布密切相关，以及如何通过熵来衡量信息的最小单元。 2. 信道模型：作者详细讨论了诸如加性高斯白噪声信道（AWGN）、香农定理等内容，这些都是设计无线和有线通信系统的基础，展示了如何在有限带宽和噪声环境中最大化传输效率。 3. 编码理论：探讨了源编码和信道编码的重要性，包括无失真编码（如哈夫曼编码）和纠错编码（如香农-费诺编码），这些编码技术对于压缩数据和保证数据传输的可靠性至关重要。 4. 数据压缩：介绍了如何利用信息熵来设计高效的压缩算法，如熵编码和预测编码，使大量数据可以被有效地压缩存储。 5. 信息处理与信号处理：书中还涵盖了概率统计在信息处理中的应用，如贝叶斯定理和滤波器设计，这些都是现代信息技术中的关键技术。 6. 版权声明：最后部分强调了版权法规，提醒读者在使用或复制本书内容时必须遵守相关规定，以尊重作者的知识产权。《信息论基础》第二版因其权威性和实用性，在计算机科学、电子工程、通信工程、数据科学等领域享有高度评价，无论是作为教材还是专业参考书，都能帮助读者深入理解信息传输和处理的核心原理。"

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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