All-optical code-division multiple-access applications: 2<sup>n</sup> extended-prime codes

Jian-Guo Zhang; Wing C. Kwong; Stelly Mann

doi:10.1364/AO.36.006664

Applied Optics
Vol. 36,
Issue 26,
pp. 6664-6667
(1997)
•https://doi.org/10.1364/AO.36.006664

All-optical code-division multiple-access applications: 2ⁿ extended-prime codes

Jian-Guo Zhang, Wing C. Kwong, and Stelly Mann

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Jian-Guo Zhang, Wing C. Kwong, and Stelly Mann, "All-optical code-division multiple-access applications: 2ⁿ extended-prime codes," Appl. Opt. 36, 6664-6667 (1997)

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Abstract

A new family of 2ⁿ codes, called 2ⁿ extended-prime codes, is proposed for all-optical code-division multiple-access networks. Such 2ⁿ codes are derived from so-called extended-prime codes so that their cross-correlation functions are not greater than 1, as opposed to 2 for recently proposed 2ⁿ prime codes. As a result, a larger number of active users can now be supported by the new codes for a given bit-error rate than can be by 2ⁿ prime codes, while power-efficient, waveguide-integrable all-serial coding and correlating configurations proposed for the 2ⁿ prime codes can still be employed.

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Equations (9)

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i	j
i	0	1	2	3	4	5	6	7	8	9	10
0	0	0	0	0	0	0	0	0	X	X	X
1	0	1	2	3	4	5	6	7	X	X	X
2	X	X	X	6	8	10	1	3	5	7	9
3	X	X	6	9	1	4	7	10	2	5	X
4	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
5	X	X	10	4	9	3	8	2	7	1	X
6	0	6	1	7	2	8	3	9	X	X	X
7	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
8	X	X	5	2	10	7	4	1	9	6	X
9	X	X	7	5	3	1	10	8	6	4	X
10	X	10	9	8	7	6	5	4	3	X	X

Prime Number	Code Length N	Code Weight	Cardinality
13	175 ≤ N ≤ 325	4	13
	N = 325	8	11
17	231 ≤ N ≤ 561	4	17
	495 ≤ N ≤ 561	8	15
	N = 561	16	9
19	259 ≤ N ≤ 703	4	19
	555 ≤ N ≤ 703	8	17
	N = 703	16	9
23	315 ≤ N ≤ 1035	4	23
	675 ≤ N ≤ 1035	8	19
	N = 1035	16	11
31	427 ≤ N ≤ 1891	4	31
	915 ≤ N ≤ 1891	8	27
	N = 1891	16	15

Prime Code				Extended-Prime Code				ΔBW
P	w	Q_m	N	P	w	Q_m	N	ΔBW
11	11	11	121	13	4	13	175a	44.6%
13	13	13	169	13	4	13	325b	92.3%
17	17	17	289	17	8	15	495a	71.3%
19	19	19	361	17	8	15	561b	55.4%
23	23	23	529	19	16	9	703	32.9%

i	j
i	0	1	2	3	4	5	6	7	8	9	10
0	0	0	0	0	0	0	0	0	X	X	X
1	0	1	2	3	4	5	6	7	X	X	X
2	X	X	X	6	8	10	1	3	5	7	9
3	X	X	6	9	1	4	7	10	2	5	X
4	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
5	X	X	10	4	9	3	8	2	7	1	X
6	0	6	1	7	2	8	3	9	X	X	X
7	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
8	X	X	5	2	10	7	4	1	9	6	X
9	X	X	7	5	3	1	10	8	6	4	X
10	X	10	9	8	7	6	5	4	3	X	X

Prime Number	Code Length N	Code Weight	Cardinality
13	175 ≤ N ≤ 325	4	13
	N = 325	8	11
17	231 ≤ N ≤ 561	4	17
	495 ≤ N ≤ 561	8	15
	N = 561	16	9
19	259 ≤ N ≤ 703	4	19
	555 ≤ N ≤ 703	8	17
	N = 703	16	9
23	315 ≤ N ≤ 1035	4	23
	675 ≤ N ≤ 1035	8	19
	N = 1035	16	11
31	427 ≤ N ≤ 1891	4	31
	915 ≤ N ≤ 1891	8	27
	N = 1891	16	15

i	j
i	0	1	2	3	4	5	6	7	8	9	10
0	0	0	0	0	0	0	0	0	X	X	X
1	0	1	2	3	4	5	6	7	X	X	X
2	X	X	X	6	8	10	1	3	5	7	9
3	X	X	6	9	1	4	7	10	2	5	X
4	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
5	X	X	10	4	9	3	8	2	7	1	X
6	0	6	1	7	2	8	3	9	X	X	X
7	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
8	X	X	5	2	10	7	4	1	9	6	X
9	X	X	7	5	3	1	10	8	6	4	X
10	X	10	9	8	7	6	5	4	3	X	X

i	j
i	0	1	2	3	4	5	6	7	8	9	10
0	0	0	0	0	0	0	0	0	X	X	X
1	0	1	2	3	4	5	6	7	X	X	X
2	X	X	X	6	8	10	1	3	5	7	9
3	X	X	6	9	1	4	7	10	2	5	X
4	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
5	X	X	10	4	9	3	8	2	7	1	X
6	0	6	1	7	2	8	3	9	X	X	X
7	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
8	X	X	5	2	10	7	4	1	9	6	X
9	X	X	7	5	3	1	10	8	6	4	X
10	X	10	9	8	7	6	5	4	3	X	X

i	j
i	0	1	2	3	4	5	6	7	8	9	10
0	0	0	0	0	0	0	0	0	X	X	X
1	0	1	2	3	4	5	6	7	X	X	X
2	X	X	X	6	8	10	1	3	5	7	9
3	X	X	6	9	1	4	7	10	2	5	X
4	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
5	X	X	10	4	9	3	8	2	7	1	X
6	0	6	1	7	2	8	3	9	X	X	X
7	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
8	X	X	5	2	10	7	4	1	9	6	X
9	X	X	7	5	3	1	10	8	6	4	X
10	X	10	9	8	7	6	5	4	3	X	X

i	j
i	0	1	2	3	4	5	6	7	8	9	10
0	0	0	0	0	0	0	0	0	X	X	X
1	0	1	2	3	4	5	6	7	X	X	X
2	X	X	X	6	8	10	1	3	5	7	9
3	X	X	6	9	1	4	7	10	2	5	X
4	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
5	X	X	10	4	9	3	8	2	7	1	X
6	0	6	1	7	2	8	3	9	X	X	X
7	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
8	X	X	5	2	10	7	4	1	9	6	X
9	X	X	7	5	3	1	10	8	6	4	X
10	X	10	9	8	7	6	5	4	3	X	X

Abstract

Cited By

Figures (4)

Tables (3)

Equations (9)

Applied Optics

i	j
i	0	1	2	3	4	5	6	7	8	9	10
0	0	0	0	0	0	0	0	0	X	X	X
1	0	1	2	3	4	5	6	7	X	X	X
2	X	X	X	6	8	10	1	3	5	7	9
3	X	X	6	9	1	4	7	10	2	5	X
4	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
5	X	X	10	4	9	3	8	2	7	1	X
6	0	6	1	7	2	8	3	9	X	X	X
7	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
8	X	X	5	2	10	7	4	1	9	6	X
9	X	X	7	5	3	1	10	8	6	4	X
10	X	10	9	8	7	6	5	4	3	X	X

i	j
i	0	1	2	3	4	5	6	7	8	9	10
0	0	0	0	0	0	0	0	0	X	X	X
1	0	1	2	3	4	5	6	7	X	X	X
2	X	X	X	6	8	10	1	3	5	7	9
3	X	X	6	9	1	4	7	10	2	5	X
4	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
5	X	X	10	4	9	3	8	2	7	1	X
6	0	6	1	7	2	8	3	9	X	X	X
7	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
8	X	X	5	2	10	7	4	1	9	6	X
9	X	X	7	5	3	1	10	8	6	4	X
10	X	10	9	8	7	6	5	4	3	X	X