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New asymptotically optimal three-dimensional wave-length/space/time optical orthogonal codes for OCDMA systems

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Abstract

We present new families of three-dimensional (3-D) optical orthogonal codes for applications to optical code-division multiple access (OCDMA) networks. The families are based in the extended rational cycle used for the 2-D Moreno-Maric construction. The new families are asymptotically optimal with respect to the Johnson bound.

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References

  1. Ortiz-Ubarri, J., Moreno, O., Tirkel, A.: Three-dimensional periodic optical orthogonal code for OCDMA systems. In: Information Theory Workshop (ITW), 2011 IEEE, pp. 170–174. IEEE (2011)

  2. Moreno, O., Maric, S.V.: A new family of frequency-hop codes. IEEE Trans. Commun. 48(8), 1241–1244 (2000)

    Article  Google Scholar 

  3. Moreno, O., Zhang, Z., Vijay Kumar, P., Zinoviev, V.A.: New constructions of optimal cyclically permutable constant weight codes. IEEE Trans. Inf. Theory 41 (2), 448–455 (1995)

    Article  MathSciNet  Google Scholar 

  4. Tirkel, A., Hall, T.: New matrices with good auto and cross-correlation. IEICE Transactions on fundamentals of electronics, Communications and Computer Sciences 89(9), 2315–2321 (2006)

    Article  Google Scholar 

  5. Gomez-Perez, D., Gomez, A.-I., Tirkel, A.: Arrays composed from the extended rational cycle. Advances in Mathematics of Communications 11(2), 313–327 (2017)

    Article  MathSciNet  Google Scholar 

  6. Omrani, R., Garg, G., Vijay Kumar, P., Elia, P., Bhambhani, P.: Large families of asymptotically optimal two-dimensional optical orthogonal codes. IEEE Trans. Inf. Theory 58(2), 1163–1185 (2012)

    Article  MathSciNet  Google Scholar 

  7. Kim, S., Yu, K., Park, N.: A new family of space/wavelength/time spread three-dimensional optical code for OCDMA networks. J. Lightwave Technol. 18(4), 502–511 (2000)

    Article  Google Scholar 

  8. Shum, K.W.: Optimal three-dimensional optical orthogonal codes of weight three. Des. Codes Crypt. 75(1), 109–126 (2015)

    Article  MathSciNet  Google Scholar 

  9. Li, X., Fan, P., Shum, K.W.: Construction of space/wavelength/time spread optical code with large family size. IEEE Commun. Lett. 16(6), 893–896 (2012)

    Article  Google Scholar 

  10. Alderson, T.L.: 3-Dimensional Optical Orthogonal Codes with Ideal Autocorrelation-Bounds and Optimal Constructions. IEEE Trans. Inf. Theory 64(6), 4392–4398 (2018)

    Article  MathSciNet  Google Scholar 

  11. Chung, F.R.K., Salehi, J.A., Wei, V.K.: Optical orthogonal codes: design, analysis and applications. IEEE Trans. Inf. theor. 35(3), 595–604 (1989)

    Article  MathSciNet  Google Scholar 

  12. 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(10), 1160–1162 (1992)

    Article  Google Scholar 

  13. Mendez, A.J., Gagliardi, R.M.: Code Division Multiple Access (CDMA) Enhancement of Wavelength Division Multiplexing (WDM) Systems. In: Communications, 1995. ICC’95 Seattle,’Gateway to Globalization’, 1995 IEEE International Conference on, vol. 1, pp. 271–276. IEEE (1995)

  14. Moreno, O., Ortiz-Ubarri, J.: Group permutable constant weight codes. In: Information Theory Workshop (ITW), 2010 IEEE, pp. 1–5, Dublin, Ireland, September 2010, IEEE

  15. Alderson, T.L., Mellinger, K.E.: Spreads, arcs, and multiple wavelength codes. Discrete Math. 311(13), 1187–1196 (2011)

    Article  MathSciNet  Google Scholar 

  16. McGeehan, J.E., Motaghian Nezam, S.M.R., Saghari, P., Izadpanah, T.H., Willner, A.E., Omrani, R, Kumar, P.V.: 3D Time-Wavelength-Polarization OCDMA Coding for Increasing the Number of Users in OCDMA LANs. In: Optical Fiber Communication Conference, 2004. OFC 2004, Vol. 2, pp. 3–Pp. IEEE (2004)

  17. Johnson, S.: A new upper bound for error-correcting codes. IRE Trans. Inf. Theor. 8(3), 203–207 (1962)

    Article  MathSciNet  Google Scholar 

  18. Berlekamp, E., Moreno, O.: Extended double-error-correcting binary goppa codes are cyclic (corresp). IEEE Trans. Inf. Theor. 19(6), 817–818 (1973)

    Article  Google Scholar 

  19. Singh, J., Singh, M.L.: A new family of 3-D optical orthogonal codes for optical CDMA systems with differential detection. J. Opt. Fiber Commun. Res. 6(1), 11–21 (2009)

    Article  Google Scholar 

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Acknowledgments

This work was partially supported by the National Science Foundation under Grant No. 1438838.

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  1. Computer Science Department, University of Puerto Rico, San Juan, Puerto Rico

    José Ortiz-Ubarri

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  1. José Ortiz-Ubarri
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Correspondence to José Ortiz-Ubarri.

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Ortiz-Ubarri, J. New asymptotically optimal three-dimensional wave-length/space/time optical orthogonal codes for OCDMA systems. Cryptogr. Commun. 12, 785–794 (2020). https://doi.org/10.1007/s12095-019-00422-1

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