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Impact of Nonlinearities on Fiber Optic Communications pp 219–252Cite as

Power-Efficient Modulation Schemes

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Part of the book series: Optical and Fiber Communications Reports ((OFCR,volume 7))

Abstract

Coherent optical fiber communications had a brief period of popularity in the early 1990s, mainly because the optical links of that day were significantly power limited. Coherent detection provided a possibility of optically amplifying the signal to a power level that, after photodetection, made the thermal noise negligible. Two things, however, caused those coherent systems to be abandoned. The first was the sheer technical difficulties: a coherent receiver requires a local oscillator laser that is to be phase- and polarization-locked to the received signal. This gave rise to significant technical obstacles, and only a few limited and expensive coherent receiver solutions were demonstrated [17, 27]. The second was the development of the Erbium-doper fiber amplifier (EDFA) that provided an elegant and practical solution to the problem of the thermal noise. By 1995, the EDFA was a commodity in fiber communication systems, simple on-off keying modulation worked well enough, and coherent communication was forgotten.

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Notes

  1. 1.

    Mathematically, a “ball” is defined as the set of points in Euclidean space whose distance to a given point is upperbounded by a given constant, i.e., the region bounded by a sphere. “Although physicists often use the term ‘sphere’ to mean the solid ball, mathematicians definitely do not” states Weisstein [55].

  2. 2.

    It was erroneously stated in [1] that the transformation (5.27) is equivalent to a 45 ∘ rotation of the carrier phase of the electric field. It is, if one interchanges row 1 with 2 and row 3 with 4 of the matrix in (5.27).

References

  1. E. Agrell, M. Karlsson, J. Lightwave Technol. 27(22), 5115–5126 (2009)

    Article  ADS  Google Scholar 

  2. E. Agrell, M. Karlsson, On the symbol error rate of regular polyhedra (2010). IEEE Trans. Inform. Theor., to appear, 2011

    Google Scholar 

  3. S. Benedetto, E. Biglieri, Principles of Digital Transmission: With Wireless Applications(Kluwer, New York, 1999)

    MATH  Google Scholar 

  4. S. Benedetto, P. Poggiolini, IEEE Trans. Commun. 40(4), 708–721 (1992)

    Article  MATH  Google Scholar 

  5. S. Betti, F. Curti, G. De Marchis, E. Iannone, Electron. Lett. 26(14), 992–993 (1990).

    Article  Google Scholar 

  6. S. Betti, F. Curti, G. De Marchis, E. Iannone, J. Lightwave Technol. 9(4), 514–523 (1991).

    Article  ADS  Google Scholar 

  7. S. Betti, G. De Marchis, E. Iannone, P. Lazzaro, J. Lightwave Technol. 9(10), 1314–1320 (1991).

    Article  ADS  Google Scholar 

  8. E. Biglieri, Advanced Modulation Formats for Satellite Communications, ed. by J. Hagenauer. Advanced Methods for Satellite and Deep Space Communications (Springer, Berlin, 1992) pp. 61–80

    Google Scholar 

  9. A. Bononi, M. Bertolini, P. Serena, G. Bellotti, J. Lightwave Technol. 27(18), 3974–3983 (2009).

    Article  ADS  Google Scholar 

  10. A. Bononi, P. Serena, N. Rossi, Opt. Fiber Technol. 16, 73–85 (2010)

    Article  ADS  Google Scholar 

  11. H. Bülow, Polarization QAM modulation (POL-QAM) for coherent detection schemes. Proceedings of optical fiber communication and national fiber optic engineers conference, OFC/NFOEC’09. Paper OWG2, 2009

    Google Scholar 

  12. G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, S. Bigo, Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation. Proceedings of European conference on optical communications, ECOC’06. Paper PDP Th.4.3.6, 2006

    Google Scholar 

  13. G. Charlet, M. Salsi, J. Renaudier, O. Pardo, H. Mardoyan, S. Bigo, Electron. Lett. 43(20), 1109–1111 (2007).

    Article  Google Scholar 

  14. J.H. Conway, N.J.A. Sloane, Sphere Packings, Lattices and Groups, 3rd edn. (Springer, New York, 1999)

    MATH  Google Scholar 

  15. H.S.M. Coxeter, Regular Polytopes(Dover Publications, New York, 1973)

    Google Scholar 

  16. R. Cusani, E. Iannone, A. Salonico, M. Todaro, J. Lightwave Technol. 10(6), 777–786 (1992)

    Article  ADS  Google Scholar 

  17. F. Derr, Electron. Lett. 26(6), 401–403 (1990)

    Article  Google Scholar 

  18. N. Ekanayake, T. Tjhung, IEEE Trans. Inform. Theor. IT-28(4), 658–660 (1982)

    Google Scholar 

  19. R. Essiambre, G. Kramer, P. Winzer, G. Foschini, B. Goebel, J. Lightwave Technol. 28(4), 662–701 (2010)

    Article  ADS  Google Scholar 

  20. G. Foschini, R. Gitlin, S. Weinstein, IEEE Trans. Commun. 22(1), 28–38 (1974)

    Article  Google Scholar 

  21. J.P. Gordon, L.R. Walker, W.H. Louisell, Phys. Rev. 130(2), 806–812 (1963).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. R.L. Graham, N.J.A. Sloane, Discrete Comput. Geom. 5(1), 1–11 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  23. K.-P. Ho, Phase-Modulated Optical Communication Systems(Springer, New York, 2005)

    Google Scholar 

  24. E. Ip, A.P.T. Lau, D.J.F. Barros, J.M. Kahn, Opt. Express 16(2), 753–791 (2008); Opt. Express 16(26), 21943 (2008)

    Google Scholar 

  25. G. Jacobsen, Noise in Digital Optical Transmission Systems(Artech House Publishers, Boston, 1994)

    Google Scholar 

  26. J.M. Kahn, K.-P. Ho, IEEE J. Select. Top. Quant. Electron. 10(2), 259–272 (2004).

    Article  Google Scholar 

  27. J.M. Kahn, A.H. Gnauck, J.J. Veselka, S.K. Korotky, B.L. Kasper, IEEE Photon. Technol. Lett. 2(4), 285–287 (1990).

    Article  ADS  Google Scholar 

  28. M. Karlsson, E. Agrell, Opt. Express 17(13), 10814–10819 (2009)

    Article  Google Scholar 

  29. M. Karlsson, H. Sunnerud, J. Lightwave Technol. 24(11), 4127–4137 (2006)

    Article  ADS  Google Scholar 

  30. L. Kazovsky, S. Benedetto, A. Willner, Optical Fiber Communication Systems(Artech House Publishers, Boston, 1996)

    Google Scholar 

  31. K. Kikuchi, S. Tsukamoto, J. Lightwave Technol. 26(13), 1817–1822 (2008)

    Article  ADS  Google Scholar 

  32. H.G. Kim, 4-dimensional modulation for a bandlimited channel using Q2PSK. IEEE wireless communications and networking conference, WCNC, vol. 3, pp. 1144–1147, 1999

    Google Scholar 

  33. G. Lachs, IEEE Trans. Inform. Theor. 9(2), 95–97 (1963)

    Article  Google Scholar 

  34. D. Ly-Gagnon, K. Katoh, K. Kikuchi, Electron. Lett. 41(4), 206–207 (2005)

    Article  Google Scholar 

  35. O. Musin, Ann. Math. 168, 1–32 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  36. J.R. Pierce, IEEE Trans. Commun. 26(12), 1819–1821 (1978)

    Article  MathSciNet  Google Scholar 

  37. J.R. Pierce, IEEE Trans. Commun. COM-28(7), 1098–1099 (1980)

    Google Scholar 

  38. J.-E. Porath, T. Aulin, IEE Proc. Commun. 150(5), 317–323 (2003).

    Article  Google Scholar 

  39. J. Proakis, Digital Communications, 4th edn. (McGraw-Hill, Boston, 2001)

    Google Scholar 

  40. J. Renaudier, G. Charlet, M. Salsi, O. Pardo, H. Mardoyan, P. Tran, S. Bigo, J. Lightwave Technol. 26(1), 36–42 (2008)

    Article  ADS  Google Scholar 

  41. K. Roberts, M. O’Sullivan, K.T. Wu, H. Sun, A. Awadalla, D.J. Krause, C. Laperle, J. Lightwave Technol. 27(16), 3546–3559 (2009).

    Article  ADS  Google Scholar 

  42. D. Saha, T. Birdsall, IEEE Trans. Commun. 37(5), 437–448 (1989).

    Article  Google Scholar 

  43. C.E. Shannon, Proc. IRE 37(1), 10–21 (1949)

    Article  MathSciNet  Google Scholar 

  44. C.E. Shannon, Bell Syst. Tech. J. 38(3), 611–656 (1959)

    MathSciNet  Google Scholar 

  45. M. Simon, S. Hinedi, W. Lindsey, Digital Communication Techniques: Signal Design and Detection. (PTR, Prentice Hall, 1995)

    Google Scholar 

  46. N.J.A. Sloane, R.H. Hardin, T.S. Duff, J.H. Conway, Discrete Comput. Geom. 14(3), 237–259 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  47. N.J.A. Sloane, R.H. Hardin, T.S. Duff, J.H. Conway, Minimal-energy clusters, library of 3-d clusters, library of 4-d clusters (1997). http://www.research.att.com/~njas/cluster/

  48. N.J.A. Sloane, R.H. Hardin, T.S. Duff, J.H. Conway, Spherical codes, part 1 (2000). http://www.research.att.com/~njas/packings/

  49. E. Specht, The best known packings of equal circles in the unit circle (2009). http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html

  50. K. Stephenson, Circle packing bibliography as of September 2005 (2005). http://www.math.utk.edu/~kens/CP-bib.pdf

  51. H. Sun, K. Wu, K. Roberts, Opt. Express 16(2), 873–879 (2008)

    Article  ADS  Google Scholar 

  52. A.S. Tanenbaum, Computer Networks, 4th edn. (Pearson, Upper Saddle River, 2003)

    Google Scholar 

  53. G. Taricco, E. Biglieri, V. Castellani, Applicability of four-dimensional modulations to digital satellites: A simulation study. Proceedings of IEEE global telecommunications conference, vol. 4, pp. 28–34, 1993

    Google Scholar 

  54. S. Tsukamoto, D. Ly-Gagnon, K. Katoh, K. Kikuchi, Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission. Proceedings of optical fiber communication and national fiber optic engineers conference, OFC/NFOEC, vol. 6. Paper PDP 29, 2005

    Google Scholar 

  55. E.W. Weisstein, Ball, From Mathworld – a Wolfram Web Resource (2010). http://mathworld.wolfram.com/Ball.html

  56. G. Welti, J. Lee, IEEE Trans. Inform. Theor. 20(4), 497–502 (1974)

    Article  MATH  Google Scholar 

  57. M. Winter, C.A. Bunge, D. Setti, K. Petermann, J. Lightwave Technol. 27(17), 3739–3751 (2009)

    Article  ADS  Google Scholar 

  58. J. Wu, M.C. Wu, IEEE Trans. Vehicular Technol. 49(6), 2244–2256 (2000)

    Article  Google Scholar 

  59. L. Xiao, X. Dong, IEEE Trans. Wireless Commun. 4(4), 1418–1424 (2005)

    Article  Google Scholar 

  60. C. Xie, IEEE Photon. Technol. Lett. 21(5), 274 (2009)

    Article  ADS  Google Scholar 

  61. C. Xie, Opt. Express 17(6), 4815–4823 (2009)

    Article  ADS  Google Scholar 

  62. L. Zetterberg, H. Brändström, IEEE Trans. Commun. 25(9), 943–950 (1977)

    Article  MATH  Google Scholar 

  63. H.Y. Song, S.W. Golomb, IEEE Trans. Inform. Theor. 40(2), 504–507 (1994)

    Article  MATH  Google Scholar 

  64. M. Karlsson, E. Agrell, Four-dimensional optimized constellations for coherent optical transmission systems. Proceedings of the 36th European conference on Optical Communication, ECOC’10. Paper We.8.C.3, 2010

    Google Scholar 

  65. P. Serena, A. Vanucci, A. Bononi, The performance of polarization-wwitched QPSK (PS-QPSK) in dispersion managed WDM transmissions. Proceedings of the 36th European conference on Optical Communication, ECOC’10. Paper Th.10.E.2, 2010

    Google Scholar 

  66. P. Poggiolini, Opt. Express. 18(11), 11360–11371 (2010)

    Article  ADS  Google Scholar 

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Acknowledgements

We wish to acknowledge funding from Vinnova within the IKT grant, and the Swedish strategic research foundation (SSF). We also acknowledge numerous stimulating discussions with all the researchers within the Chalmers fiber-optic communications research center FORCE. Dr. Seb Savory is gratefully acknowledged for a useful discussion, help with the \({\mathcal{C}}_{4,16}\)cluster, and for providing a few previously overlooked references.

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Authors and Affiliations

  1. Photonics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-412 96, Göteborg, Sweden

    Magnus Karlsson

  2. Communication Systems Group, Department of Signals and Systems, Chalmers University of Technology, SE-412 96, Göteborg, Sweden

    Erik Agrell

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  1. Magnus Karlsson
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Correspondence to Magnus Karlsson .

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  1. Dept. Electrical &, Computer Engineering, McMaster University, Main Street West 1280, Hamilton, L8S 4K1, Ontario, Canada

    Shiva Kumar

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Karlsson, M., Agrell, E. (2011). Power-Efficient Modulation Schemes. In: Kumar, S. (eds) Impact of Nonlinearities on Fiber Optic Communications. Optical and Fiber Communications Reports, vol 7. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8139-4_5

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  • DOI: https://doi.org/10.1007/978-1-4419-8139-4_5

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