Optical coding theory with prime

Although several books cover the coding theory of wireless communications and the hardware technologies and coding techniques of optical CDMA, no book has been specifically dedicated to optical coding theory¿until now. Written by renowned authorities in the field, Optical Coding Theory with Prime gathers together in one volume the fundamentals and developments of optical coding theory, with a focus on families of prime codes, supplemented with several families of non-prime codes. The book also explores potential applications to coding-based optical systems and networks.

Learn How to Construct and Analyze Optical Codes

The authors use a theorem-proof approach, breaking down theories into digestible form so that readers can understand the main message without searching through tedious proofs. The book begins with the mathematical tools needed to understand and apply optical coding theory, from Galois fields and matrices to Gaussian and combinatorial analytical tools. Using a wealth of examples, the authors show how optical codes are constructed and analyzed, and detail their performance in a variety of applications. The book examines families of 1-D and 2-D asynchronous and synchronous, multilength, and 3-D prime codes, and some non-prime codes.

Get a Working Knowledge of Optical Coding Theory to Help You Design Optical Systems and Networks

Prerequisites include a basic knowledge of linear algebra and coding theory, as well as a foundation in probability and communications theory. This book draws on the authors¿ extensive research to offer an authoritative reference on the emerging field of optical coding theory. In addition, it supplies a working knowledge of the theory and optical codes to help readers in the design of coding-based optical systems and networks.

For more on the technological aspects of optical CDMA, see Optical Code Division Multiple Access: Fundamentals and Applications (CRC Press 2005).

Author Notes

Wing C. Kwong received his Ph.D. in electrical engineering from Princeton University, NJ.

Dr. Kwong is associate professor in the department of engineering, Hofstra University, Hempstead, NY. p 050

List of Figures	p. xi
List of Tables	p. xix
Preface	p. xxi
About the Authors	p. xxv
Chapter 1 Fundamental Materials and Tools	p. 1
1.1 Galois Fields	p. 1
1.1.1 Primitive Elements	p. 5
1.2 Vector Space	p. 7
1.2.1 Linear Operations in Vector Space over a Field	p. 9
1.3 Matrix Theory	p. 11
1.3.1 Basic Definitions	p. 12
1.3.2 Basic Operations and Properties	p. 13
1.3.3 Determinant	p. 15
1.3.4 Eigenvalues and Eigenvectors	p. 16
1.4 Hamming Distance and Weight	p. 18
1.5 Correlation Functions	p. 19
1.5.1 1-D Auto- and Cross-Correlation Functions	p. 19
1.5.2 2-D Auto- and Cross-Correlation Functions	p. 20
1.6 Cardinality Upper Bound	p. 21
1.7 Markov Chain	p. 23
1.8 Algebraic Tools for Performance Analysis	p. 24
1.8.1 Gaussian Approximation for Unipolar Codes	p. 25
1.8.2 Gaussian Approximation for Bipolar Codes	p. 29
1.8.3 Combinatorial Analysis for Unipolar Codes	p. 31
1.8.4 Hard-Limiting Analysis for Unipolar Codes	p. 32
1.8.5 Soft-Limiting Analysis without Chip Synchronization	p. 35
1.8.6 Hard-Limiting Analysis without Chip Synchronization	p. 42
1.8.7 Spectral Efficiency	p. 47
1.9 Summary	p. 47
Chapter 2 Optical Coding Schemes	p. 51
2.1 1 -D Temporal Amplitude Coding	p. 55
2.2 1-D Temporal Phase Coding	p. 60
2.3 1-D Spectral Phase Coding	p. 61
2.4 1-D Spectral Amplitude Coding	p. 63
2.5 2-D Spatial-Temporal Amplitude Coding	p. 65
2.6 2-D Spectral-Temporal Amplitude Coding	p. 68
2.7 Three-Dimensional Coding	p. 69
2.8 Multirate and Multiple-QoS Coding	p. 69
2.9 Multicode Keying and Shifted-Code Keying	p. 71
2.10 Enabling Hardware Technologies	p. 75
2.10.1 Wavelength-A ware Hard-Limiting Detector	p. 75
2.10.2 Fiber Bragg Gratings	p. 76
2.10.3 Arrayed Waveguide Gratings	p. 77
2.11 Potential Applications	p. 81
2.12 Summary	p. 82
Chapter 3 1-D Asynchronous Prime Codes	p. 89
3.1 Original Prime Codes	p. 89
3.1.1 Performance Analysis	p. 92
3.2 Extended Prime Codes	p. 96
3.2.1 Performance Analysis	p. 97
3.3 Generalized Prime Codes	p. 100
3.3.1 Performance Analysis	p. 103
3.4 2" Prime Codes	p. 106
3.4.1 Performance Analysis	p. 116
3.5 Optical Orthogonal Codes	p. 117
3.5.1 Constructions of (N, w, 1,1) OOC	p. 117
3.5.2 Constructions of (N, w, 1,2) OOC	p. 119
3.5.3 Constructions of (N,w,2,1) OOC	p. 120
3.5.4 Performance Analysis	p. 122
3.6 Summary	p. 124
Chapter 4 1-D Synchronous Prime Codes	p. 127
4.1 Synchronous Prime Codes	p. 128
4.1.1 Performance Analysis	p. 130
4.2 Synchronous Multilevel Prime Codes	p. 134
4.2.1 Performance Analysis	p. 138
4.3 Synchronous Coding Applications	p. 143
4.4 Summary	p. 146
Chapter 5 2-D Asynchronous Prime Codes	p. 149
5.1 Carrier-Hopping Prime Codes	p. 150
5.1.1 Performance Analysis	p. 153
5.2 Multilevel Carrier-Hopping Prime Codes	p. 156
5.2.1 Performance Analysis	p. 160
5.3 Shifted Carrier-Hopping Prime Codes	p. 164
5.3.1 Construction 1: Time Shifts	p. 166
5.3.2 Construction 2: Wavelength Shifts	p. 166
5.3.3 Performance Analysis	p. 168
5.3.4 Spectral Efficiency Study	p. 171
5.4 Extended Carrier-Hopping Prime Codes	p. 176
5.4.1 Performance Analysis	p. 182
5.5 Expanded Carrier-Hopping Prime Codes	p. 184
5.5.1 Performance Analysis	p. 187
5.6 Quadratic-Congruence Carrier-Hopping Prime Codes	p. 191
5.6.1 Performance Analysis	p. 193
5.6.2 Multicode and Shifted-Code Keying	p. 195
5.6.3 Spectral Efficiency Study	p. 200
5.7 Prime-Permuted Codes with Unipolar Codes	p. 202
5.7.1 Performance Analysis	p. 209
5.8 Prime-Permuted Codes with Bipolar Codes	p. 218
5.8.1 Performance Analysis	p. 226
5.9 Quadratic-Congruence-Permuted Codes	p. 234
5.9.1 Performance Analysis	p. 237
5.10 2-D Optical Orthogonal Codes	p. 239
5.10.1 Construction 1: From 1-D (N,w, 1,1) OOC	p. 240
5.10.2 Construction 2: From Reed-Solomon Code	p. 242
5.10.3 Performance Analysis	p. 244
5.11 Summary	p. 244
Chapter 6 2-D Synchronous Prime Codes	p. 249
6.1 Synchronous Original. Expanded, and Quadratic-Congruence Carrier-Hopping Prime Codes	p. 249
6.1.1 Performance Analysis	p. 253
6.2 Synchronous Multilevel Carrier-Hopping Prime Codes	p. 256
6.2.1 Performance Analysis	p. 259
6.3 Synchronous Prime-Permuted Codes	p. 264
6.3.1 Performance Analysis	p. 267
6.4 Summary	p. 270
Chapter 7 Multilength Prime Codes	p. 273
7.1 Multilength Carrier-Hopping Prime Codes	p. 274
7.1.1 Performance Analysis	p. 280
7.2 Multilength Expanded Carrier-Hopping Prime Codes	p. 285
7.2.1 Performance Analysis	p. 288
7.3 Multilength Quadratic-Congruence Carrier-Hopping Prime Codes	p. 291
7.3.1 Performance Analysis	p. 294
7.3.2 Multicode Keying	p. 297
7.3.3 Spectral Efficiency Study	p. 301
7.4 2-D Multilength Prime-Permuted Codes	p. 303
7.4.1 Performance Analysis	p. 306
7.5 Variable-Weight Coding with Same Bit Power	p. 309
7.6 Multilength 1-D Optical Orthogonal Codes	p. 319
7.6.1 Construction 1: Cross-Correlation of One	p. 319
7.6.2 Construction 2: Cross-Correlation of Two	p. 321
7.6.3 Performance Analysis	p. 324
7.7 Summary	p. 328
Chapter 8 3-D Prime Codes	p. 333
8.1 Concatenated Prime Codes	p. 333
8.1.1 Performance Analysis	p. 336
8.2 Multicarrier Prime Codes	p. 338
8.2.1 Performance Analysis	p. 341
8.3 Summary	p. 344
Index	p. 345

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