信息论基础第二版英文教材全文阅读

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"信息论基础第二版英文教材(Elements Of Information Theory) - 高清英文电子档" 本资源是一本关于信息论基础的英文教材——《信息理论基础》的第二版，由Thomas M. Cover和Joy A. Thomas共同撰写，由John Wiley & Sons, Inc. 出版。该教材是信息论领域的经典著作，对理解信息处理、通信系统和数据压缩等主题具有重要价值。信息论是研究信息的量化、传输和处理的数学理论，起源于20世纪40年代，由克劳德·香农(Claude Shannon)创立。该理论主要关注如何在噪声环境中有效地编码和传输信息，以及如何从噪声中恢复原始信息。本书涵盖了信息论的基本概念和核心理论，包括以下几个方面： 1. **熵（Entropy）**：熵是衡量信息不确定性的度量，它定义了信息源的平均信息量。在统计力学中，熵与系统的无序度有关；在信息论中，熵表示一个消息的平均信息含量，用于量化信息源的信息产出率。 2. **互信息（Mutual Information）**：互信息是衡量两个随机变量之间相互依赖程度的量，它表示知道一个随机变量后对另一个随机变量不确定性减少的程度。 3. **信道容量（Channel Capacity）**：信道容量是指一个通信信道在满足一定错误率要求下，能传输的最大信息速率。香农定理阐述了信道容量与信道特性、噪声水平之间的关系。 4. **编码理论（Coding Theory）**：编码理论研究如何有效地编码信息，以提高传输的可靠性和效率。这包括纠错码，如汉明码、卷积码和涡轮码，以及数据压缩编码，如哈夫曼编码和算术编码。 5. **最大似然估计（Maximum Likelihood Estimation）**：在信号检测和参数估计中，最大似然估计是一种常用的方法，通过选择最可能产生观测数据的模型参数来进行估计。 6. **信息理论与概率统计的关系**：信息论与概率统计紧密相连，许多信息论的概念，如条件熵、联合熵和相对熵，都基于概率论中的概率分布和期望值。 7. **信息理论的应用**：信息论不仅在通信工程中有着广泛的应用，还被用于数据压缩、密码学、机器学习、神经科学、经济学等多个领域。这本书的第二版可能包含了一些更新的内容，比如对新兴技术如网络编码、信息理论在无线通信中的应用的讨论，以及对最新研究成果的介绍。对于学生、研究人员和工程师来说，这是一本深入理解信息论原理及其应用的重要参考资料。

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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