Error Coding for Engineers

Front Cover
Springer Science & Business Media, Sep 30, 2001 - Computers - 246 pages
Error Coding for Engineers provides a useful tool for practicing engineers, students, and researchers, focusing on the applied rather than the theoretical. It describes the processes involved in coding messages in such a way that, if errors occur during transmission or storage, they are detected and, if necessary, corrected. Very little knowledge beyond a basic understanding of binary manipulation and Boolean algebra is assumed, making the subject accessible to a broad readership including non-specialists.
The approach is tutorial: numerous examples, illustrations, and tables are included, along with over 30 pages of hands-on exercises and solutions.
Error coding is essential in many modern engineering applications. Engineers involved in communications design, DSP-based applications, IC design, protocol design, storage solutions, and memory product design are among those who will find the book to be a valuable reference. Error Coding for Engineers is also suitable as a text for basic and advanced university courses in communications and engineering.
 

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Contents

Introduction
1
12 The Hamming Bound
4
13 The Gilbert Bound
6
14 Where do Errors Come From?
7
15 A Brief History of Error Coding
12
16 Summary
13
A Little Maths
15
21 Polynomials and Finite Fields
16
82 Punctured Codes
121
83 Interleaving
125
84 Error Forecasting
130
85 Discussion
131
Convolutional Coding
133
91 Error Correction with Convolutional Codes
135
92 Finding the Correct Path
136
93 Decoding with Soft Decisions
138

22 Manipulating Field Elements
19
23 Summary
24
Error Detection
25
32 The Cyclic Redundancy Check
27
33 Longhand Calculation of the CRC
28
34 Performance
31
35 Hardware Implementation
32
36 TableBased Calculation of the CRC
35
37 Discussion
39
Error Correction by Parity
41
41 Correcting a Single Bit
43
42 Extending the Message Size
45
Error Correction Using the CRC
49
51 A Hardware Error Locator
52
52 Multiple Bit Errors
53
53 Expurgated Codes
54
54 The Perfect Golay Code
56
55 Fire Codes
63
ReedMuller Codes
67
62 Encoding With the Hadamard Matrix
74
63 Discussion
77
ReedSolomon Codes
79
72 Calculating Check Symbols for One Error
80
73 Correcting Two Symbols
83
74 Error Correction in the Frequency Domain
88
75 Recursive Extension
91
76 The BerlekampMassey Algorithm
97
77 The Forney Algorithm
100
78 MixedDomain Error Coding
101
79 Higher Dimensional Data Structures
107
710 Discussion
118
Augmenting Error Coding
119
94 Performance of Convolutional Codes
140
95 Concatenated Codes
141
96 Iterative Decoding
142
97 Turbo Decoding
143
98 Discussion
144
Hardware
147
102 Multiplication
149
103 Division
153
104 Logs and Exponentials
158
105 Reciprocal
160
106 Discussion
164
Bit Error Rates
165
112 Estimating the Bit Error Rate
166
113 Applications
172
114 Discussion
176
Exercises
177
122 CRC Exercises
178
123 Finite Field Algebra
180
124 Convolutional Coding Exercises
183
126 Solutions to Parity Exercises
184
127 Solutions to CRC Exercises
186
128 Solutions to Finite Field Algebra
192
129 Solutions to Convolutional Coding
202
1210 Solutions to Other Codes
203
1211 Closing Remarks
208
Primitive Polynomials
211
The Golay Code
219
Solving for Two Errors
223
Solving some Key Equations
229
Software Library
233
Index
245
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