Communication Theory

Front Cover
Cambridge University Press, Nov 7, 1991 - Computers - 210 pages
0 Reviews
This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Economical representations noiseless coding
4
11 Sources messages codes
5
the prefix condition
8
Decisiontree representation
9
Exercises
10
13 The Kraft inequality
11
Exercises
13
Exercises
16
Exercises
101
36 Reliable transmission through the memory less Gaussian channel
102
The memoryless Gaussian channel MGC
103
Reliable transmission
105
Exercises
108
Channel coding theorems
109
The Hu correspondence
111
Exercises
112

15 Segmented block codes
18
Exercises
19
16 ShannonFano encoding
20
Exercises
23
18 Further topics
24
Universal coding
26
Other reading
27
19 Problems
28
Properties of a message source
34
Probability spaces
35
The random source
36
Exercise
37
Telegraph English
38
Exercises
40
23 The First Coding Theorem FCT
41
The First Coding Theorem FCT
42
Exercises
43
24 Asymptotic Equipartition Property AEP
44
Exercise
45
Exercises
46
26 Finite Markov chains
47
Geometric ergodicity
48
Exercises
52
27 Markov sources
53
Higherorder Markov sources
55
28 The genetic code
56
Location of redundancy
58
Joint entropy
60
210 Conditional entropy
62
Conditional independence
63
Exercises
65
The Ergodic Theorem
67
Exercises
68
The Shannon McMillanBreiman Theorem
69
Failure of ergodicity
72
Exercises
73
213 Further topics
74
Epsilonentropy metric entropy and algorithmic information theory
77
Statistical inference
78
Ergodic theory
79
214 Problems
80
Reliable transmission
87
Exercise
89
32 Decoding receiver optimization
90
The discrete case
91
ML decoding
92
33 Random coding
93
Exercise
94
34 Introduction to channels
95
Exercises
96
35 Reliable transmission through the BSC
97
42 The Second Coding Theorem SCT
113
43 The discrete memoryless channel DMC
117
Exercises
119
44 Symmetric channels
120
Exercises
121
45 Continuous entropy and mutual information
122
Mutual information
125
Exercises
126
46 The memoryless channel with additive white noise
127
The memoryless Gaussian channel MGC
129
Capacity under signalpower constraint
130
Exercises
132
47 Further topics
133
Magnitude of the probability of error
134
Channels with input costs
135
Inequalities
136
Other channels and systems
137
Errorcontrol codes
144
Exercises
148
52 Linear codes
149
Syndrome decoding
153
Exercises
154
53 Constructing codes from other codes
155
Exercises
157
Exercises
161
55 ReedMuller codes
162
Decoding ReedMuller codes
165
Exercises
167
56 Further topics
168
57 Problems
169
Cyclic codes
172
Exercises
174
62 BCH codes
175
Exercises
177
Exercise
178
65 Problems
179
Appendix rings fields and vector spaces
181
Exercises
183
72 Fields
184
Exercises
186
Exercises
188
Exercises
189
76 Problems
190
Bibliography
191
References
193
Notation summary
196
Vectors strings matrices
197
Entropy information
198
Algebraic objects
199
Index
200
Copyright

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »