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Codes for Optical CDMA

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Sequences and Their Applications – SETA 2006 (SETA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

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Abstract

There has been a recent upsurge of interest in applying Code Division Multiple Access (CDMA) techniques to optical networks. Conventional spreading codes for OCDMA, known as optical orthogonal codes (OOC) spread the signal in the time domain only, which often results in the requirement of a large chip rate. By spreading in both time and wavelength using two-dimensional OOCs, the chip rate can be reduced considerably. This paper presents an overview of 1-D and 2-D optical orthogonal codes as well as some new results relating to bounds on code size and code construction.

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References

  1. Salehi, J.A.: Code division multiple-access techniques in optical fiber networks-part I: Fundamental principles. IEEE Trans. Communication 37, 824–833 (1989)

    Article  Google Scholar 

  2. Johnson, S.M.: A new upper bound for error-correcting codes. IRE Trans. Information Theory, 203–207 (April 1962)

    Google Scholar 

  3. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, New York (1977)

    MATH  Google Scholar 

  4. Agrell, E., Vardy, A., Zeger, K.: Upper bounds for constant-weight codes. IEEE Trans. Information Theory 46, 2373–2395 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Moreno, O., Omrani, R., Kumar, P.V.: New bounds on the size of optical orthogonal codes, and constructions. The IEEE Transactions on Information Theory (submitted to be preprint)

    Google Scholar 

  6. Chung, F.R.K., Salehi, J.A., Wei, V.K.: Optical orthogonal codes: Design, analysis, and applications. IEEE Trans. Information Theory 35, 595–604 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chung, H., Kumar, P.V.: Optical orthogonal codes - new bounds and an optimal construction. IEEE Trans. Information Theory 36, 866–873 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  8. Nguyen, Q.A., Györfi, L., Massey, J.L.: Constructions of binary constant-weight cyclic codes and cyclically permutable codes. IEEE Trans. Information Theory 38, 940–949 (1992)

    Article  MATH  Google Scholar 

  9. Moreno, O., Zhang, Z., Kumar, P.V., Zinoviev, V.A.: New constructions of optimal cyclically permutable constant weight codes. IEEE Trans. Information Theory 41, 448–455 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bitan, S., Etzion, T.: Constructions for optimal constant weight cyclically permutable codes and difference families. IEEE Trans. Information Theory 41, 77–87 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  11. Yang, G., Fuja, T.E.: Optical orthogonal codes with unequal auto- and cross-correlation constraints. IEEE Trans. Information Theory 41, 96–106 (1995)

    Article  MATH  Google Scholar 

  12. Buratti, M.: A powerful method for constructing difference families and optimal optical orthogonal codes. Designs, Codes and cryptography 5, 13–25 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Yin, J.: Some combinatorial constructions for optical orthogonal codes. Discrete Mathematics 185, 201–219 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Fuji-Hara, R., Miao, Y.: Optical orthogonal codes: Their bounds and new optimal constructions. IEEE Trans. Information Theory 46, 2396–2406 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ge, G., Yin, J.: Constructions for optimal (v,4,1) optical orthogonal codes. IEEE Trans. Information Theory 47, 2998–3004 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  16. Fuji-Hara, R., Miao, Y., Yin, J.: Optimal (9v,4,1) optical orthogonal codes. SIAM Journal on Discrete Mathematics 14, 256–266 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  17. Tang, Y., Yin, J.: The combinatorial construction for a class of optimal optical orthogonal codes. Science in China (Series A) 45, 1268–1275 (2002)

    MATH  MathSciNet  Google Scholar 

  18. Buratti, M.: Cyclic designs with block size 4 and related optimal optical orthogonal codes. Designs, Codes and cryptography 26, 111–125 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Chu, W., Golomb, S.W.: A new recursive construction for optical orthogonal codes. IEEE Trans. Information Theory 49, 3072–3076 (2003)

    Article  MathSciNet  Google Scholar 

  20. Ding, C., Xing, C.: Several classes of (2m − 1,w,2) optical orthogonal codes. Discrete Applied Mathematics 128, 103–120 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Chang, Y., Fuji-Hara, R., Miao, Y.: Combinatorial constructions of optimal optical orthogonal codes with weight 4. IEEE Trans. Information Theory 49, 1283–1292 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  22. Chang, Y., Miao, Y.: Constructions for optical orthogonal codes. Discrete Mathematics 261, 127–139 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. Chang, Y., Ji, L.: Optimal (4up,5,1) optical orthogonal codes. Journal of Combinatorial Designs 12, 346–361 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  24. Abel, R.J.R., Buratti, M.: Some progress on (v,4,1) difference families and optical orthogonal codes. Journal of Combinatorial Theory, Series A 106, 59–75 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  25. Chang, Y., Yin, J.: Further results on optimal optical orthogonal codes with weight 4. Discrete Mathematics 279, 135–151 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  26. Chu, W., Colbourn, C.J.: Optimal (n,4,2)-OOC of small orders. Discrete Mathematics 279, 163–172 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  27. Chu, W., Colbourn, C.J.: Recursive constructions for optimal (n,4,2)-oocs. Journal of Combinatorial Designs 12, 333–345 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  28. Miyamoto, N., Mizuno, H., Shinohara, S.: Optical orthogonal codes obtained from conics on finite projective planes. Finite Fields and Their Applications 10, 405–411 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  29. Moreno, O., Kumar, P.V., Lu, H., Omrani, R.: New construction for optical orthogonal codes, distinct difference sets and synchronous optical orthogonal codes. In: Proc. Int. Symposium on Information Theory, p. 60 (2003)

    Google Scholar 

  30. Singer, J.: A theorem in finite projective geometry and some applications to number theory. Trans. Amer. Math. Soc. 43, 377–385 (1938)

    Article  MATH  MathSciNet  Google Scholar 

  31. Bose, R.C., Chowla, S.: On the construction of affine difference sets. Bull. Calcutta Math. Soc. 37, 107–112 (1945)

    MATH  MathSciNet  Google Scholar 

  32. Bose, R.C.: An affine analogue of Singer’s theorem. J. Indian. Math. Soc. 6, 1–15 (1942)

    MATH  MathSciNet  Google Scholar 

  33. Omrani, R., Elia, P., Kumar, P.V.: New constructions and bounds for 2-D optical orthogonal codes. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 389–395. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  34. Yang, G.C., Kwong, W.C.: Performance comparison of multiwavelength CDMA and WDMA+CDMA for fiber-optic networks. IEEE Trans. Commununication 45, 1426–1434 (1997)

    Article  Google Scholar 

  35. Lempel, A., Greenberger, H.: Families of sequences with optimal hamming correlation properties. IEEE Trans. Information Theory 20, 90–94 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  36. Simon, M.K., Omura, J.K., Scholtz, R.A., Levitt, B.K.: Spread Sprctrum Communications Handbook. McGraw-Hill, Inc., New York (2002)

    Google Scholar 

  37. Einarsson, G.: Address assignment for a time-frequency-coded, spread-spectrum system. Bell System Tech. Journal 59, 1241–1255 (1980)

    Google Scholar 

  38. Kumar, P.V.: Frequency-hopping code sequence design having large linear span. IEEE Trans. Information Theory 34, 146–151 (1988)

    Article  Google Scholar 

  39. Sarwate, D.V.: Reed-Solomon codes and the design of sequences for spread-spectrum multiple-access communications. In: Wicker, S.B., Bhargava, V.K. (eds.) Reed-Solomon Codes and Their Applications. IEEE Press, Piscatawa (1994)

    Google Scholar 

  40. Moreno, O., Maric, S.V.: A new family of frequency-hop codes. IEEE Trans. Communication 48, 1241–1244 (2000)

    Article  MATH  Google Scholar 

  41. Park, E., Mendez, A.J., Garmire, E.M.: Temporal/spatial optical CDMA networks-design, demonstration, and comparison with temporal networks. IEEE Photon. Technol. Lett. 4, 1160–1162 (1992)

    Article  Google Scholar 

  42. Kitayama, K.: Novel spatial spread spectrum based fiber optic CDMA networks for image transmission. IEEE Journal on Selected Areas in Communications 12, 762–772 (1994)

    Article  Google Scholar 

  43. Tančevski, L., Andonovic, I.: Hybrid wavelength hopping/time spreading schemes for use in massive optical networks with increased security. IEEE Journal of Lightwave Tech. 14, 2636–2647 (1996)

    Article  Google Scholar 

  44. Tančevski, L., Andonovic, I., Tur, M., Budin, J.: Massive optical LAN’s using wavelength hopping/time spreading with increased security. IEEE Photon. Technol. Lett. 8, 935–937 (1996)

    Article  Google Scholar 

  45. Yang, G.C., Kwong, W.C.: Two-dimensional spatial signature patterns. IEEE Trans. Communication 44, 184–191 (1996)

    Article  Google Scholar 

  46. Shivaleela, E.S., Sivarajan, K.N., Selvarajan, A.: Design of a new family of two-dimensional codes for fiber-optic CDMA networks. IEEE Journal of Lightwave Tech. 16, 501–508 (1998)

    Article  Google Scholar 

  47. Fathallah, H., Rusch, L.A., LaRochelle, S.: Passive optical fast frequency-hop CDMA communications system. IEEE Journal of Lightwave Tech. 17, 397–405 (1999)

    Article  Google Scholar 

  48. Mendez, A.J., Gagliardi, R.M., Feng, H.X.C., Heritage, J.P., Morookian, J.M.: Strategies for realizing optical CDMA for dense, high-speed, long span, optical network applications. IEEE Journal of Lightwave Tech. 168, 1685–1695 (2000)

    Article  Google Scholar 

  49. Yim, R.M.H., Chen, L.R., Bajcsy, J.: Design and performance of 2-D codes for wavelength-time optical CDMA. IEEE Photon. Technol. Lett. 14, 714–716 (2002)

    Article  Google Scholar 

  50. Mendez, A.J., Gagliardi, R.M., hernandez, V.J., Bennett, C.V., Lennon, W.j.: Design and performance analysis of wavelength/time (W/T) matrix codes for optical CDMA. IEEE Journal of Lightwave Tech. 21, 2524–2533 (2003)

    Article  Google Scholar 

  51. Kwong, W.C., Yang, G.C.: Extended carrier-hopping prime codes for wavelength-time optical code-division multiple access. IEEE Trans. Communication 52, 1084–1091 (2004)

    Article  Google Scholar 

  52. Kwong, W.C., Yang, G.C., Baby, V., Bres, C.S., Prucnal, P.R.: Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA. IEEE Trans. Communication 53, 117–123 (2005)

    Article  Google Scholar 

  53. Lidl, R., Niederreiter, H.: Encyclopedia of Mathematics and Its Applications 20: Finite Fields. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  54. Berlekamp, E.R., Moreno, O.: Extended double-error-correcting binary goppa codes are cyclic. IEEE Trans. Information Theory 19, 817–818 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  55. Yang, G.C., Kwong, W.C., Chang, C.Y.: Multiple-wavelength optical orthogonal codes under prime-sequence permutations. In: Proc. Int. Symposium on Information Theory, p. 367 (2004)

    Google Scholar 

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Omrani, R., Kumar, P.V. (2006). Codes for Optical CDMA. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_4

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  • DOI: https://doi.org/10.1007/11863854_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

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