Prime codes with applications to optical and wireless networks

Due to the rapid development of optical and wireless technologies, prime codes used in signal transmissions have quickly become of great interest to today's wireless and telecommunications engineers. This book provides professionals with the latest research on prime codes and their advanced applications in both wireless and optical communications. It describes in clear, concise language the fundamental issues involved in prime codes and their relationships to modern communications. Examples are used to illustrate the fundamental concepts and how prime codes are designed.

Author Notes

Guu-Chang Yang received his Ph.D. in electrical engineering from the University of Maryland at College Park, MD.

Mr. Yang is professor and chairman of the department of electrical engineering at the National Chung-Hsing University.

050

Preface	p. xiii
1 Preliminary Materials	p. 1
1.1 Galois Fields	p. 1
1.2 Vector Spaces	p. 6
1.3 Matrix Theory	p. 11
1.3.1 Basic Definitions	p. 11
1.3.2 Basic Operations and Properties	p. 13
1.3.3 Matrices over Finite Fields	p. 16
1.4 Polynomials	p. 18
1.5 Primitive Elements	p. 22
1.6 Polynomial Representations of Vectors	p. 23
1.7 Hamming Distance and Weight	p. 26
1.8 Correlation Functions	p. 27
1.8.1 One-Dimensional Correlation Function	p. 27
1.8.2 Two-Dimensional Correlation Function	p. 28
1.9 Basic Tools for Performance Analyses	p. 29
1.9.1 Gaussian Approximation for Incoherent CDMA	p. 31
1.9.2 Incoherent CDMA Systems with Soft-Limiters	p. 37
1.9.3 Incoherent CDMA Systems with Hard-Limiters	p. 38
1.10 Summary	p. 41
References	p. 41
2 Families of Prime Codes	p. 43
2.1 Prime Code	p. 44
2.2 Extended Prime Code	p. 48
2.3 Synchronized Prime Code	p. 53
2.3.1 Coding Algorithm	p. 53
2.3.2 Correlation Properties	p. 54
2.4 2[superscript n] Prime Code	p. 57
2.4.1 Basic Construction	p. 60
2.4.2 Validity Test	p. 64
2.4.3 General Coding Algorithm	p. 75
2.5 Generalized Prime Code	p. 76
2.6 Carrier-Hopping Prime Code	p. 79
2.6.1 Coding Algorithms	p. 82
2.6.2 Correlation Properties	p. 84
2.6.3 Cardinality	p. 87
2.7 Multilength Carrier-Hopping Prime Code	p. 87
2.7.1 Coding Algorithms	p. 88
2.7.2 Correlation Properties	p. 91
2.7.3 Cardinality	p. 94
2.8 Concatenated Prime Code	p. 97
2.9 Multicarrier Prime Code	p. 103
2.10 Summary	p. 107
References	p. 108
3 Code-Division Multiple-Access Optical Networks	p. 113
3.1 Optical Multiple Accessing Schemes	p. 114
3.1.1 Time-Domain Optical Multiple-Access Schemes	p. 115
3.1.2 Frequency-Domain Optical Multiple-Access Schemes	p. 116
3.2 Optical Code-Division Multiple-Access	p. 117
3.3 Optical Signal Processing in Optical CDMA	p. 120
3.4 Experimental Demonstration of Optical CDMA	p. 124
3.5 Performance Analysis of Optical CDMA with the Original Prime Code	p. 126
3.6 Performance Analysis of Optical CDMA with the Extended Prime Code	p. 135
3.7 Performance Analysis of Optical CDMA Without Chip Synchronization	p. 136
3.7.1 Partial Cross-Correlation Functions	p. 137
3.7.2 Probabilities of Partial Cross-Correlation Functions	p. 143
3.7.3 Performance of the Extended Prime Code Without Chip Synchronization	p. 147
3.8 Summary	p. 151
References	p. 153
4 Synchronous CDMA Optical Networks	p. 157
4.1 S/CDMA System Description	p. 159
4.2 Experimental Demonstration of S/CDMA	p. 160
4.3 Applications of S/CDMA	p. 164
4.4 Performance Analysis of S/CDMA with the Synchronized Prime Code	p. 167
4.5 Summary	p. 177
References	p. 177
5 2[superscript n] CDMA Optical Networks	p. 181
5.1 Optical CDMA Coding Configurations	p. 183
5.1.1 Prime Encoders and Decoders	p. 184
5.1.2 2[superscript n] Encoders and Decoders	p. 186
5.1.3 Modified 2[superscript n] Encoders and Decoders	p. 188
5.1.4 2[superscript n] Prime Encoders and Decoders	p. 190
5.2 Normalized Delay Length of Optical Encoders and Decoders	p. 194
5.2.1 Prime Encoders and Decoders	p. 194
5.2.2 2[superscript n] Encoders and Decoders	p. 197
5.2.3 Modified 2[superscript n] Encoders and Decoders	p. 197
5.2.4 2[superscript n] Prime Encoders and Decoders	p. 198
5.2.5 Numerical Examples	p. 199
5.3 Ideal Power Loss of Optical Encoders and Decoders	p. 201
5.3.1 Prime Encoders and Decoders	p. 202
5.3.2 2[superscript n] Encoders and Decoders	p. 203
5.3.3 Modified 2[superscript n] Encoders and Decoders	p. 204
5.3.4 2[superscript n] Prime Encoders and Decoders	p. 205
5.3.5 Numerical Examples	p. 205
5.4 Experimental Demonstrations of Serial Coding Configuration	p. 207
5.4.1 Fiber-Optic Experiment	p. 207
5.4.2 Free-Space Experiment	p. 208
5.5 Applications	p. 213
5.5.1 CDMA Optical Networks	p. 213
5.5.2 Waveguide Implementation	p. 215
5.5.3 Microarea Networks	p. 216
5.6 Performance Analysis of Optical CDMA with the 2[superscript n] Prime Code	p. 217
5.7 Supplementary--Even-Spaced 2[superscript n] Code	p. 218
5.8 Summary	p. 222
References	p. 223
6 Synchronization for CDMA Optical Networks	p. 227
6.1 Cross-Correlation Properties of Synchronization and Data Signature Sequences	p. 230
6.2 Application	p. 233
6.3 Performance Analyses	p. 235
6.3.1 Probabilities	p. 235
6.3.2 Performance Analysis of the Synchronization Process	p. 238
6.3.3 Performance Analysis of the Whole System	p. 242
6.4 Discussion	p. 245
6.5 Supplementary--Quadratic Congruence Codes	p. 246
6.6 Summary	p. 249
References	p. 250
7 Multiwavelength CDMA Optical Networks	p. 253
7.1 System Models	p. 256
7.1.1 Temporal-Spatial CDMA Optical Network	p. 256
7.1.2 Multiwavelength CDMA Optical Network	p. 258
7.2 Performance Analysis of Multiwavelength CDMA with the Carrier-Hopping Prime Code	p. 260
7.3 Summary	p. 266
References	p. 267
8 Frequency-Hopping CDMA Wireless Networks	p. 271
8.1 Basic CDMA System Models	p. 274
8.1.1 DS-CDMA System	p. 274
8.1.2 FH-CDMA System	p. 276
8.2 MFSK/FH-CDMA System Model	p. 278
8.3 Discussion of FH Codes	p. 280
8.4 Performance Analysis of MFSK/FH-CDMA with One-Hit FH Codes	p. 284
8.4.1 Effect of Multiple-Access Interference	p. 286
8.4.2 Effects of Fading and AWGN	p. 288
8.5 Performance Comparison of One-Hit and Random FH Codes	p. 291
8.6 Applications	p. 294
8.6.1 FH-TDMA Scheme	p. 294
8.6.2 FH/TH-TDMA Scheme	p. 295
8.7 Summary	p. 297
References	p. 297
9 FH-CDMA Wireless Networks with Multimedia Services	p. 301
9.1 Multimedia FH-CDMA System Model	p. 305
9.2 Double-Media MFSK/FH-CDMA System Model	p. 307
9.3 Discussion of Multilength FH Codes	p. 307
9.4 Performance Analysis of MFSK/FH-CDMA with One-Hit, Double-Length FH Codes	p. 311
9.4.1 Effect of Multiple-Access Interference	p. 312
9.4.2 Effects of Fading and AWGN	p. 315
9.5 Performance Comparison of One-Hit and Random, Double-Length FH Codes	p. 318
9.6 Summary	p. 321
References	p. 321
10 Multicarrier FH-CDMA Wireless Networks	p. 325
10.1 Multicarrier MFSK/FH-CDMA System Model	p. 327
10.2 Performance Analysis of Multicarrier MFSK/FH-CDMA with One-Hit, Multicarrier FH Codes	p. 335
10.3 Summary	p. 339
References	p. 340
About the Authors	p. 341
Index	p. 343

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