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Codes on Graphs, Coded Modulation and Compensation of Nonlinear Impairments by Turbo Equalization

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Impact of Nonlinearities on Fiber Optic Communications

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

Abstract

As the response to the ever-increasing demands of telecommunication needs, the network operators already consider beyond 100Gb/s per dense wavelength division multiplexing (DWDM) channel transmission [1]. At those data rates, the performance of fiberoptic communication systems is degraded significantly due to intra- and interchannel fiber nonlinearities, polarization-mode dispersion (PMD), and chromatic dispersion [2–5]. To deal with those channel impairments novel advanced techniques in modulation and detection, coding and signal processing should be developed; and some important aspects are described in this chapter.

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Notes

  1. 1.

    The Q-factor is defined as Q = (μ1 − μ0) ∕ (σ1 + σ0), where μ j and σ j (j = 0, 1) represent the mean and the standard deviation corresponding to the bits j = 0, 1.

  2. 2.

    A (w c,  w r ) – regular LDPC code is a linear block code whose H-matrix contains exactly w c 1’s in each column and exactly w r = w c n ∕ (n − k) 1’s in each column, where w c ≪ n − k.

References

  1. T. Schmidt, C. Malouin, S. Liu, in Proceedings of 2009 IEEE LEOS annual meeting, Belek-Antalya, Turkey, Paper WM3, 4–8 October 2009

    Google Scholar 

  2. I.B. Djordjevic, M. Arabaci, L. Minkov, IEEE/OSA J. Lightw. Technol. 27, 3518–3530 (2009). (Invited Paper.)

    Google Scholar 

  3. W. Shieh, I. Djordjevic, OFDM for Optical Communications (Elsevier, Amsterdam, 2009)

    Google Scholar 

  4. I.B. Djordjevic, W. Ryan, B. Vasic, Coding for Optical Channels (Springer, Berlin, 2010)

    Book  Google Scholar 

  5. I.B. Djordjevic, L.L. Minkov, H.G. Batshon, IEEE J. Select. Areas Commun. Opt. Commun. Netw. 26, 73–83 (2008)

    Article  Google Scholar 

  6. ITU, Telecommunication Standardization Sector: Forward error correction for submarine systems, Rec. G.975 (Geneva, 1996)

    Google Scholar 

  7. ITU, Telecommunication Standardization Sector: Forward error correction for high bit rate DWDM submarine systems, Rec. G. 975.1 (02/2004)

    Google Scholar 

  8. T. Mizuochi et al., IEEE J. Select. Top. Quant. Electron. 10, 376–386 (2004)

    Article  Google Scholar 

  9. T. Mizuochi et al., Next generation FEC for optical transmission systems, in Proceedings of optical fiber communication conference (OFC 2003), vol. 2, pp. 527–528, 2003

    Google Scholar 

  10. R.G. Gallager, Low Density Parity Check Codes (MIT, Cambridge, 1963)

    Google Scholar 

  11. S. Chung et al., IEEE Commun. Lett. 5, 58–60 (2001)

    Article  Google Scholar 

  12. F.M. Ingels, Information and Coding Theory (Intext Educational Publishers, Scranton, 1971)

    MATH  Google Scholar 

  13. S. Lin, D.J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, NJ, 1983)

    Google Scholar 

  14. J.B. Anderson, S. Mohan, Source and Channel Coding: An Algorithmic Approach (Kluwer, Boston, MA, 1991)

    MATH  Google Scholar 

  15. F.J. MacWilliams, N.J.A. Sloane, The Theory of Error-Correcting Codes (North Holland, Amsterdam, 1977)

    MATH  Google Scholar 

  16. S.B. Wicker, Error Control Systems For Digital Communication And Storage (Prentice-Hall, Englewood Cliffs, NJ, 1995)

    MATH  Google Scholar 

  17. D.B. Drajic, An Introduction to Information Theory and Coding, 2nd edn. (Akademska Misao, Belgrade, 2004) (in Serbian)

    Google Scholar 

  18. S. Haykin, Communication Systems (Wiley, New York, 2004)

    Google Scholar 

  19. J.G. Proakis, Digital Communications (McGaw-Hill, Boston, MA, 2001)

    Google Scholar 

  20. T.M. Cover, J.A. Thomas, Elements of Information Theory (Wiley, New York, 1991)

    Book  MATH  Google Scholar 

  21. P. Elias, IRE Trans. Inf. Theory IT-4, 29–37 (1954)

    Google Scholar 

  22. R.H. Morelos-Zaragoza, The Art of Error Correcting Coding. (Wiley, Boston, MA, 2002)

    Google Scholar 

  23. O.A. Sab, FEC techniques in submarine transmission systems, in Proceedings of optical fiber communication conference (OFC 2001), vol. 2, TuF1–1-TuF1–3, 2001

    Google Scholar 

  24. C. Berrou, A. Glavieux, P. Thitimajshima, Proceedings of 1993 international conference on communication (ICC 1993), pp. 1064–1070, 1993

    Google Scholar 

  25. C. Berrou, A. Glavieux, IEEE Trans. Commun. 44, 1261–1271 (1996)

    Article  Google Scholar 

  26. R.M. Pyndiah, IEEE Trans. Commun. 46, 1003–1010 (1998)

    Article  MATH  Google Scholar 

  27. O.A. Sab, V. Lemarie, Block turbo code performances for long-haul DWDM optical transmission systems, in Proceedings of OFC 2001, vol. 3, pp. 280–282, 2001

    Google Scholar 

  28. T. Mizuochi, IEEE J. Select. Top. Quant. Electron. 12, 544–554 (2006)

    Article  Google Scholar 

  29. W.E. Ryan, in Wiley Encyclopedia in Telecommunications, ed. by J.G. Proakis (Wiley, New York, 2003)

    Google Scholar 

  30. I.B. Djordjevic, S. Sankaranarayanan, S.K. Chilappagari, B. Vasic, IEEE/LEOS J. Select. Top. Quant. Electron. 12(4), 555–562 (2006)

    Article  Google Scholar 

  31. I.B. Djordjevic, O. Milenkovic, B. Vasic, IEEE/OSA J. Lightw. Technol. 23, 1939–1946 (2005)

    Article  ADS  Google Scholar 

  32. B. Vasic, I.B. Djordjevic, R. Kostuk, IEEE/OSA J. Lightw. Technol. 21, 438–446 (2003)

    Article  ADS  Google Scholar 

  33. I.B. Djordjevic et al., IEEE/OSA J. Lightw. Technol. 22, 695–702 (2004)

    Article  ADS  Google Scholar 

  34. O. Milenkovic, I.B. Djordjevic, B. Vasic, IEEE/LEOS J. Select. Top. Quant. Electron. 10, 294–299 (2004)

    Article  Google Scholar 

  35. B. Vasic, I.B. Djordjevic, IEEE Photon. Technol. Lett. 14, 1208–1210 (2002)

    Article  ADS  Google Scholar 

  36. D.J.C. MacKay, IEEE Trans. Inf. Theory 45, 399–431 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  37. I.B. Djordjevic, L. Xu, T. Wang, M. Cvijetic, Large girth low-density parity-check codes for long-haul high-speed optical communications, in Proceedings of OFC/NFOEC, IEEE/OSA, San Diego, CA, Paper no. JWA53, 2008

    Google Scholar 

  38. W.E. Ryan, in CRC Handbook for Coding and Signal Processing for Recording Systems, ed. by B. Vasic (CRC Press, Boca Raton, FL, 2004)

    Google Scholar 

  39. R.M. Tanner, IEEE Trans. Inf. Theory IT-27, 533–547 (1981)

    Google Scholar 

  40. M.P.C. Fossorier, IEEE Trans. Inf. Theory, 50, 1788–1793 (2004)

    Article  MathSciNet  Google Scholar 

  41. H. Xiao-Yu, E. Eleftheriou, D.M. Arnold, A. Dholakia, Efficient implementations of the sum-product algorithm for decoding of LDPC codes, in Proceedings of IEEE Globecom, vol. 2, pp. 1036–1036E, Nov 2001

    Google Scholar 

  42. I. Anderson, Combinatorial Designs and Tournaments (Oxford University Press, Oxford, 1997)

    MATH  Google Scholar 

  43. I.B. Djordjevic, B. Vasic, IEEE/OSA J. Lightw. Technol. 24, 420–428 (2006)

    Article  ADS  Google Scholar 

  44. I.B. Djordjevic, M. Cvijetic, L. Xu, T. Wang, IEEE/OSA J. Lightw. Technol. 25, 3619–3625 (2007)

    Article  ADS  Google Scholar 

  45. I.B. Djordjevic, B. Vasic, OSA J. Opt. Netw. 7, 217–226, (2008)

    Article  Google Scholar 

  46. J. Hou, P.H. Siegel, L.B. Milstein, H.D. Pfitser, IEEE Trans. Inf. Theory 49(9), 2141–2155 (2003)

    Article  Google Scholar 

  47. G.D. Forney Jr., Concatenated Codes (MIT, Cambridge, MA, 1966)

    Google Scholar 

  48. I.B. Djordjevic, L. Xu, T. Wang, Opt. Express 16(18), 14163–14172 (2008)

    Article  ADS  Google Scholar 

  49. E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, H.V. Poor, MIMO Wireless Communications (Cambridge University Press, Cambridge, 2007)

    Book  Google Scholar 

  50. I.B. Djordjevic, L. Xu, T. Wang, Opt. Express 16(19), 14845–14852 (2008)

    Article  ADS  Google Scholar 

  51. I.B. Djordjevic, L. Xu, T. Wang, Beyond 100 Gb/s Optical Transmission based on Polarization Multiplexed Coded-OFDM with Coherent Detection, IEEE/OSA J. Opt. Commun. Netw. 1(1), 50–56 (2009)

    Article  Google Scholar 

  52. VPITransmisionMaker, http://www.vpiphotonics.com

  53. C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, A. Glavieux, Eur. Trans. Telecommun. (6), 507–511 (1995)

    Google Scholar 

  54. M. Tüchler, R. Koetter, A.C. Singer, IEEE Trans. Commun. 50(5), 754–767 (2002)

    Article  Google Scholar 

  55. L.R. Bahl, J. Cocke, F. Jelinek, J. Raviv, IEEE Trans. Inf. Theory IT-20(2), 284–287 (1974)

    Google Scholar 

  56. M. Ivkovic, I. Djordjevic, P. Rajkovic, B. Vasic, IEEE Photon. Technol. Lett. 19(20), 1604–1606 (2007)

    Article  ADS  Google Scholar 

  57. J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, X.Y. Hu, IEEE Trans. Commun. 53, 1288–1299 (2005)

    Article  Google Scholar 

  58. I.B. Djordjevic, H.G. Batshon, L. Xu, T. Wang, Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission, in Proceedings of OFC/NFOEC 2010, Paper No. OMK2, San Diego, CA, 21–25 March 2010

    Google Scholar 

  59. E. Ip, J.M. Kahn, in Optical Fibre, New Developments, In-Tech, Vienna, Austria, December 2009

    Google Scholar 

  60. B. McMillan, Ann. Math. Stat. 24, 196–219 (1952)

    Article  MathSciNet  Google Scholar 

  61. A.I. Khinchin, Mathematical Foundations of Information Theory (Dover Publications, New York, 1957)

    MATH  Google Scholar 

  62. L.L. Minkov, I.B. Djordjevic, L. Xu, T. Wang, F. Kueppers, Opt. Express 16, 13450–13455 (2008)

    Article  ADS  Google Scholar 

  63. I.B. Djordjevic, L.L. Minkov, L. Xu, T. Wang, IEEE/OSA J. Opt. Commun. Netw. 1, 555–564 (2009)

    Article  Google Scholar 

  64. L.R. Bahl, J. Cocke, F. Jelinek, J. Raviv, IEEE Trans. Inf. Theory IT-20(3), 284–287 (1974)

    Google Scholar 

  65. F.M. Reza, An Introduction to Information Theory (McGraw-Hill, New York, 1961)

    Google Scholar 

  66. D.P. Bertsekas, Nonlinear Programming, 2nd edn. (Athena Scientific, Belmont, MA, 1999)

    MATH  Google Scholar 

  67. E.K.P. Chong, S.H. Zak, An Introduction to Optimization, 3rd edn. (Wiley, New York, 2008)

    MATH  Google Scholar 

  68. R.J. Essiambre, G.J. Foschini, G. Kramer, P.J. Winzer, Phys. Rev. Lett. 101, 163901–1–163901–4 (2008)

    Google Scholar 

  69. W.T. Webb, R. Steele, IEEE Trans. Commun. 43, 2223–2230 (1995)

    Article  Google Scholar 

  70. H.D. Pfitser, J.B. Soriaga, P.H. Siegel, On the achievable information rates of finite state ISI channels, in Proceedings of Globecom 2001, San Antonio, TX, pp. 2992–2996, 25–29 Nov 2001

    Google Scholar 

  71. E.E. Narimanov, P. Mitra, IEEE/OSA J. Lightw. Technol. 20(3), 530–537 (2002)

    Article  ADS  Google Scholar 

  72. E. Narimanov, P. Patel, Channel capacity of fiber optics communications systems: WDM vs. TDM, in Proceedings of conference on lasers and electro-optics (CLEO ’03), pp. 1666–1668, 2003

    Google Scholar 

  73. P.P. Mitra, J.B. Stark, Nature 411, 1027–1030 (2001)

    Article  ADS  Google Scholar 

  74. K.S. Turitsyn, S.A. Derevyanko, I.V. Yurkevich, S.K. Turitsyn, Phys. Rev. Lett. 91(20), 203 901 (2003)

    Google Scholar 

  75. J. Tang, IEEE/OSA J. Lightw. Technol. 19, 1110–1115 (2001)

    Article  ADS  Google Scholar 

  76. A. Mecozzi, M. Shtaif, IEEE Photon. Technol. Lett. 13, 1029–1031 (2001)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  78. I.B. Djordjevic, B. Vasic, Approaching Shannon’s capacity limits of fiber optics communications channels using short LDPC codes, in Proceedings of CLEO/IQEC, Paper CWA7, 2004

    Google Scholar 

  79. I.B. Djordjevic, B. Vasic, M. Ivkovic, I. Gabitov, IEEE/OSA J. Lightw. Technol. 23(11), 3755–3763 (2005)

    Article  ADS  Google Scholar 

  80. I.B. Djordjevic, L. Xu, T. Wang, On the channel capacity of multilevel modulation schemes with coherent detection, in Proceedings of Asia communications and photonics conference and exhibition (ACP) 2009, Paper ThC4, Shangai, China, 2–6 November 2009

    Google Scholar 

  81. M. Ivkovic, I.B. Djordjevic, B. Vasic, IEEE/OSA J. Lightw. Technol. 25(5), 1163–1168 (2007)

    Article  ADS  Google Scholar 

  82. I.B. Djordjevic, N. Alic, G. Papen, S. Radic, IEEE Photon. Technol. Lett. 19, 12–14 (2007)

    Article  ADS  Google Scholar 

  83. L.L. Minkov, I.B. Djordjevic, H.G. Batshon, L. Xu, T. Wang, M. Cvijetic, F. Kueppers, IEEE Photon. Technol. Lett. 19, 1852–1854 (2007)

    Article  ADS  Google Scholar 

  84. D. Arnold, A. Kavcic, H.A. Loeliger, P.O. Vontobel, W. Zeng, Simulation-based computation of information rates: upper and lower bounds, in Proceedings of IEEE international symposium on information theory (ISIT 2003), p. 119, 2003

    Google Scholar 

  85. D. Arnold, H.A. Loeliger, On the information rate of binary-input channels with memory, in Proceedings of 2001 international conference communications, Helsinki, Finland, pp. 2692–2695, 11–14 June 2001

    Google Scholar 

  86. Z.H. Peric, I.B. Djordjevic, S.M. Bogosavljevic, M.C. Stefanovic, Design of signal constellations for Gaussian channel by iterative polar quantization, in Proceedings of 9th mediterranean electrotechnical conference, vol. 2, Tel-Aviv, Israel, pp. 866–869, 18–20 May 1998

    Google Scholar 

  87. H.G. Batshon, I.B. Djordjevic, L.L. Minkov, L. Xu, T. Wang, M. Cvijetic, Proposal to achieve 1 Tb/s per wavelength transmission using 3-dimensional LDPC-coded modulation, IEEE Photon. Technol. Lett. 20(9), 721–723 (2008)

    Article  ADS  Google Scholar 

  88. H.G. Batshon, I.B. Djordjevic, Beyond 240 Gb/s per wavelength optical transmission using coded hybrid subcarrier/amplitude/phase/polarization modulation, IEEE Photon. Technol. Lett. 22(5), 299–301 (2010)

    Article  Google Scholar 

  89. H.G. Batshon, I.B. Djordjevic, L. Xu, T. Wang, Modified hybrid subcarrier/amplitude/ phase/polarization LDPC-coded modulation for 400 Gb/s optical transmission and beyond, optics express, 18(13), 14108–14113 (2010)

    Google Scholar 

  90. H.G. Batshon, I.B. Djordjevic, T. Schmidt, Ultra high speed optical transmission using subcarrier-multiplexed four-dimensional LDPC-coded modulation, Optics Express, 18(19), 20546–20551 (2010)

    Article  Google Scholar 

  91. I. Djordjevic, H.G. Batshon, L. Xu, T. Wang, Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission, Opt. Express, 19(2), 876–882 (2011)

    Google Scholar 

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Acknowledgments

This work was supported in part by the National Science Foundation (NSF) under Grants CCF-0952711, ECCS-0725405 and EEC-0812072; and in part by NEC Labs.

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  1. Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ, 85721, USA

    Ivan B. Djordjevic

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Correspondence to Ivan B. Djordjevic .

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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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Djordjevic, I.B. (2011). Codes on Graphs, Coded Modulation and Compensation of Nonlinear Impairments by Turbo Equalization. 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_12

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