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Codes for Error Control and Synchronization

By: Djimitri Wiggert

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Hardcover | 1 August 1998

At a Glance

Hardcover
216 Pages

Dimensions(cm)
24.13 x 16.51 x 1.91

Hardcover

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Preface	p. ix
Introduction and Overview	p. 1
General	p. 1
Overview of the Book	p. 2
Model of a Communication System	p. 3
Communication Theory Considerations	p. 9
Introduction	p. 9
Binary Antipodal Signaling	p. 9
Bits, Bauds, Symbols, and Chips	p. 16
Demodulator Limit on Coding Gain	p. 17
Conclusion	p. 18
Introduction to Parity-Check Codes	p. 21
Introduction	p. 21
Why Study Abstract Algebra?	p. 21
Properties of Mathematical Systems	p. 22
Groups	p. 22
Fields and Vector Spaces	p. 23
Linear Codes	p. 28
The Concept of Distance	p. 34
Basic Results in Word Error Probability	p. 37
Decoding Procedures	p. 39
The Standard Array and Syndrome Decoding	p. 42
The Golay Code and Related Matters	p. 45
Errors versus Erasures	p. 46
Abstract Algebra and Cyclic Codes	p. 47
Introduction	p. 47
Properties of Polynomials over a Field	p. 47
Some Properties of Galois Fields	p. 50
Introduction to Cyclic Codes	p. 53
Encoding Cyclic Codes	p. 57
Bose-Chaudhuri-Hocquenghem and Reed-Solomon Codes	p. 61
Introduction	p. 61
Definition, Construction, and Properties of BCH Codes	p. 62
Decoding	p. 65
Performance of BCH Codes	p. 69
Reed-Solomon Codes	p. 70
Convolutional Codes and Encoding	p. 75
Convolutional Encoding	p. 75
Graphical Representation of Convolutional Codes	p. 80
Analytical Representation of Convolutional Codes	p. 85
Distance Properties	p. 91
Distance Bounds for Convolutional Codes	p. 93
Known Good Convolutional Codes	p. 95
Nonbinary Convolutional Codes	p. 108
Threshold Decoding	p. 111
Introduction	p. 111
Orthogonal Parity-Check Equations	p. 113
The Threshold Decoding Algorithm	p. 117
Error Propagation: Analysis and Prevention	p. 120
Performance Assessment	p. 121
The Viterbi Decoding Algorithm	p. 125
Introduction	p. 125
Decoder Operation	p. 128
Decoder Parameters	p. 132
Soft Decisions	p. 133
Simulation and Implementation Results	p. 133
Assessment and Conclusions	p. 135
Sequential Decoding	p. 137
Introduction	p. 137
A Fundamental Limit on Sequential Decoding	p. 138
Sequential Decoding: General Technique	p. 139
The Fano Sequential Decoding Algorithm	p. 141
"Stack" Decoding	p. 147
Decoder Parameters	p. 151
Summary and Conclusions	p. 152
Coding to Combat Impulse Noise	p. 153
Introduction	p. 153
Coding with Feedback	p. 154
Interleaving	p. 157
Burst-Correcting Block Codes	p. 160
Burst Correction with Convolutional Codes	p. 163
Code Combining	p. 166
Summary	p. 168
Applications and Trade-Off Analyses	p. 169
Introduction	p. 169
Example #1: A Floating Data-Collection Platform	p. 170
Example #2: Satellite and Space Communication	p. 172
Synchronization Codes	p. 175
Background	p. 175
Scope of the Chapter	p. 176
PN Codes	p. 177
Barker Codes	p. 180
Introduction to Matrices	p. 183
Definitions and Notation	p. 183
Elementary Operations on Matrices	p. 184
Calculation of the Inverse	p. 187
Reduction to Triangular Form	p. 190
Bibliography	p. 195
Index	p. 201
Table of Contents provided by Syndetics. All Rights Reserved.

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