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Journal of Lightwave Technology

Journal of Lightwave Technology


  • Vol. 28, Iss. 4 — Feb. 15, 2010
  • pp: 662–701

Capacity Limits of Optical Fiber Networks

René-Jean Essiambre, Gerhard Kramer, Peter J. Winzer, Gerard J. Foschini, and Bernhard Goebel

Journal of Lightwave Technology, Vol. 28, Issue 4, pp. 662-701 (2010)

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We describe a method to estimate the capacity limit of fiber-optic communication systems (or “fiber channels”) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the ``fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.

© 2010 IEEE

René-Jean Essiambre, Gerhard Kramer, Peter J. Winzer, Gerard J. Foschini, and Bernhard Goebel, "Capacity Limits of Optical Fiber Networks," J. Lightwave Technol. 28, 662-701 (2010)

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  1. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379–423 and 623–656 (1948).
  2. R. G. Gallager, Information Theory and Reliable Communication (Wiley, 1968).
  3. T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, 2006).
  4. D. J. C. MacKay, Information Theory, Inference and Learning Algorithms (Cambridge Univ. Press, 2003).
  5. J. M. Wozencraft, B. Reiffen, Sequential Decoding (MIT Press and Wiley, 1961).
  6. J. Massey, "Channel models for random-access systems," NATO Advances Studies Institutes Series E142 (1988) pp. 391-402.
  7. I. Kalet, S. Shamai, "On the capacity of a twisted-wire pair: Gaussian model," IEEE Trans. Commun. 38, 379-383 (1990).
  8. J. J. Werner, "The HDSL environment," IEEE J. Sel. Areas Commun. 9, 785-800 (1991).
  9. M. Gagnaire, "An overview of broadband access technologies," Proc. IEEE 85, 1958-1972 (1997).
  10. A. Sendonaris, V. V. Veeravalli, B. Aazhang, "Joint signaling strategies for approaching the capacity of twisted-pair channels," IEEE Trans. Commun. 46, 673-685 (1998).
  11. The Communications Handbook (CRC Press, 1997).
  12. G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Tech. J. 1, 41-59 (1996).
  13. D. Tse, P. Viswanath, Fundamentals of Wireless Communication (Cambridge Univ. Press, 2005).
  14. A. Goldsmith, Wireless Communications (Cambridge Univ. Press, 2005).
  15. A. F. Molisch, Wireless Communications (Wiley, 2005).
  16. J. P. Gordon, "Quantum effects in communications systems," Proc. IRE 50, 1898-1908 (1962).
  17. J. Pierce, "Optical channels: Practical limits with photon counting," IEEE Trans. Commun. COM-26, 1819-1821 (1978).
  18. D. O. Caplan, "Laser communication transmitter and receiver design," J. Opt. Fiber Commun. Res. 4, 225-362 (2007).
  19. E. T. Whittaker, "On the functions which are represented by the expansions of the interpolation theory," Proc. R. Soc. Edinburgh 35, 181-194 (1915).
  20. H. Nyquist, "Certain topics of telegraph transmission theory," Trans. Amer. Inst. Electr. Eng. 47, 617-644 (1928).
  21. A. Jerri, "The Shannon sampling theorem—Its various extensions and applications: A tutorial review," Proc. IEEE 65, 1565-1596 (1977).
  22. J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, 1965).
  23. S. Haykin, Communication Systems (Wiley, 2001).
  24. J. G. Proakis, Digital Communications (McGraw-Hill, 2001).
  25. B. Sklar, Digital Communications (Prentice-Hall, 2001).
  26. R. G. Gallager, Principles of Digital Communication (Cambridge Univ. Press, 2008).
  27. A. Lapidoth, A Foundation in Digital Communication (Cambridge Univ. Press, 2009).
  28. J. G. Proakis, D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications (Macmillan, 2007).
  29. R. G. Lyons, Understanding Digital Signal Processing (Prentice Hall, 2004).
  30. P. Kabal, S. Pasupathy, "Partial-response signaling," IEEE Trans. Commun. COM-23, 921-934 (1975).
  31. T. Aulin, N. Rydbeck, C. E. Sundberg, "Continuous phase modulation—Part 2: Partial response signaling," IEEE Trans. Commun. COM-29, 210-225 (1981).
  32. T. Aulin, C. E. Sundberg, "Continuous phase modulation—Part 1: Full response signaling," IEEE Trans. Commun. COM-29, 196-209 (1981).
  33. J. B. Anderson, T. Aulin, C. E. Sundberg, Digital Phase Modulation (Plenum, 1986).
  34. A. Lender, "Correlative level coding for binary data transmission," IEEE Spectrum 3, 104-115 (1966).
  35. J. L. Massey, "The how and why of channel coding," Proc. Int. Zurich Semin. (1984) pp. 67-73.
  36. S. Pasupathy, "Minimum shift keying: A spectrally efficient modulation," IEEE Commun. Mag. 17, 14-22 (1979).
  37. J. Massey, "A generalized formulation of minimum shift keying modulation," Proc. IEEE Int. Conf. Commun. (1980) pp. 26.5.1-26.5.4.
  38. B. E. Rimoldi, "A decomposition approach to CPM," IEEE Trans. Inf. Theory 34, 260-270 (1988).
  39. J. G. Proakis, M. Salehi, Digital Communications (McGraw-Hill, 2007).
  40. S. Lin, D. J. Costello, Error Control Coding (Prentice-Hall, 2004).
  41. R. H. Walden, "Performance trends for analog to digital converters," IEEE Commun. Mag. 37, 96-101 (1999).
  42. R. H. Walden, "Analog-to-digital converter survey and analysis," IEEE J. Sel. Areas Commun. 17, 539-550 (1999).
  43. R. H. Walden, "Analog-to-digital converters and associated IC technologies," Proc. IEEE Compound Semicond. Integr. Circuits Symp. (2008) pp. 1-2.
  44. R. M. Gray, Source Coding Theory (Springer-Verlag, 1989).
  45. M. Bayes, M. Price, "An essay towards solving a problem in the doctrine of chances," Philos. Trans. R. Soc. Lond. 53, 370-418 (1763).
  46. A. Papoulis, S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).
  47. G. Kramer, A. Ashikhmin, A. J. van Wijngaarden, X. Wei, "Spectral efficiency of coded phase-shift keying for fiber-optic communication," J. Lightw. Technol. 21, 2438-2445 (2003).
  48. J. Hancock, R. Lucky, "Performance of combined amplitude and phase-modulated communication systems," Commun. Syst., IRE Trans. 8, 232-237 (1960).
  49. J. M. Geist, "Capacity and cutoff rate for dense M-ary PSK constellations," Proc. IEEE Mil. Commun. Conf. Record (1990) pp. 768-770.
  50. P. J. Winzer, R. J. Essiambre, "Advanced optical modulation formats," Proc. IEEE 94, 952-985 (2006).
  51. P. J. Winzer, R.-J. Essiambre, Optical Fiber Telecommunications VB (Academic, 2008) pp. 232-304.
  52. F. Gray, Pulse Code Communication U.S. Patent 2 632 058 (1953).
  53. S. Verdú, "Spectral efficiency in the wideband regime," IEEE Trans. Inf. Theory 48, 1319-1343 (2002).
  54. R. Tkach, "Scaling optical communications for the next decade and beyond," Bell Labs Tech. J. 14, 3-9 (2010).
  55. J. B. Stark, "Fundamental limits of information capacity for optical communications channels," Proc. Eur. Conf. Opt. Commun. (1999) pp. I-28.
  56. E. Desurvire, "A quantum model for optically amplified nonlinear transmission systems," Opt. Fiber Technol. 8, 210-230 (2002).
  57. E. Desurvire, "A common quantum noise model for optical amplification and nonlinearity in WDM transmission," Proc. Eur. Conf. Opt. Commun. (2002) pp. Tu3.1.1.
  58. E. Desurvire, Classical and Quantum Information Theory (Cambridge Univ. Press, 2009).
  59. J. Tang, "The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission," J. Lightw. Technol. 19, 1104-1109 (2001).
  60. P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).
  61. E. Narimanov, P. P. Mitra, "The channel capacity of a fiber optics communication system: Perturbation theory," J. Lightw. Technol. 20, 530-537 (2002).
  62. J. Tang, "The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and an ideal coherent optical receiver," J. Lightw. Technol. 20, 1095-1101 (2002).
  63. K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, S. K. Turitsyn, "Information capacity of optical fiber channels with zero average dispersion," Phys. Rev. Lett. 91, (2003) Paper 203901.
  64. L. G. L. Wegener, M. L. Povinelli, A. G. Green, P. P. Mitra, J. B. Stark, P. B. Littlewood, "The effect of propagation nonlinearities on the information capacity of WDM optical fiber systems: Cross-phase modulation and four-wave mixing," Physica D 189, 81-99 (2004).
  65. M. H. Taghavi, G. C. Papen, P. H. Siegel, "On the multiuser capacity of WDM in a nonlinear optical fiber: Coherent communication," IEEE Trans. Inf. Theory 52, 5008-5022 (2006).
  66. K.-P. Ho, "Channel capacity of WDM systems using constant-intensity modulation formats," Proc. Opt. Fiber Commun. Conf. (2002) pp. 731-733.
  67. I. Djordjevic, B. Vasic, M. Ivkovic, I. Gabitov, "Achievable information rates for high-speed long-haul optical transmission," J. Lightw. Technol. 23, 3755-3763 (2005).
  68. M. Ivkovic, I. Djordjevic, B. Vasic, "Calculation of achievable information rates of long-haul optical transmission systems using instanton approach," J. Lightw. Technol. 25, 1163-1168 (2007).
  69. I. Djordjevic, L. Xu, T. Wang, "On the channel capacity of multilevel modulation schemes with coherent detection," Proc. Asia Commun. Photon. Conf. Exhib. (2009) pp. ThC4.
  70. I. Djordjevic, "Ultimate information capacity of fiber optic networks," SPIE Photon. West , 7619-7621 (2010).
  71. R.-J. Essiambre, G. J. Foschini, P. J. Winzer, G. Kramer, E. C. Burrows, "The capacity of fiber-optic communication systems," Proc. Opt. Fiber Commun. Conf. (2008) pp. OTuE1.
  72. R.-J. Essiambre, G. J. Foschini, G. Kramer, P. J. Winzer, "Capacity limits of information transport in fiber-optic networks," Phys. Rev. Lett. 101, (2008) Paper 163901.
  73. R.-J. Essiambre, G. J. Foschini, P. J. Winzer, G. Kramer, "Exploring capacity limits of fibre-optic communication systems," Proc. Eur. Conf. Opt. Commun. (2008).
  74. R.-J. Essiambre, G. Kramer, G. J. Foschini, P. J. Winzer, "High spectral efficiency modulation for high capacity transmission," Proc. IEEE/LEOS Summer Top. Meet. 113-114 (2008).
  75. R.-J. Essiambre, G. J. Foschini, P. J. Winzer, G. Kramer, "Capacity limits of fiber-optic communication systems," Proc. Opt. Fiber Commun. Conf. (2009).
  76. H. Haunstein, M. Mayrock, "OFDM spectral efficiency limits from fiber and system non-linearities," Proc. Opt. Fiber Commun. Conf. (2010).
  77. O. A. Sab, V. Lemaire, "Block turbo code performances for longhaul DWDM optical transmission systems," Proc. Opt. Fiber Commun. Conf. (2000) pp. 280-282.
  78. T. Mizuochi, "Recent progress in forward error correction and its interplay with transmission impairments," IEEE J. Sel. Topics Quantum Electron. 12, 544-554 (2006).
  79. T. Mizuochi, "Next generation FEC for optical communication," Proc. Opt. Fiber Commun. Conf. (2008).
  80. D. F. Grosz, A. Agarwal, S. Banerjee, D. N. Maywar, A. P. Küng, "All-Raman ultralong-haul single-wideband DWDM transmission systems with OADM capability," J. Lightw. Technol. 22, 423-432 (2004).
  81. S. Radic, N. Vukovic, S. Chandrasekhar, A. Velingker, A. Srivastava, "Forward error correction performance in the presence of rayleigh-dominated transmission noise," IEEE Photon. Technol. Lett. 15, 326-328 (2003).
  82. P. J. Winzer, M. Pfennigbauer, R.-J. Essiambre, "Coherent crosstalk in ultradense WDM systems," J. Lightw. Technol. 23, 1734-1744 (2005).
  83. R.-J. Essiambre, P. J. Winzer, "Fibre nonlinearities in electronicaly pre-distorted transmission," Proc. European Conf. Opt. Commun. (2005).
  84. R.-J. Essiambre, P. J. Winzer, X. Q. Wang, W. Lee, C. A. White, E. C. Burrows, "Electronic predistortion and fiber nonlinearity," IEEE Photon. Technol. Lett. 18, 1804-1806 (2006).
  85. P. J. Winzer, "Modulation and multiplexing in optical communication systems," LEOS Newsletter (2009) http://www.ieee.org/organizations/pubs/newsletters/leos/feb09/index.html.
  86. P. J. Winzer, G. Raybon, C. R. Doerr, M. Duelk, C. Dorrer, "107-Gb/s optical signal generation using electronic time-division multiplexing," J. Lightw. Technol. 24, 3107-3113 (2006).
  87. T. Itoi, K. Fukuchi, T. Kasamatsu, "Enabling technologies for 10 Tb/s transmission capacity and beyond," Proc. Eur. Conf. Opt. Commun. (2001) pp. 598-601.
  88. F. Boubal, E. Brandon, L. Buet, S. Chernikov, V. Havard, A. Heerdt, C. , Hugbart, W. Idler, L. Labrunie, P. Le Roux, S. A. E. Lewis, A. Pham, L. Piriou, R. Uhel, J.-P. Blondel, "Wideband and ultra-dense WDM transmission technologies toward over 10-Tb/s capacity," Proc. Eur. Conf. Opt. Commun. (2001) pp. 58-59.
  89. K. Fukuchi, "Wideband and ultra-dense WDM transmission technologies toward over 10-Tb/s capacity," Proc. Opt. Fiber Commun. Conf. (OFC) (2002) pp. 558-559.
  90. Optical Fiber Telecommunications V ${\rm A}+{\rm B}$ (Academic, 2008).
  91. A. R. Chraplyvy, "Limitations on lightwave communications imposed by optical-fiber nonlinearities," J. Lightw. Technol. 8, 1548-1557 (1990).
  92. I. P. Kaminow, C. R. Doerr, C. Dragone, T. Koch, U. Koren, A. A. M. Saleh, A. J. Kirby, C. M. Özveren, B. Schofield, R. E. Thomas, R. A. Bany, D. M. Castagnozzi, V. W. S. Chan, B. R. Hemenway, D. Marquis, S. A. Parikh, M. L. Stevens, E. A. Swanson, S. G. Finn, R. G. Gallager, "A wideband all-optical WDM network," IEEE J. Sel. Areas Commun. 14, 780-799 (1996).
  93. E. E. B. Basch, R. Egorov, S. Gringeri, S. Elby, "Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems," IEEE J. Select. Topics Quantum Electron. 12, 615-626 (2006).
  94. R. Ramaswami, K. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, 2001).
  95. B. Mukherjee, Optical WDM Networks (Springer-Verlag, 2006).
  96. J. Simmons, Optical Network Design and Planning (Springer-Verlag, 2008).
  97. R.-J. Essiambre, B. Mikkelsen, G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," IEE Electron. Lett. 35, 1576-1578 (1999).
  98. R.-J. Essiambre, G. Raybon, B. Mikkelsen, Optical Fiber Telecommunications IV (Academic, 2002) pp. 232-304.
  99. M. van Deventer, Fundamentals of Bidirectional Transmission Over a Single Optical Fibre (Kluwer, 1996).
  100. C. Kim, Y. Chung, "2.5 Gb/s$\,\times\,$16-channel bidirectional WDM transmission system using bidirectional erbium-doped fiber amplifier based on spectrally interleaved synchronized etalon filters," IEEE Photon. Technol. Lett. 11, 745-747 (1999).
  101. S. Radic, S. Chandrasekhar, "Limitations in dense bidirectional transmission in absence of optical amplification," IEEE Photon. Technol. Lett. 14, 95-97 (2002).
  102. S. Radic, S. Chandrasekhar, P. Bernasconi, J. Centanni, C. Abraham, N. Copner, K. Tan, "Feasibility of hybrid Raman/EDFA amplification in bidirectional optical transmission," IEEE Photon. Technol. Lett. 14, 221-223 (2002).
  103. J. Ko, S. Kim, J. Lee, S. Won, Y. Kim, J. Jeong, "Estimation of performance degradation of bidirectional WDM transmission systems due to Rayleigh backscattering and ASE noises using numerical and analytical models," J. Lightw. Technol. 21, 938-946 (2003).
  104. P. J. Winzer, Wiley Encyclopedia of Telecommunications (Wiley, 2002) pp. 1824-1840.
  105. G. Einarsson, Principles of Lightwave Communications (Wiley, 1996).
  106. P. Henry, "Error-rate performance of optical amplifiers," Proc. Opt. Fiber Commun. Conf. (1989).
  107. D. Marcuse, "Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers," J. Lightw. Technol. 8, 1816-1823 (1990).
  108. J. Lee, C. Shim, "Bit-error-rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain," J. Lightw. Technol. 12, 1224-1229 (1994).
  109. P. J. Winzer, "Performance estimation of receivers corrupted by optical noise," Proc. Opt. Amplifiers Appl. 60, 268-273 (2001).
  110. T. Li, M. Teich, "Bit-error rate for a lightwave communication system incorporating an erbium-doped fibre amplifier," IEE Electron. Lett. 27, 598-600 (1991).
  111. P. J. Winzer, S. Chandrasekhar, H. Kim, "Impact of filtering on RZ-DPSK reception," IEEE Photon. Technol. Lett. 15, 840-842 (2003).
  112. A. H. Gnauck, P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightw. Technol. 23, 115-130 (2005).
  113. X. Liu, S. Chandrasekhar, A. Leven, Optical Fiber Telecommunications VB (Academic, 2008) pp. 131-178.
  114. W. Schottky, "Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern," Annalen der Physik 57, 541-567 (1918).
  115. J. Pierce, "Physical sources of noise," Proc. IRE 44, 601-608 (1956).
  116. H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer-Verlag, 2000).
  117. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 2007).
  118. B. E. A. Saleh, Photoelectron Statistics: With Applications to Spectroscopy and Optical Communication (Springer-Verlag, 1978).
  119. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).
  120. P. J. Winzer, "Linking equations between photon statistics and photocurrent statistics for time-varying stochastic photon rates," Quantum Semiclass. Opt.: J. Eur. Opt. Soc. Part B 10, 643-655 (1998).
  121. E. Säckinger, Broadband Circuits for Optical Fiber Communication (Wiley, 2005).
  122. S. Alexander, Optical Communication Receiver Design (Institution of Engineering and Technology, 1997).
  123. A. Einstein, "On the quantum theory of radiation," Phys. Zeits. 18, 121 (1917).
  124. C. W. Gardiner, P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods With Applications to Quantum Optics (Springer-Verlag, 2004).
  125. E. Desurvire, D. Bayart, B. Desthieux, S. Bigo, Erbium-Doped Fiber Amplifiers and Device and System Developments (Wiley, 2002).
  126. P. Diament, M. C. Teich, "Evolution of the statistical properties of photons passed through a traveling-wave laser amplifier," IEEE J. Quantum Electron. 28, 1325-1334 (1992).
  127. T. Li, M. C. Teich, "Photon point process for traveling-wave laser amplifiers," IEEE J. Quantum Electron. 29, 2568-2578 (1993).
  128. J. P. Gordon, W. H. Louisell, L. R. Walker, "Quantum fluctuations and noise in parametric processes II," Phys. Rev. 129, 481-485 (1963).
  129. J. P. Gordon, L. R. Walker, W. H. Louisell, "Quantum statistics of masers and attenuators," Phys. Rev. 130, 806-812 (1963).
  130. J. R. Barry, D. G. Messerschmitt, E. A. Lee, Digital Communication (Springer-Verlag, 2003).
  131. A. Mecozzi, "Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers," J. Lightw. Technol. 12, 1993-2000 (1994).
  132. C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Science (Springer-Verlag, 2004).
  133. P. C. Becker, N. A. Olsson, J. R. Simpson, Erbium-Doped Fiber Amplifiers, Fundamentals and Technology (Academic, 1999).
  134. A. Bjarklev, Optical Fiber Amplifiers: Design and System Applications (Artech House, 1993).
  135. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1999).
  136. R. H. Stolen, E. P. Ippen, "Raman gain in glass optical waveguides," Appl. Phys. Lett. 22, 276-278 (1973).
  137. J. Bromage, "Raman amplification for fiber communications systems," J. Lightw. Technol. 22, 79-93 (2004).
  138. V. E. Perlin, H. G. Winful, "On trade-off between noise and nonlinearity in WDM systems with distributed Raman amplification," Proc. Opt. Fiber Commun. Conf. (OFC) (2002) pp. 178-180.
  139. V. E. Perlin, H. G. Winful, "Optimizing the noise performance of broadband WDM systems with distributed Raman amplification," IEEE Photon. Technol. Lett. 14, 1199-1201 (2002).
  140. L. F. Mollenauer, J. P. Gordon, Solitons in Optical Fibers: Fundamentals and Applications (Academic, 2006).
  141. J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
  142. T. J. Ellingham, J. D. Ania-Castanón, R. Ibbotson, X. Chen, L. Zhang, S. K. Turitsyn, "Quasi-lossless optical links for broadband transmission and data processing," IEEE Photon. Technol. Lett. 18, 268-270 (2006).
  143. P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, D. J. DiGiovanni, "Rayleigh scattering limitations in distributed Raman pre-amplifiers," 343-345 (1997).
  144. S. A. E. Lewis, S. V. Chernikov, J. R. Taylor, "Characterization of double Rayleigh scatter noise in Raman amplifiers," IEEE Photon. Technol. Lett. 12, 528-530 (2000).
  145. R. Boyd, Nonlinear Optics (Academic, 2008).
  146. J. Bromage, P. J. Winzer, R.-J. Essiambre, Raman Amplifiers and Oscillators in Telecommunications (Springer-Verlag, 2003).
  147. M. Nissov, K. Rottwitt, H. Kidorf, M. Ma, "Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers," IEE Electron. Lett. 35, 997-998 (1999).
  148. G. P. Agrawal, Lightwave Technology: Components and Devices (Wiley, 2004).
  149. D. Gloge, "Dispersion in weakly guiding fibers," Appl. Opt. 10, 2442-2445 (1971).
  150. Optical-Fiber Transmission (Sams Technical Publishing, 1986).
  151. Optical Fiber Telecommunications II (Academic, 1988).
  152. Y. Akasaka, R. Sugizaki, A. Umeda, T. Kamiya, F. Ltd, J. Chiba, "High-dispersion-compensation ability and low nonlinearity of w-shaped DCF," Proc. Opt. Fiber Commun. Conf. (1996) pp. 201-202.
  153. A. Vengsarkar, "Dispersion compensating fibers," Proc. Opt. Fiber Commun. Conf. (1997) pp. 233-234.
  154. L. Grüner-Nielsen, S. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. Larsen, H. Damsgaard, "Dispersion compensating fibers," Opt. Fiber Technol. 6, 164-180 (2000).
  155. L. Grüner-Nielsen, M. Wandel, P. Kristensen, C. Jørgensen, L. Jørgensen, B. Edvold, B. Pálsdóttir, D. Jakobsen, "Dispersion-compensating fibers," J. Lightw. Technol. 23, 3566-3579 (2005).
  156. M. Nishimura, "Optical fibers and fiber dispersion compensators for high-speed optical communication," J. Opt. Fiber Commun. Rep. 2, 115-139 (2005).
  157. P. Nouchi, L. de Montmorillon, P. Sillard, A. Bertaina, "Advance in long-haul fibers," Proc. Opt. Fiber Commun. Conf. (OFC) (2003) pp. 154-155.
  158. G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2006).
  159. R. Lundin, "Dispersion flattening in a w fiber," Appl. Opt. 33, 1011-1014 (1994).
  160. D. Marcuse, "Single-channel operation in very long nonlinear fibers with optical amplifiers at zero dispersion," J. Lightw. Technol. 9, 356-361 (1991).
  161. D. Marcuse, A. R. Chraplyvy, R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightw. Technol. 9, 121-128 (1991).
  162. L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
  163. S. Haykin, Adaptive Filter Theory (Prentice-hall, 2002).
  164. A. Sayed, Fundamentals of Adaptive Filtering (Wiley, 2003).
  165. J. Kerr, "A new relation between electricity and light: Dielectrified media birefringent," Phil. Mag. 50, 3337 (1875).
  166. G. P. Agrawal, Lightwave Technology: Telecommunication Systems (Wiley, 2005).
  167. E. Ippen, R. Stolen, "Stimulated Brillouin scattering in optical fibers," Appl. Phys. Lett. 21, 539-541 (1972).
  168. R. Smith, "Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering," Appl. Opt. 11, 2489-2494 (1972).
  169. R. H. Stolen, Optical Fiber Telecommunications (Academic, 1979) pp. 125-150.
  170. A. R. Chraplyvy, P. S. Henry, "Performance degradation due to stimulated Raman scattering in wavelength-division-multiplexed optical-fibre systems," IEE Electron. Lett. 19, 641-642 (1983).
  171. R. Tkach, A. Chraplyvy, R. Derosier, "Spontaneous Brillouin scattering for single-mode optical-fibre characterisation," IEE Electron. Lett. 22, 1011-1013 (1986).
  172. N. Bloembergen, "The stimulated Raman effect," Amer. J. Phys. 35, 989-1023 (1967).
  173. R. Hellwarth, J. Cherlow, T. T. Yang, "Origin and frequency dependence of nonlinear optical susceptibilities of glasses," Phys. Rev. B 11, 964-967 (1975).
  174. R. Stolen, "Nonlinearity in fiber transmission," Proc. IEEE 68, 1232-1236 (1980).
  175. R. Stolen, J. Gordon, W. Tomlinson, H. Haus, "Raman response function of silica-core fibers," J. Opt. Soc. Amer. B 6, 1159-1166 (1989).
  176. K. Blow, D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989).
  177. P. Mamyshev, S. Chernikov, "Ultrashort-pulse propagation in optical fibers," 15, 1076-1078 (1990).
  178. S. Chernikov, P. Mamyshev, "Femtosecond soliton propagation in fibers with slowly decreasing dispersion," J. Opt. Soc. Am. B 8, 1633-1641 (1991).
  179. L. Eskildsen, P. Hansen, P. Koren, B. Miller, M. Young, K. Dreyer, "Stimulated Brillouin scattering suppression with low residual AM using a novel temperature wavelength-dithered DFB laser diode," IEE Electron. Lett. 32, 1387-1389 (1996).
  180. M. Van Deventer, A. Boot, "Polarization properties of stimulated Brillouin scattering insingle-mode fibers," J. Lightw. Technol. 12, 585-590 (1994).
  181. D. Christodoulides, R. Jander, "Evolution of stimulated Raman crosstalk in wavelength division multiplexed systems," IEEE Photon. Technol. Lett. 8, 1722-1724 (1996).
  182. M. Zirngibl, "Analytical model of Raman gain effects in massive wavelength division multiplexed transmission systems," IEE Electron. Lett. 34, 789-790 (1998).
  183. A. Chraplyvy, J. Nagel, R. Tkach, "Equalization in amplified WDM lightwave transmission systems," IEEE Photon. Technol. Lett. 4, 920-922 (1992).
  184. A. Tomita, "Cross talk caused by stimulated Raman scattering in singlemode wavelength-division multiplexed systems," Opt. Lett. 8, 412-414 (1983).
  185. W. Jiang, P. Ye, "Crosstalk in fiber Raman amplification for WDM systems," J. Lightw. Technol. 7, 1407-1411 (1989).
  186. F. Forghieri, R. W. Tkach, A. R. Chraplyvy, "Effect of modulation statistics on Raman crosstalk in WDM systems," IEEE Photon. Technol. Lett. 7, 101-103 (1995).
  187. Raman Amplifiers for Telecommunications 1: Physical Principles (Springer-Verlag, 2004).
  188. C. Headley, G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Academic, 2005).
  189. R.-J. Essiambre, P. J. Winzer, J. Bromage, C. H. Kim, "Design of bidirectionally pumped fiber amplifiers generating double Rayleigh backscattering," IEEE Photon. Technol. Lett. 14, 914-916 (2002).
  190. H. A. Haus, "The noise figure of optical amplifiers," IEEE Photon. Technol. Lett. 10, 1602-1604 (1998).
  191. H. J. Landau, "On the recovery of a band-limited signal, after instantaneous companding and subsequent band limiting," Bell Syst. Tech. J. 39, 351-364 (1960).
  192. H. J. Landau, W. L. Miranker, "The recovery of distorted bandlimited signals," J. Math Anal. Appl. 2, 97-104 (1961).
  193. S. Bigo, "Modelling of WDM terrestrial and submarine links for the design of WDM networks," Proc. Opt. Fiber Commun. Conf. (2006).
  194. A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445-447 (2001).
  195. T. Freckmann, R.-J. Essiambre, P. J. Winzer, G. J. Foschini, G. Kramer, "Fiber capacity limits with optimized ring constellations," IEEE Photon. Technol. Lett. 21, 1496-1498 (2009).
  196. M. Eiselt, "Does spectrally periodic dispersion compensation reduce non-linear effects?," Proc. European Conf. Opt. Commun. (1999) pp. 144-145.
  197. G. Bellotti, S. Bigo, "Cross-phase modulation suppressor for multispan dispersion-managed WDM transmissions," IEEE Photon. Technol. Lett. 12, 726-728 (2000).
  198. G. Bellotti, S. Bigo, S. Gauchard, P. Cortes, S. LaRochelle, "10$\,\times\,$10 gb/s cross-phase modulation suppressor using WDM narrowband fiber Bragg gratings," IEEE Photon. Technol. Lett. 12, 1403-1405 (2000).
  199. C. Xie, "Suppression of inter-channel nonlinearities in WDM coherent PDM-QPSK systems using periodic-group-delay dispersion compensators," Proc. Eur. Conf. Opt. Commun. (ECOC) (2009) pp. Paper P4.08.
  200. J. Yu, X. Zhou, M.-F. Huang, Y. Shao, D. Qian, T. Wang, M. Cvijetic, P. Magill, L. Nelson, M. Birk, S. Ten, H. B. Matthew, S. K. Mishra, "17 Tb/s (161 114 Gb/s) PolMux-RZ-8PSK transmission over 662 km of ultra-low loss fiber using C-band EDFA amplification and digital coherent detection," Proc. Eur. Conf. Opt. Commun. (ECOC) (2008).
  201. H. Takahashi, A. A. Amin, S. L. Jansen, I. Morita, H. Tanaka, "8$\,\times\,$66.8-Gbit/s coherent PDM-OFDM transmission over 640 km of SSMF at 5.6-bit/s/Hz spectral efficiency," Proc. Eur. Conf. Opt. Commun. (ECOC) (2008).
  202. P. J. Winzer, A. H. Gnauck, "112-Gb/s polarization-multiplexed 16-QAM on a 25-GHz WDM grid," Proc. Eur. Conf. Opt. Commun. (ECOC) (2008).
  203. H. Takahashi, A. A. Amin, S. L. Jansen, I. Morita, H. Tanaka, "DWDM transmission with 7.0 bit/s/Hz spectral efficiency using 8$\,\times\,$65.1 Gbit/s coherent PDM OFDM signals," Proc. Opt. Fiber Commun. Conf. (OFC) (2009).
  204. A. H. Gnauck, P. J. Winzer, C. R. Doerr, L. L. Buhl, "10 112-Gb/s PDm 16-QAM transmission over 630 km of fiber with 6.2-b/s/Hz spectral efficiency," Proc. Opt. Fiber Commun. Conf. (OFC) (2009).
  205. P. J. Winzer, A. Kalmar, "Sensitivity enhancement of optical receivers by impulsive coding," J. Lightw. Technol. 17, 171-177 (1999).
  206. N. A. Olsson, "Lightwave systems with optical amplifiers," J. Lightw. Technol. 7, 1071-1082 (1989).
  207. J. Forney, Jr., G. D. , L.-F. Wei, "Multidimensional constellations—Part 1: Introduction, figures of merit, and generalized cross constellations," IEEE J. Sel. Areas Commun. 7, 877-892 (1989).
  208. G. D. Forney, Jr.G. Ungerboeck, "Modulation and coding for linear Gaussian channels," IEEE Trans. Inf. Theory 44, 2384-2415 (1998).
  209. B. W. Kernighan, S. Lin, "Heuristic solution of a signal design optimization problem," Bell Syst. Tech. J. 52, 1145-1159 (1973).
  210. G. F. Foschini, R. D. Gitlin, S. B. Weinstein, "Optimization of two dimensional signal constellations in the presence of Gaussian noise," IEEE Trans. Commun. 22, 28-38 (1974).
  211. G. D. Forney, Jr.R. G. Gallager, G. R. Lang, F. M. Longstaff, S. U. Qureshi, "Efficient modulation for band-limited channels," IEEE J. Sel. Areas Commun. SAC-2, 632-647 (1984).
  212. L. Hanzo, W. Webb, T. Keller, Single- and Multi-Carrier Quadrature Amplitude Modulation (Wiley, 2000).
  213. J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer-Verlag, 1993).

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