Abstract

We investigate a general scheme of frequency-hopping optical orthogonal codes with a specified distance between adjacent frequency symbols and propose a novel code that allows time blanks between adjacent frequency symbols in code sequences. A time blank represents the absence of frequency symbols in code sequences and makes no interference with frequency components. The insertion of time-blank patterns can provide ample scope to generate much more code sequences than the conventional codes lacking in time-blank patterns, and we show this by constructing an algorithm to generate the proposed code. The performance analysis demonstrates that its performance is superior to that of the conventional codes in terms of the bit error rate. We also derive the upper bound on the proposed code set.

© 2002 Optical Society of America

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References

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  1. H. Fathallah, L. A. Rusch, S. LaRochelle, “Passive optical fast frequency-hop CDMA communication system,” J. Lightwave Technol. 17, 397–405 (1999).
    [CrossRef]
  2. J. Salehi, “Code division multiple-access techniques in optical fiber networks—Part I: Fundamental principles,” IEEE Trans. Commun. 37, 824–833 (1989).
    [CrossRef]
  3. L. Bin, “One-coincidence sequences with specified distance between adjacent symbols for frequency-hopping multiple access,” IEEE Trans. Commun. 45, 408–410 (1997).
    [CrossRef]
  4. V. Maric, M. D. Hahm, E. L. Titlebaum, “Construction and performance analysis of a new family of optical orthogonal codes for CDMA fiber-optic networks,” IEEE Trans. Commun. 43, 485–489 (1995).
    [CrossRef]
  5. E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
    [CrossRef]
  6. W. C. Kwong, P. A. Perrier, P. P. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber optic local area networks,” IEEE Trans. Commun. 39, 1625–1634 (1991).
    [CrossRef]
  7. J. Salehi, C. A. Brackett, “Code division multiple-access techniques in optical fiber networks—Part 2: System performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
    [CrossRef]

1999 (1)

1997 (1)

L. Bin, “One-coincidence sequences with specified distance between adjacent symbols for frequency-hopping multiple access,” IEEE Trans. Commun. 45, 408–410 (1997).
[CrossRef]

1995 (2)

V. Maric, M. D. Hahm, E. L. Titlebaum, “Construction and performance analysis of a new family of optical orthogonal codes for CDMA fiber-optic networks,” IEEE Trans. Commun. 43, 485–489 (1995).
[CrossRef]

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

1991 (1)

W. C. Kwong, P. A. Perrier, P. P. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber optic local area networks,” IEEE Trans. Commun. 39, 1625–1634 (1991).
[CrossRef]

1989 (2)

J. Salehi, C. A. Brackett, “Code division multiple-access techniques in optical fiber networks—Part 2: System performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
[CrossRef]

J. Salehi, “Code division multiple-access techniques in optical fiber networks—Part I: Fundamental principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[CrossRef]

Bin, L.

L. Bin, “One-coincidence sequences with specified distance between adjacent symbols for frequency-hopping multiple access,” IEEE Trans. Commun. 45, 408–410 (1997).
[CrossRef]

Brackett, C. A.

J. Salehi, C. A. Brackett, “Code division multiple-access techniques in optical fiber networks—Part 2: System performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
[CrossRef]

Fathallah, H.

Gough, P. T.

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

Hahm, M. D.

V. Maric, M. D. Hahm, E. L. Titlebaum, “Construction and performance analysis of a new family of optical orthogonal codes for CDMA fiber-optic networks,” IEEE Trans. Commun. 43, 485–489 (1995).
[CrossRef]

Kwong, W. C.

W. C. Kwong, P. A. Perrier, P. P. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber optic local area networks,” IEEE Trans. Commun. 39, 1625–1634 (1991).
[CrossRef]

LaRochelle, S.

Maric, V.

V. Maric, M. D. Hahm, E. L. Titlebaum, “Construction and performance analysis of a new family of optical orthogonal codes for CDMA fiber-optic networks,” IEEE Trans. Commun. 43, 485–489 (1995).
[CrossRef]

Perrier, P. A.

W. C. Kwong, P. A. Perrier, P. P. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber optic local area networks,” IEEE Trans. Commun. 39, 1625–1634 (1991).
[CrossRef]

Prucnal, P. P.

W. C. Kwong, P. A. Perrier, P. P. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber optic local area networks,” IEEE Trans. Commun. 39, 1625–1634 (1991).
[CrossRef]

Rusch, L. A.

Salehi, J.

J. Salehi, C. A. Brackett, “Code division multiple-access techniques in optical fiber networks—Part 2: System performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
[CrossRef]

J. Salehi, “Code division multiple-access techniques in optical fiber networks—Part I: Fundamental principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[CrossRef]

Smith, E. D. J.

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

Taylor, D. P.

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

Titlebaum, E. L.

V. Maric, M. D. Hahm, E. L. Titlebaum, “Construction and performance analysis of a new family of optical orthogonal codes for CDMA fiber-optic networks,” IEEE Trans. Commun. 43, 485–489 (1995).
[CrossRef]

Electron. Lett. (1)

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

IEEE Trans. Commun. (5)

W. C. Kwong, P. A. Perrier, P. P. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber optic local area networks,” IEEE Trans. Commun. 39, 1625–1634 (1991).
[CrossRef]

J. Salehi, C. A. Brackett, “Code division multiple-access techniques in optical fiber networks—Part 2: System performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
[CrossRef]

J. Salehi, “Code division multiple-access techniques in optical fiber networks—Part I: Fundamental principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[CrossRef]

L. Bin, “One-coincidence sequences with specified distance between adjacent symbols for frequency-hopping multiple access,” IEEE Trans. Commun. 45, 408–410 (1997).
[CrossRef]

V. Maric, M. D. Hahm, E. L. Titlebaum, “Construction and performance analysis of a new family of optical orthogonal codes for CDMA fiber-optic networks,” IEEE Trans. Commun. 43, 485–489 (1995).
[CrossRef]

J. Lightwave Technol. (1)

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Figures (6)

Fig. 1
Fig. 1

Simple decoder design of the FHOOC/TB CDMA system using Bragg gratings.

Fig. 2
Fig. 2

BER comparison between Bin’s code (q = 15, w = 8) and the FHOOC/TB (q = 15, w = 8, k = 7). Bin’s code supports 15 users and the FHOOC/TB supports 30 users.

Fig. 3
Fig. 3

BER comparison between Bin’s code (q = 41, w = 6) and the FHOOC/TB (q = 41, w = 6, k = 5). Bin’s code supports 41 users and the FHOOC/TB supports 246 users.

Fig. 4
Fig. 4

BER comparison between Bin’s code (q = 35, w = 8) and the FHOOC/TB (q = 17, w = 8) when the maximum numbers of users are 35 and 34, respectively.

Fig. 5
Fig. 5

BER comparison between Bin’s code (q = 29, w = 14) and the FHOOC/TB (q = 29, w = 6, k = 8) when the code lengths are equal.

Fig. 6
Fig. 6

BER comparison between Bin’s code (q = 41, w = 10) and the FHOOC/TB (q = 41, w = 6, k = 5) when the code lengths are similar.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

r=j-i-1if i<j,q+j-i-1if i>j.
wtx= iL : xi*.
wtx= xi : xi* for iL.
Hxyτ=i=0L-1 hxi, yi+τfor x, y˜qLand τL,
ha, b=0for ab or a=b=*1for a=bq
i=0w-1 di0mod q
sjD,B=s0D,B+i=0nl-1B dimod qif j=nlB for some lw*otherwise
s0=sD,B, sji=sj0+i.
GijD,B=distsnjBD,B, snjB+i+1D,Bif snjB+i+1D,B**otherwise
GD,B=*7636**5131**35128****18***344013**29*6**35*2812*1*23*7**29*33*636*2840***34355* and GD,B=5***3435**6362840***2933**7123**12*3528***1329**618*34*40**8***12131*355*636***7.
sD,B=0, *, 5, 12, 18, 13, *, *, *, 6, *, sD,B=0, 5, *, *, *, 12, *, 18, *, 13, 6,
0, *, 5, 12, 18, 13, *, *, *, 6, *,1, *, 6, 13, 19, 14, *, *, *, 7, *,40, *, 4, 11, 17, 12, *, *, *, 5, *,0, 5, *, *, *, 12, *, 18, *, 13, 6,1, 6, *, *, *, 13, *, 19, *, 14, 7,40, 4, *, *, *, 11, *, 17, *, 12, 5.
sD1,B1=0, *, 5, 12, 18, 13, *, *, *, 6, *,sD1,B2=0, 5, *, *, *, 12, *, 18, *, 13, 6,sD2,B1=0, *, 8, 17, 27, 19, *, *, *, 10, *,sD2,B2=0, 8, *, *, *, 17, *, 27, *, 19, 10,sD3,B1=0, *, 11, 23, 37, 26, *, *, *, 14, *,sD3,B2=0, 11, *, *, *, 23, *, 37, *, 26, 14,
Ni=0l-1q-maxd-i,0P2+q-maxd-l,0P2w-k,
i=0w Niw-i= A.
i=1w-1 Niw-iq-dP2,
Nw=C i=0m-1q-maxd-i-1,0P2+ q-maxd-m-1,0P2w-k.
Ni=0l-1q-maxd-iγ,0P2+ q-maxd-lγ,0P2w-k,
cit=j=1L fsjit-jTc,
rt= i=1K picit-τi,
y=0T c1trtdt=p1w+MAI,
σi,j2=12w+k-1s=-w-k+1w+k-1Ri,js- R¯i,j2

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