List of Tables
1.1 Multiplication Table of GF(p),WrittenintheFormofaPrimitiveEle-
ment
α
..............................................................................................................7
2.1 Comparisons of Common Optical Multiple-Access Schemes........................ 52
2.2 Classifications of Optical Coding Schemes....................................................53
2.3 Periodic-Wavelength Assignment of an 8 ×8AWG......................................78
2.4 Transmission Wavelengths of Spectral-Amplitude Code Based on the
Maximal-Length Sequen ces of Length 7 and Walsh Code of Length8.........79
3.1 Prime Sequences and Codewords over GF(5) ................................................90
3.2 Prime Sequences and Codewords over GF(7) ................................................90
3.3 Extended Prime Codewords over GF(5)......................................................... 9 6
3.4 Generalized Prime Sequences and Codewords over GF(3) with k = 2........102
3.5 Prime Sequences over GF(11) ......................................................................115
3.6 Cyclic Adjacent-Pulse Separations for Prime Sequences over GF(11)
with z
j
= 1andn = 3....................................................................................115
3.7 Valid 2
3
Prime Sequences over GF(11)........................................................115
4.1 First 35 Synchronous Prime Sequences and Codewords over GF(7) ...........129
4.2 Twenty-Five Synchronous Trilevel Prime Sequences and Codewords
over GF(5) with i
3
= 1andn = 2.................................................................139
5.1 Spectral Efficiencies of the Quadratic-Congruence Carrier-Hopping
Prime Codes in Multicode Keying and the Carrier -Hopping Prime Codes
in OOK for Various Error Probabilities from Figure 5.18............................ 202
5.2 Composition, Property, and Cardinality Comparisons of Prime- and QC-
Permuted Codes ............................................................................................ 203
5.3 Shifted Prime Sequences over GF(7)............................................................204
5.4 (7 ×13, 4,2,2) Prime-Permuted Code over GF(7) with 7 Wavelengths
and the Time-Spreading (13,4,1 , 2) OOC Codeword 1011000100000 ....... 204
5.5 Shifted Prime Sequences over GF(2
3
).........................................................206
5.6 Non-Prime Sequences for p = 12................................................................. 207
5.7 Code Composition, Modulation Format, and Cardinality ofthe(L ×
N, w, 1,1) Prime-Permuted Codes over GF(p) of a Prime p,whereΦ
Denotes the Cardinality of the Time-Spreading Codes ................................219
5.8 Multiwavelength Codes, Based on the Maximal-Length Sequences of
Length 7 and Walsh Code of Length 8 .........................................................220
5.9 OOK-Based (L ×7,3,1, 1) Prime-Permuted Code over GF(7), Based on
the Multiwavelength Codes in Table 5.8 and Time-Spreading (7,3,1,1)
OOC Codeword 1011000 ............... . .............................................................221
xix
xx List of Tables
5.10 Multiwavelength Codes and Their Wavelength-Conjugates, Based on the
Modified Maximal-Length Sequences and Walsh Code of Length 8...........223
5.11 CIK-based (8 ×5, 5,1,1) Prime-Permuted Code over GF(7), Based on
the Multiwavelength Codes in Table 5.10 and Time-Spreading Barker
Sequence (+1,+1, +1,−1, +1) ...................................................................224
5.12 CIK-Based (8 ×7, 7,1,1) Prime-Permuted Code over GF(7), Based on
the Multiwavelength Codes in Table 5.10 and Time-Spreading Gold Se-
quence (+1,+1, +1,−1,+1,−1,+1 )..........................................................225
5.13 Shifted QC Sequences over GF(5) ................................................................2 3 5
6.1 Some Synchronous Original Carrier-Hopping Prime Codewords with
k = 2, p
1
= 3, p
2
= 5, and w = 3..................................................................252
6.2 Synchronous Trilevel Carrier-Hopping Prime Codewords over GF(5)
with w = 4, i
1,3
= 0, and k = 1.....................................................................260
6.3 Synchronous Prime-Permuted Codewords over GF(7), Basedonthe7
Multiwavelength Codewords of Length 8 in Table 5 .8, and the Time-
Spreading Walsh Codeword (+1,−1, +1,−1) ............................................265
7.1 Spectral Efficiency Comparison of the Single-Weight, Double-Length
Quadratic-Congruence Carrier-Hopping Pr im e Codes in Multicode-
Keying, Based on Figure 7.12 with P
e,2,hard
≈ 10
−9
.....................................304
7.2 Double-Length Prime-Permuted Codewords over GF(7) of Short Length
N
1
= 13, Weight w = 3, and L = 7Wavelengths,fromtheTime-
Spreading 1-D Short OOC Codeword 1010000010000 ...............................305
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