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信息论编码与密码学(英文)
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本书主要为信息论编码与密码学的知识,里面含有信道编码、信源编码、以及通信安全编码三大部分的章节,适合基础学习
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Acknowledgements
I would like to thank the
Department
of
Electrical Engineering at the Indian Institute
of
Technology (liT), Delhi for providing a stimulating academic environment that inspired this
book.
In
particular, I would like to
thank
Prof. S.C. Dutta Roy, Prof. Surendra Prasad,
Prof. H.M. Gupta, Prof.
V.K
Jain, Prof.
Vinod
Chandra, Prof. Santanu Chaudhury, Prof. S.D.
Joshi, Prof. Sheel Aditya, Prof. Devi Chadha, Prof. D. Nagchoudri, Prof. G.S. Visweswaran,
Prof.
R
K.
Patney, Prof. V. C. Prasad, Prof.
S. S.
Jamuar
and Prof. R K
P.
Bhatt. I
am
also
thankful to Dr.
Subrat Kar, Dr. Ranjan
K.
Mallik
and
Dr. Shankar Prakriya for friendly
discussions. I have
been
fortunate
to
have several batches
of
excellent students whose feedback
have helped
me
improve the contents
of
this book. Many of the problems given at the
end
of
the
chapters have
been
tested either as assignment problems or examination problems.
My
heartfelt gratitude
is
due to Prof. Bernard D. Steinberg, University of Pennsylvania, who
has
been
my
guide, mentor, friend
and
also
my
Ph.D
thesis advisor. I
am
also grateful to
Prof. Avraham Freedman, Tel Aviv University, for his support
and
suggestions as
and
when
sought
by
me. I would like to thank Prof.
B.
Sundar Rajan
of
the Electrical Communication
Engineering group at the Indian Institute
of
Science, Bangalore, with whom I
had
a preliminary
discussion about writing this book.
I wish to acknowledge valuable feedback on this initial manuscript from Prof. Ravi Motwani,
liT
Kanpur, Prof. A.K. Chaturvedi,
liT
Kanpur, Prof.
N.
Kumaravel,
Anna
University, Prof. V.
Maleswara Rao, College of Engineering, GITAM, Visakhapatnam, Prof. M. Chandrasekaran,
Government College of Engineering,
Salem
and
Prof. Vikram Gadre,
liT
Mumbai.
I
am
indebted to my parents, for their love
and
moral support throughout my life. I am also
grateful to my grandparents for their blessings,
and
to
my
younger brother, Shantanu, for the
infinite discussions on finite topics.
Finally, I would like to thank
my
wife
and
best friend, Aloka, who encouraged me at· every
stage
of
writing this book.
Her
constructive suggestions
and
balanced criticism have been instru-
mental in making the book more readable
and
palatable. It was
her
infinite patience, unending
support, understanding and the sense
of
humour
that were critical in transforming my
~ream
into this book.
RANJAN
BosE
New Delhi
Contents
Preface
Acknowledgements
Part
I
Information
Theory
and
Source
Coding
1.
Source
Coding
1.1
Introduction to Information Theory 3
~
Uncertainty And Information 4
~Average
Mutual Information And Entropy
77
1.4
Information Measures For Continuous
~dom
Variables
74
\.LV
Source Coding Theorem 7 5
1.6 Huffman Coding 2 7
I. 7 The Lempel-Ziv Algorithm 28
1.8
Run
Length Encoding and the PCX Format
30
1.9 Rate Distortion Function
33
1.10
Optimum Quantizer Design
36
1.11 Introduction
to
Image Compression
37
1.12 The
Jpeg
Standard for Lossless Compression
38
1.13 The
Jpeg
Standard for Lossy Compression 39
1.14 Concluding Remarks 4 7
Summary
42
Problems
44
Computer
Problems
46
2.
Channel
Capacity
and
Coding
2.1 Introduction
47
2.2 Channel Models 48
~
Channel Capacity
50
2.4 Channel Coding
52
W Information Capacity Theorem
56
IX
XII
3
47
2.6
The
Shannon Limit 59
2.
7
Random
Selection of Codes
67
2.8 Concluding Remarks 67
Summary
68
Problems
69
Computer
Problems
77
Part
II
~
~.
1
Error
Control
Coding
~Jt
1JM"
~
(Channel Coding)
3. ·
ear
Block Codes for
Error
Correction
~
Introduction to Error Correcting Codes 75
3.2
JBasic
Definitions 77
3.3
vMatrix
Description of Linear Block Codes
87
Equivalent Codes 82
3.5
v'Parity
Check Matrix 85
3.6 l.JDecoding
of
a Linear Block
Code
87
3.
7
Jsyndrome
Decoding 94
3.8 Error Probability after
Coding
(Probability of Error Correction)
95
3.9 Perfect Codes
97
3.10
Hamming
Codes 7 00
3.11 Optimal Linear Codes
702
3.12 Maximum Distance Separable (MDS) Codes
702
3.13 Concluding Remarks
102
Summary
703
Problems
7 05
Computer
Problems
7 06
4.
Cyclic Codes
~~
~.1
4.1
Introduction to Cyclic Codes
708
\tY
Polynomials 7 09
\,!Y
The
Division Algorithm for Polynomials 7 7 0
V A Method for Generating Cyclic Codes 7 7 5
W Matrix Description of Cyclic Codes 7 7 9
4.6 Burst Error Correction 7 2 7
75
108
4.7 Fire Codes
723
4.8 Golay Codes 7 24
4.9 Cyclic Redundancy Check (CRC) Codes
725
4.10
4.11
Circuit Implementation
of
Cyclic Codes
Concluding Remarks
7 32
728
Summary
732
Problems
134
Computer
Problems
7
35
5. Bose-Chaudhuri
Hocquenghem
(BCH)
Codes
~~.
nJJ:,-idft
~
z-id<.
.'If~
5.1
Introduction to
BCH
Codes 736
~
Primitive Elements 737
\e.)" Minimal Polynomials 7 39
~
Generator Polynomials in Terms
of
Minimal Polynomials
\2.Y Some Examples
of
BCH
Codes 7 43
5.6 Decoding of
BCH
Codes 747
V Reed-Solomon Codes 7 50
747
5.8 Implementation
of
Reed-Solomon Encoders and Decoders 7 53
5.9 Nested Codes
753
5.10 Concluding Remarks 7 55
Summary
756
Problems
7
57
Computer
Problems
7 58
136
6.
Convolutional Codes
159
6.1 Introduction to Convolutional Codes
15~
iJ.
J)
iJ
~
1 ! '\,
~L
~
Tree Codes
and
Trellis Codes 7 60
JJt
~~l
fo4!
~
~
A/
'1/A
~
~olynomial
Description of Convolutional Codes
~~
1 .
(;__
(Analytical Representation) 7 65
V Distance Notions for Convolutional Codes 7
70
~
The
Generating Function 773
6.6 Matrix Description
of
Convolutional Codes 776
~.
~
\V/ Viterbi Decoding of Convolutional Codes
778
R}1.L
GSM
/U~~ifo~.
6.8 Distance Bounds for Convolutional Codes 7 85 1
6.9
Performance Bounds 7 87
6.10 Known Good Convolutional Codes 7 88
6.11 Turbo Codes 7 90
6.12 Turbo Decoding 7 92
6.13 Concluding Remarks 798
Summary
799
Problems
207
Computer
Problems
203
7.
Trellis
Coded
Modulation
7.1
Introduction
to
TCM
206
7.2
The
Concept of
Coded
Modulation
207
7.3 Mapping by Set Partitioning 2 7 2
7.4 Ungerboeck's
TCM
Design Rules
276
7.5 Tern Decoder 220
7.6 Performance Evaluation for Awgn Channel 227
7.7 Computation of
tip.ee
227
7.8 Tern for Fading Channels 228
7.9 Concluding Remarks · 232
Summary
233
Problems
234
Computer
Problems
238
Partm
Coding
for
Secure
Communications
.
Cryptography
8.1
Introduction to Cryptography
24
7 L j
8.2 An Overview
of
Encryption Techniques 242
~
~
~~~
8.3 Operations Used By Encryption Algorithms 245
8.4 Symmetric (Secret Key) Cryptography
246
8.5 Data Encryption Standard
(DES)
248
8.6 International Data Encryption Algorithm (IDEA) 252
8.
7
RC
Ciphers 253
8.8 Asymmetric (Public-Key) Algorithms 254
8.9 The RSA Algorithm 254
8.10 Pretty Good Privacy (PGP)
256
8.11 One-Way Hashing 259
8.12
Other
Techniques
260
8.13 Secure Communication Using Chaos Functions 267
/xvul
8.14
Cryptanalysis
262
8.15
Politics of Cryptography
264
8.16
Concluding Remarks
265
Summary
268
Problems
269
206
Computer
Problems
277
Index
273
241
1
Source Coding
,
Not-
~
tluU: ca.t'\1
be-
~
~
a.n.d.-
n.ot
~
tluU;
CCf.U'\.t¥
au\~
be-~
.
-Alberl"
E~
(1879-1955)
1.1
INTRODUCTION
TO
INFORMATION
THEORY
Today we live in the information
age.
The internet has become an integral part of our lives,
making this, the
third planet from the sun, a global village. People talking over the cellular
phones
is
a common sight, sometimes even in cinema theatres. Movies can be rented in the
form of a DVD
disk.
Email addresses and web addresses are common on business cards. Many
people prefer to send emails and e-cards to their friends rather than the regular snail mail.
Stock
quotes can be checked over the mobile phone.
Information has become the key to success
(it
has always been a key to success,
but
in today's
world it
is tlu key). And behind all this information and its exchange lie the tiny
l's
and
O's
{the
omnipresent bits) that hold information by merely the way they sit next to one another. Yet the
information
age that we live in today owes its existence, primarily,
to
a seminal paper published
in 1948 that laid the foundation of the wonderful field
of
Information
Theory-a
theory
initiated by one man, the American Electrical Engineer Claude
E.
Shannon, whose ideas
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