[完整版]Information Theory-Jan C.A van der Lubbe（附习题答案）
1997年Jan C.A van der Lubbe所著教材]Information Theory的再版，1997年版由Cambridge University Press出版，再版由Delft Academic Press出版。每章节最后的Solutions部分附上了每张练习的答案。原版英文。PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
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CAMERIDGE UNIVERSLTY PRESS
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Originally published in Dutch as informatietheorie by vSSD and a vSSD
1988
C English translation Cambridge University Press 1997
The book is in copyright, Subject to statutory exception and to the provisions
take place without the written permission of cambridge University Press,
of relevant collective licensing agreements, no reproduction of any part m
First published in English by Cambridge University Press 1997 as
Information Theory
Panted in the United kingdon at the University Press, Canbridge
Typeset in Times
A catalogue record for this book is available fiom the British Library
ISBN 0 521 461987 hardback
ISBN0 $21467608 paperback
Preface
On all levels of society systems have been introduced that deal with the
transmission, storage and processing of information. we live in what is
usually called the infomation society Information has become a key word
in our society. It is not surprising therefore that from all sorts of quarters
interest has been shown in what information really is and consequently in
quiring a better knowledge as to how information can be dealt with as
fficiently as possible
Information theory is characterized by a quantitative approach to the notion
of information. By means of the introduction of measures for intormation
answers will be sought to such questions as: How to transmit and store
information as compactly as possible? What is the maxinum quantity of
information that can be transmitted through a channel? How can security
best be arranged? Etcetera. Crucial questions that enable us to enhance the
performance and to grasp the limits of our information systems
This book has the purpose of introducing a number of basic notions of
information theory and clarifying them by showing their significance in
present applications. Matters that will be described are, among others:
Shannons information measure. discrete and continuous information
sources and information channels with or without memory, source and
hannel decoding, rate distortion theory, error-correcting codes and the
information theoretical approach to cryptology Special attention has been
paid to multiterminal or network information theory; an area with still lots
of unanswered questions, but which is of great significance because most of
our information is transmitted by networks
All chapters are concluded with questions and worked solutions. That
makes the book suitable for self study
xii Preface
The content of the book has been largely based on the present lectures b
the author for students in Electrical Engincering, Tcchnical Mathematics
and Informatics, Applied Physics and Mechanical Engincering at the Delft
University of Technology, as well as on former lecture notes by profs
Ysbrand Boxma, Dick Boekec and Jan Biemond. The questions have becn
derived from recent exams
The author wishes to express his gratitude to the colleagues mentioncd
above as well as the other colleagues who in one way or other contributed to
this textbook. Especially I wish to thank e. Prof. Ysbrand Boxma, who
lectured on information theory at the delft university of technology when i
was a student and who introduced me to information theory. Under his
inspiring guidance I rcceived my M.Sc. in Elcctrical Engineering and my
Ph.D. in the techrical sciences. In writing this book his old lecture notes
were still very helpful to me. His influence has been a determining factor in
my later career.
Delft, December 1996
Jan C.A. van der Lubbe
Contents
reace
page xr
Discrete information
1.1 The ongin of information theory
2 The concept of probability
4
1. 3 Shannon's information measure
8
1. 4 Conditional, joint and mutual information measures
16
1.5 Axiomatic foundations
22
1. 6 The communication model
d7 Exercises
27
1. 8 Solutions
29
2 The discrete memoryless information source
39
2.1 The discrete information source
39
2.2 Source coding
43
2.3 Coding strategies
49
2. 4 Most probable messages
56
2.5 Exercises
2.6 Solutions
3
The discrete information source with memory
79
3.1 Markov processes
79
3.2 The information of a discrete source with memory
85
3.3 Coding aspects
9
3.4 Exercises
95
3.5 Solutions
98
The discrete communication channel
l09
4.1 Capacity of noiseless channels
109
4.2 Capacity of noisy channels
l16
4.3 Error probability and equivocation
126
vila Contents
4.4 Coding theorem for discrete memory less channeis
4.5 Cascading of channels
133
4.6 Channels with memory
136
47 Exercises
138
4.8 Solutions
42
s The continue
nformation source
155
5.1 Probability density functions
155
5.2 Stochastic signals
164
5.3 The continuous information measure
171
5.4 Information measures and sources with memory
176
5.5 Information power
186
56 Exercises
190
5.7 Solutions
194
6 The continuous communication changel
209
6. 1 The capacity of continuous communication channe]s
209
6.2 The capacity in the case of additive gaussian white noise
214
6.3 Capacity bounds in the case of non-gaussian white noise
215
6. 4 Channel coding theorem
218
6.5 The capacity of a gaussian channel with memory
222
6.6 Exercises
227
6.7 Solutions
229
7 Rate distortion theory
238
7.1 The discrete rate distortion function
238
7.2 Properties of the r(D) function
243
7.3 The binary case
250
7.4 Source coding and information transmission thcorems
253
7.5 The continuous rate distortion function
25
7.6 Exercise
264
TI Solutions
265
Network information theory
268
8.1 Introduction
268
8.2 MulLi-access communication channel
269
8. 3 Broadcast channels
28I
8.4 Two-way channels
292
8.5 Exercises
298
8.6 Solutions
9 Error-correcting codes
305
9.1 Introduction
305
Contents
9.2 Linear block codes
307
9.3 Syndrome coding
3I2
9.4 Hamming codes
316
9.5 Exercises
318
9.6 Solutions
319
10 Cryptology
324
10.1 Cryptography and cryptanalysis
324
10.2 The general scheme of cipher systems
325
10.3 Cipher systems
327
10.4 Amount of information and security
334
10.5 The unicity dislance
33
10.6 Exercises
340
10.7 Solutions
341
Bibliography
345
Index
347
1
Discrete information
1.I The origin of information theory
Information theory is the science which deals with the concept informa
tion, its measurement and its applications. In its broadest sense distinction
can be made between the American and British traditions in information
theory
In general there are three types of informaLion
syntactic information, related to the symbols from which messages are
built up and to their interrelations
semantic information, related to the meaning of messages, their
referential aspect
pragmatic informarion, related to the usage and effect of messages
This being so, syntactic information mainly considers the form of
nformation, whereas semantic and pragmatic information are related to the
information content
Consider the following sentences
(O John was brought to the railway station by taxi
(U The taxi brought John to the railway station
(i) There is a traffic jam on highway A3, between Nuremberg and Munich
in Germany.
iv) There is a traffic jam on highway A3 in Germany.
The sentences(i)and (ii)are syntactically different. HoweveR, semantically
and pragmatically they are identical. They bave the same meaning and are
both equally informative
The sentences (ii)and (iv) do not differ only with respect to their syntax
but also with respect to their semantics Sentence (iii)gives more precise
information than sentence (iv)
2 Discrete information
The pragmatic aspect of information mainly depends on the context. The
information contained in the sentences (iii) and (iv) for example is relevant
for someone in Germany, but not for someone in the USA
The semantic and pragmatic aspects of information are studied in the british
tradition of information theory. This being So, the British tradition is closely
related to philosophy, psychology and biology. The British tradition is
influenced mainly by scientists like MacKay, Carnap, Bar-Hillel, Ackoff
and hintikka
The American tradition deals with the syntactic aspects of information. I
this approach there is full abstraction from the meaning aspects of informa
tion. There, basic questions are the measurement of syntactic information
the fundamental limits on the amount of information which can be trans
mitted, the fundamental limits on the compression of information which can
be achieved and how to build information processing systems approaching
these limits. A rather technical approach to information remains
The American tradition in information theory is sometimes referred to as
communication theory, mathematical information theory or in short as
information theory. Well-known scientists of the American tradition are
Shannon, Renyi, Gallager and Csiszar among others
However, Claude E. Shannon, who published his article"A mathematical
theory of communication in 1948, is generally considered to be the founder
of the American tradition in information theory. There are, nevertheless, a
number of forerunners to Shannon who attempted to formalise the efficient
use of communication systems.
In 1924 H. Nyquist published an article wherein he raised the matter of how
messages (or characters, to use his own words) could be sent over a
telegraph channel with maximum possible speed, but without distortion. The
term information however was not yet used by him as such
It was R.Y. L. Hartley(1928)whc first tried to define a measure of
information. He went about it in the following manner.
Assume that for every symbol of a message one has a choice of s
possibilities. By now considering messages of I symbols, one can distinguish
s messages. Hartley now defined the amount of information as the
logarithm of the number of distinguishable messages. In the case of
messages of length I one therefore finds
HH(s)=log[sF=I log(s).
For messages of length 1 one would find
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