信息论基础第二版：英文经典教程

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"信息论基础（第二版）英文 Cover" 这篇摘要提及的是一本关于信息论的经典教程——"Elements of Information Theory"的第二版，由Thomas M. Cover 和 Joy A. Thomas 合著。这本书由John Wiley & Sons, Inc. 出版，并在2006年获得版权。同时，它在美国和其他地方同步发行。信息论是通信工程、计算机科学、统计学和数学等领域的一个重要分支，主要研究如何有效地传输、存储和处理信息。本书作为信息论的经典教程，可能涵盖了以下几个关键知识点： 1. **熵（Entropy）**：信息论中的基本概念，用来衡量一个随机变量的不确定性或信息量。熵越大，信息的不确定性越高。 2. **互信息（Mutual Information）**：衡量两个随机变量之间的相关性，表示知道一个变量后对另一个变量的信息增益。 3. **信源编码（Source Coding）**：研究如何用最少的比特数来表示信息源输出的符号序列，例如哈夫曼编码和香农-福利特编码。 4. **信道容量（Channel Capacity）**：一个通信信道能够无错误地传输信息的最大速率，由香农定理给出。 5. **信道编码（Channel Coding）**：通过添加冗余信息来保护原始数据，使得在信道噪声存在的情况下，接收端仍能恢复原始信息，如里德-索洛蒙码和卷积码。 6. **噪声和信噪比（Noise and Signal-to-Noise Ratio, SNR）**：在通信系统中，噪声干扰信号的传输，信噪比是衡量信号质量的重要指标。 7. **最大似然估计（Maximum Likelihood Estimation, MLE）**：一种统计推断方法，用于估计参数的最佳估计值。 8. **率失真理论（Rate-Distortion Theory）**：研究在有限的带宽下，如何在失真与压缩率之间找到最佳平衡。 9. **网络信息论（Network Information Theory）**：包括多用户信息论和多天线通信等，研究在复杂网络结构中的信息传输问题。 10. **马尔科夫决策过程（Markov Decision Processes, MDPs）**：在动态环境中，基于当前状态做出决策，以最大化长期奖励的理论，与信息理论有交叉应用。这本教材可能会深入讨论这些概念，通过数学模型和实例解析，帮助读者理解并掌握信息论的基本原理及其在实际问题中的应用。此外，还可能包含练习题和案例研究，以加强学习效果。对于想要深入了解信息论的读者，这无疑是一本极具价值的参考资料。

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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信息论基础第二版：英文经典教程

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