Abstract

We demonstrate data rates above the threshold imposed by nonlinearity on conventional optical signals by applying novel probability distribution, which we call ripple distribution, adapted to the properties of the fiber channel. Our results offer a new direction for signal coding, modulation and practical nonlinear distortions compensation algorithms.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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  1. A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” Tech. Digest of European Conference on Optical Communication paper MoC2.4. (1993).
  2. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027–1030 (2001).
    [Crossref] [PubMed]
  3. R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
    [Crossref] [PubMed]
  4. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
    [Crossref]
  5. E. E. Narimanov and P. Mitra, “The channel capacity of a fiber optics communication system: perturbation theory,” J. Lightwave Technol. 20(3), 530–537 (2002).
    [Crossref]
  6. D. J. Richardson, “Filling the light pipe,” Science 330, 327–328 (2010).
    [Crossref] [PubMed]
  7. E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
    [Crossref] [PubMed]
  8. P. J. Winzer, “Scaling optical fiber networks: challenges and solutions,” Optics and Photonics News,  26, 28–35 (2015).
    [Crossref]
  9. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
    [Crossref]
  10. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
    [Crossref]
  11. I. B. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. Optical Fiber Communication Conference, Los Angeles, CA, Mar. 2010, p. OMK2
  12. T. Fehenberger, A. Alvarado Segovia, G. Bocherer, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett. 28(7) 786–789 (2016).
    [Crossref]
  13. C. Pan and F. R. Kschischang, “Probabilistic 16-QAM Shaping in WDM Systems,” Journal of Lightwave Technology (in press).
  14. F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
    [Crossref]
  15. E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightwave Technol. 32(16), 2862–2876 (2014).
    [Crossref]
  16. M. Sorokina, A. Ellis, and S. Turitsyn, “Optical information capacity processing,” chapter in All-Optical Signal Processing325–354 (2015).
  17. E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiberoptic channels: A primer,” IEEE Information Theory Workshop (2015).
  18. M. H. Taghavi, G. C. Papen, and P.H. Siegel, “On the multiuser capacity of WDM in a nonlinear optical fiber: coherent communication,” IEEE Trans. Inf. Theory, 52(11), 5008–5022 (2006).
    [Crossref]
  19. H. Song and M. Brandt-Pearce, “A 2-D discrete-time model of physical impairments in wavelength-division multiplexing systems,” J. Lightwave Technol. 30(5), 713–726 (2012).
    [Crossref]
  20. R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Optics Letters 39, 398–401 (2014).
    [Crossref] [PubMed]
  21. Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
    [Crossref]
  22. M. Secondini and E. Forestieri, “Scope and limitations of the nonlinear Shannon limit,” online version of 24.10.2016 http://ieeexplore.ieee.org/document/7637002/ .
  23. M. Secondini, chapter in “Roadmap of optical communications,” by E. Agrell et al. Journal of Optics 18 (6), 063002 (2016).
    [Crossref]
  24. M. Sorokina, S. Sygletos, and S. K. Turitsyn, “Shannon capacity of nonlinear communication channels,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper SM3F.4.
  25. M. Sorokina, S. Sygletos, and S. K. Turitsyn, “Ripple distribution for nonlinear fiber-optic channels,” https://arxiv.org/abs/1610.06937
  26. P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
    [Crossref]
  27. M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightwave Technol. 31(23), 3839–3852 (2013).
    [Crossref]
  28. L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60(11), 3440–3450 (2012).
    [Crossref]
  29. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express 21(22), 25685–25699 (2013).
    [Crossref] [PubMed]
  30. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: modeling and mitigation,” J. Lightwave Technol. 33(5), 1044–1053 (2015).
    [Crossref]
  31. M. Shtaif, R. Dar, A. Mecozzi, and M. Feder, “Nonlinear interference noise in WDM systems and approaches for its cancelation,” in Optical Communication (ECOC 2014), 39th European Conference and Exhibition on Optical Communications, paper We1.3.1.
  32. K. S. Turitsyn, S.A. Derevyanko, I.V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Letters 91, 203901 (2003).
    [Crossref]
  33. M. Secondini, E. Forestieri, and C. R. Menyuk, “A combined regular-logarithmic perturbation method for signal-noise interaction in amplified optical systems”, J. Lightwave Technol. 27(16), 3358–3369 (2009).
    [Crossref]
  34. K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers”, J. Lightwave Technol. 15(12), 2232–2241 (1997).
    [Crossref]
  35. M. Schetzen, “The Volterra and Wiener theories of nonlinear systems”. (Krieger, 2006).
  36. A. Amari, P. Ciblat, and Y. Jaouen, “Fifth-order Volterra series based nonlinear equalizer for long-haul high data rate optical fiber communications,” Asilomar Conference ACSSC (2014).
  37. M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method,” Opt. Express 24(26), 30433–30443 (2016).
    [Crossref]
  38. Z. Li, W.-R. Peng, F. Zhu, and Y. Bai, “Optimum quantization of perturbation coefficients for perturbative fiber nonlinearity mitigation,” Tech. Digest of European Conference on Optical Communication paper We.1.3.4. (2014).
  39. A. Ghazisaeidi and R.-J. Essiambre, “Calculation of coefficients of perturbative nonlinear pre-compensation for Nyquist pulses,” Tech. Digest of European Conference on Optical Communication paper We.1.3.3. (2014).
  40. S. Verdu and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory 40(4) 1147–1157 (1994).
    [Crossref]
  41. B. Picinbono, “Second-order complex random vectors and normal distributions,” IEEE Transactions on Signal Processing 442637–2640 (1996).
    [Crossref]
  42. E. Agrell and M. Karlsson, “Satellite constellations: towards the nonlinear channel capacity,” 25th IEEE Photonics Conference pp. 316–317 (2012).
  43. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA, July 2014.
  44. D. Rafique and A. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011).
    [Crossref] [PubMed]
  45. M. A. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
    [Crossref] [PubMed]
  46. T. Freckmann, R. J. Essiambre, P. J. Winzer, G. J. Foschini, and G. Kramer, “Fiber capacity limits with optimized ring constellations,” IEEE Photonics Technology Letters 21(20), 1496–1498 (2009).
    [Crossref]

2016 (4)

T. Fehenberger, A. Alvarado Segovia, G. Bocherer, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett. 28(7) 786–789 (2016).
[Crossref]

M. Secondini, chapter in “Roadmap of optical communications,” by E. Agrell et al. Journal of Optics 18 (6), 063002 (2016).
[Crossref]

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method,” Opt. Express 24(26), 30433–30443 (2016).
[Crossref]

2015 (4)

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: modeling and mitigation,” J. Lightwave Technol. 33(5), 1044–1053 (2015).
[Crossref]

Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
[Crossref]

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

P. J. Winzer, “Scaling optical fiber networks: challenges and solutions,” Optics and Photonics News,  26, 28–35 (2015).
[Crossref]

2014 (3)

R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Optics Letters 39, 398–401 (2014).
[Crossref] [PubMed]

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightwave Technol. 32(16), 2862–2876 (2014).
[Crossref]

M. A. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (2)

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60(11), 3440–3450 (2012).
[Crossref]

H. Song and M. Brandt-Pearce, “A 2-D discrete-time model of physical impairments in wavelength-division multiplexing systems,” J. Lightwave Technol. 30(5), 713–726 (2012).
[Crossref]

2011 (2)

D. Rafique and A. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011).
[Crossref] [PubMed]

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[Crossref]

2010 (2)

2009 (2)

M. Secondini, E. Forestieri, and C. R. Menyuk, “A combined regular-logarithmic perturbation method for signal-noise interaction in amplified optical systems”, J. Lightwave Technol. 27(16), 3358–3369 (2009).
[Crossref]

T. Freckmann, R. J. Essiambre, P. J. Winzer, G. J. Foschini, and G. Kramer, “Fiber capacity limits with optimized ring constellations,” IEEE Photonics Technology Letters 21(20), 1496–1498 (2009).
[Crossref]

2008 (1)

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[Crossref] [PubMed]

2006 (1)

M. H. Taghavi, G. C. Papen, and P.H. Siegel, “On the multiuser capacity of WDM in a nonlinear optical fiber: coherent communication,” IEEE Trans. Inf. Theory, 52(11), 5008–5022 (2006).
[Crossref]

2003 (1)

K. S. Turitsyn, S.A. Derevyanko, I.V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Letters 91, 203901 (2003).
[Crossref]

2002 (1)

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027–1030 (2001).
[Crossref] [PubMed]

1997 (1)

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers”, J. Lightwave Technol. 15(12), 2232–2241 (1997).
[Crossref]

1996 (1)

B. Picinbono, “Second-order complex random vectors and normal distributions,” IEEE Transactions on Signal Processing 442637–2640 (1996).
[Crossref]

1994 (1)

S. Verdu and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory 40(4) 1147–1157 (1994).
[Crossref]

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[Crossref]

Agrell, E.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightwave Technol. 32(16), 2862–2876 (2014).
[Crossref]

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60(11), 3440–3450 (2012).
[Crossref]

E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiberoptic channels: A primer,” IEEE Information Theory Workshop (2015).

E. Agrell and M. Karlsson, “Satellite constellations: towards the nonlinear channel capacity,” 25th IEEE Photonics Conference pp. 316–317 (2012).

Alic, N.

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

Alvarado, A.

Alvarado Segovia, A.

T. Fehenberger, A. Alvarado Segovia, G. Bocherer, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett. 28(7) 786–789 (2016).
[Crossref]

Amari, A.

A. Amari, P. Ciblat, and Y. Jaouen, “Fifth-order Volterra series based nonlinear equalizer for long-haul high data rate optical fiber communications,” Asilomar Conference ACSSC (2014).

Ataie, V.

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

Bai, Y.

Z. Li, W.-R. Peng, F. Zhu, and Y. Bai, “Optimum quantization of perturbation coefficients for perturbative fiber nonlinearity mitigation,” Tech. Digest of European Conference on Optical Communication paper We.1.3.4. (2014).

Batshon, H. G.

I. B. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. Optical Fiber Communication Conference, Los Angeles, CA, Mar. 2010, p. OMK2

Beygi, L.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60(11), 3440–3450 (2012).
[Crossref]

Bocherer, G.

T. Fehenberger, A. Alvarado Segovia, G. Bocherer, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett. 28(7) 786–789 (2016).
[Crossref]

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

Bosco, G.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[Crossref]

Brandt-Pearce, M.

H. Song and M. Brandt-Pearce, “A 2-D discrete-time model of physical impairments in wavelength-division multiplexing systems,” J. Lightwave Technol. 30(5), 713–726 (2012).
[Crossref]

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers”, J. Lightwave Technol. 15(12), 2232–2241 (1997).
[Crossref]

Buchali, F.

Carena, A.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[Crossref]

Ciblat, P.

A. Amari, P. Ciblat, and Y. Jaouen, “Fifth-order Volterra series based nonlinear equalizer for long-haul high data rate optical fiber communications,” Asilomar Conference ACSSC (2014).

Curri, V.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[Crossref]

Dar, R.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: modeling and mitigation,” J. Lightwave Technol. 33(5), 1044–1053 (2015).
[Crossref]

R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Optics Letters 39, 398–401 (2014).
[Crossref] [PubMed]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express 21(22), 25685–25699 (2013).
[Crossref] [PubMed]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA, July 2014.

M. Shtaif, R. Dar, A. Mecozzi, and M. Feder, “Nonlinear interference noise in WDM systems and approaches for its cancelation,” in Optical Communication (ECOC 2014), 39th European Conference and Exhibition on Optical Communications, paper We1.3.1.

Derevyanko, S.A.

K. S. Turitsyn, S.A. Derevyanko, I.V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Letters 91, 203901 (2003).
[Crossref]

Djordjevic, I. B.

I. B. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. Optical Fiber Communication Conference, Los Angeles, CA, Mar. 2010, p. OMK2

Dou, L.

Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
[Crossref]

Durisi, G.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightwave Technol. 32(16), 2862–2876 (2014).
[Crossref]

E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiberoptic channels: A primer,” IEEE Information Theory Workshop (2015).

Ellis, A.

D. Rafique and A. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011).
[Crossref] [PubMed]

M. Sorokina, A. Ellis, and S. Turitsyn, “Optical information capacity processing,” chapter in All-Optical Signal Processing325–354 (2015).

Essiambre, R. J.

T. Freckmann, R. J. Essiambre, P. J. Winzer, G. J. Foschini, and G. Kramer, “Fiber capacity limits with optimized ring constellations,” IEEE Photonics Technology Letters 21(20), 1496–1498 (2009).
[Crossref]

Essiambre, R.-J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[Crossref] [PubMed]

A. Ghazisaeidi and R.-J. Essiambre, “Calculation of coefficients of perturbative nonlinear pre-compensation for Nyquist pulses,” Tech. Digest of European Conference on Optical Communication paper We.1.3.3. (2014).

Fan, Y.

Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
[Crossref]

Feder, M.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: modeling and mitigation,” J. Lightwave Technol. 33(5), 1044–1053 (2015).
[Crossref]

R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Optics Letters 39, 398–401 (2014).
[Crossref] [PubMed]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express 21(22), 25685–25699 (2013).
[Crossref] [PubMed]

M. Shtaif, R. Dar, A. Mecozzi, and M. Feder, “Nonlinear interference noise in WDM systems and approaches for its cancelation,” in Optical Communication (ECOC 2014), 39th European Conference and Exhibition on Optical Communications, paper We1.3.1.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA, July 2014.

Fehenberger, T.

T. Fehenberger, A. Alvarado Segovia, G. Bocherer, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett. 28(7) 786–789 (2016).
[Crossref]

Forestieri, E.

Forghieri, F.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[Crossref]

Foschini, G. J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

T. Freckmann, R. J. Essiambre, P. J. Winzer, G. J. Foschini, and G. Kramer, “Fiber capacity limits with optimized ring constellations,” IEEE Photonics Technology Letters 21(20), 1496–1498 (2009).
[Crossref]

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[Crossref] [PubMed]

Freckmann, T.

T. Freckmann, R. J. Essiambre, P. J. Winzer, G. J. Foschini, and G. Kramer, “Fiber capacity limits with optimized ring constellations,” IEEE Photonics Technology Letters 21(20), 1496–1498 (2009).
[Crossref]

Ghazisaeidi, A.

A. Ghazisaeidi and R.-J. Essiambre, “Calculation of coefficients of perturbative nonlinear pre-compensation for Nyquist pulses,” Tech. Digest of European Conference on Optical Communication paper We.1.3.3. (2014).

Goebel, B.

Han, T. S.

S. Verdu and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory 40(4) 1147–1157 (1994).
[Crossref]

Hanik, N.

T. Fehenberger, A. Alvarado Segovia, G. Bocherer, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett. 28(7) 786–789 (2016).
[Crossref]

Hoshida, T.

Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
[Crossref]

Idler, W.

Jaouen, Y.

A. Amari, P. Ciblat, and Y. Jaouen, “Fifth-order Volterra series based nonlinear equalizer for long-haul high data rate optical fiber communications,” Asilomar Conference ACSSC (2014).

Johannisson, P.

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
[Crossref]

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60(11), 3440–3450 (2012).
[Crossref]

E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiberoptic channels: A primer,” IEEE Information Theory Workshop (2015).

Karlsson, M.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightwave Technol. 32(16), 2862–2876 (2014).
[Crossref]

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
[Crossref]

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60(11), 3440–3450 (2012).
[Crossref]

E. Agrell and M. Karlsson, “Satellite constellations: towards the nonlinear channel capacity,” 25th IEEE Photonics Conference pp. 316–317 (2012).

Kramer, G.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

T. Freckmann, R. J. Essiambre, P. J. Winzer, G. J. Foschini, and G. Kramer, “Fiber capacity limits with optimized ring constellations,” IEEE Photonics Technology Letters 21(20), 1496–1498 (2009).
[Crossref]

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[Crossref] [PubMed]

Kschischang, F. R.

C. Pan and F. R. Kschischang, “Probabilistic 16-QAM Shaping in WDM Systems,” Journal of Lightwave Technology (in press).

Kuo, B.P.-P.

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

Kurtzke, C.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” Tech. Digest of European Conference on Optical Communication paper MoC2.4. (1993).

Li, Z.

Z. Li, W.-R. Peng, F. Zhu, and Y. Bai, “Optimum quantization of perturbation coefficients for perturbative fiber nonlinearity mitigation,” Tech. Digest of European Conference on Optical Communication paper We.1.3.4. (2014).

Liu, L.

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

Mecozzi, A.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: modeling and mitigation,” J. Lightwave Technol. 33(5), 1044–1053 (2015).
[Crossref]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express 21(22), 25685–25699 (2013).
[Crossref] [PubMed]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA, July 2014.

M. Shtaif, R. Dar, A. Mecozzi, and M. Feder, “Nonlinear interference noise in WDM systems and approaches for its cancelation,” in Optical Communication (ECOC 2014), 39th European Conference and Exhibition on Optical Communications, paper We1.3.1.

Menyuk, C. R.

Mitra, P.

Mitra, P. P.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027–1030 (2001).
[Crossref] [PubMed]

Myslivets, E.

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

Narimanov, E. E.

Pan, C.

C. Pan and F. R. Kschischang, “Probabilistic 16-QAM Shaping in WDM Systems,” Journal of Lightwave Technology (in press).

Papen, G. C.

M. H. Taghavi, G. C. Papen, and P.H. Siegel, “On the multiuser capacity of WDM in a nonlinear optical fiber: coherent communication,” IEEE Trans. Inf. Theory, 52(11), 5008–5022 (2006).
[Crossref]

Peddanarappagari, K.

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers”, J. Lightwave Technol. 15(12), 2232–2241 (1997).
[Crossref]

Peng, W.-R.

Z. Li, W.-R. Peng, F. Zhu, and Y. Bai, “Optimum quantization of perturbation coefficients for perturbative fiber nonlinearity mitigation,” Tech. Digest of European Conference on Optical Communication paper We.1.3.4. (2014).

Petermann, K.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” Tech. Digest of European Conference on Optical Communication paper MoC2.4. (1993).

Picinbono, B.

B. Picinbono, “Second-order complex random vectors and normal distributions,” IEEE Transactions on Signal Processing 442637–2640 (1996).
[Crossref]

Poggiolini, P.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[Crossref]

Prati, G.

Radic, S.

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

Rafique, D.

Rasmussen, J. C.

Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
[Crossref]

Richardson, D. J.

D. J. Richardson, “Filling the light pipe,” Science 330, 327–328 (2010).
[Crossref] [PubMed]

Schetzen, M.

M. Schetzen, “The Volterra and Wiener theories of nonlinear systems”. (Krieger, 2006).

Schmalen, L.

Schulte, P.

Secondini, M.

Shannon, C. E.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[Crossref]

Shtaif, M.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: modeling and mitigation,” J. Lightwave Technol. 33(5), 1044–1053 (2015).
[Crossref]

R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Optics Letters 39, 398–401 (2014).
[Crossref] [PubMed]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express 21(22), 25685–25699 (2013).
[Crossref] [PubMed]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA, July 2014.

M. Shtaif, R. Dar, A. Mecozzi, and M. Feder, “Nonlinear interference noise in WDM systems and approaches for its cancelation,” in Optical Communication (ECOC 2014), 39th European Conference and Exhibition on Optical Communications, paper We1.3.1.

Siegel, P.H.

M. H. Taghavi, G. C. Papen, and P.H. Siegel, “On the multiuser capacity of WDM in a nonlinear optical fiber: coherent communication,” IEEE Trans. Inf. Theory, 52(11), 5008–5022 (2006).
[Crossref]

Song, H.

Sorokina, M.

M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method,” Opt. Express 24(26), 30433–30443 (2016).
[Crossref]

M. Sorokina, A. Ellis, and S. Turitsyn, “Optical information capacity processing,” chapter in All-Optical Signal Processing325–354 (2015).

M. Sorokina, S. Sygletos, and S. K. Turitsyn, “Shannon capacity of nonlinear communication channels,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper SM3F.4.

Sorokina, M. A.

M. A. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
[Crossref] [PubMed]

Splett, A.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” Tech. Digest of European Conference on Optical Communication paper MoC2.4. (1993).

Stark, J. B.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027–1030 (2001).
[Crossref] [PubMed]

Steiner, F.

Sygletos, S.

M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method,” Opt. Express 24(26), 30433–30443 (2016).
[Crossref]

M. Sorokina, S. Sygletos, and S. K. Turitsyn, “Shannon capacity of nonlinear communication channels,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper SM3F.4.

Taghavi, M. H.

M. H. Taghavi, G. C. Papen, and P.H. Siegel, “On the multiuser capacity of WDM in a nonlinear optical fiber: coherent communication,” IEEE Trans. Inf. Theory, 52(11), 5008–5022 (2006).
[Crossref]

Tao, Z.

Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
[Crossref]

Temprana, E.

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

Turitsyn, K. S.

K. S. Turitsyn, S.A. Derevyanko, I.V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Letters 91, 203901 (2003).
[Crossref]

Turitsyn, S.

M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method,” Opt. Express 24(26), 30433–30443 (2016).
[Crossref]

M. Sorokina, A. Ellis, and S. Turitsyn, “Optical information capacity processing,” chapter in All-Optical Signal Processing325–354 (2015).

Turitsyn, S. K.

M. A. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
[Crossref] [PubMed]

K. S. Turitsyn, S.A. Derevyanko, I.V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Letters 91, 203901 (2003).
[Crossref]

M. Sorokina, S. Sygletos, and S. K. Turitsyn, “Shannon capacity of nonlinear communication channels,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper SM3F.4.

Verdu, S.

S. Verdu and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory 40(4) 1147–1157 (1994).
[Crossref]

Wang, T.

I. B. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. Optical Fiber Communication Conference, Los Angeles, CA, Mar. 2010, p. OMK2

Winzer, P. J.

P. J. Winzer, “Scaling optical fiber networks: challenges and solutions,” Optics and Photonics News,  26, 28–35 (2015).
[Crossref]

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

T. Freckmann, R. J. Essiambre, P. J. Winzer, G. J. Foschini, and G. Kramer, “Fiber capacity limits with optimized ring constellations,” IEEE Photonics Technology Letters 21(20), 1496–1498 (2009).
[Crossref]

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[Crossref] [PubMed]

Wymeersch, H.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60(11), 3440–3450 (2012).
[Crossref]

Xu, L.

I. B. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. Optical Fiber Communication Conference, Los Angeles, CA, Mar. 2010, p. OMK2

Yurkevich, I.V.

K. S. Turitsyn, S.A. Derevyanko, I.V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Letters 91, 203901 (2003).
[Crossref]

Zhao, Y.

Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
[Crossref]

Zhu, F.

Z. Li, W.-R. Peng, F. Zhu, and Y. Bai, “Optimum quantization of perturbation coefficients for perturbative fiber nonlinearity mitigation,” Tech. Digest of European Conference on Optical Communication paper We.1.3.4. (2014).

Bell Syst. Tech. J. (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[Crossref]

IEEE Photon. Technol. Lett. (2)

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[Crossref]

T. Fehenberger, A. Alvarado Segovia, G. Bocherer, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett. 28(7) 786–789 (2016).
[Crossref]

IEEE Photonics Technology Letters (1)

T. Freckmann, R. J. Essiambre, P. J. Winzer, G. J. Foschini, and G. Kramer, “Fiber capacity limits with optimized ring constellations,” IEEE Photonics Technology Letters 21(20), 1496–1498 (2009).
[Crossref]

IEEE Trans. Commun. (1)

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60(11), 3440–3450 (2012).
[Crossref]

IEEE Trans. Inf. Theory (1)

S. Verdu and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory 40(4) 1147–1157 (1994).
[Crossref]

IEEE Trans. Inf. Theory, (1)

M. H. Taghavi, G. C. Papen, and P.H. Siegel, “On the multiuser capacity of WDM in a nonlinear optical fiber: coherent communication,” IEEE Trans. Inf. Theory, 52(11), 5008–5022 (2006).
[Crossref]

IEEE Transactions on Signal Processing (1)

B. Picinbono, “Second-order complex random vectors and normal distributions,” IEEE Transactions on Signal Processing 442637–2640 (1996).
[Crossref]

J. Lightwave Technol. (11)

H. Song and M. Brandt-Pearce, “A 2-D discrete-time model of physical impairments in wavelength-division multiplexing systems,” J. Lightwave Technol. 30(5), 713–726 (2012).
[Crossref]

Z. Tao, Y. Zhao, Y. Fan, L. Dou, T. Hoshida, and J. C. Rasmussen, “Analytical intrachannel nonlinear models to predict the nonlinear noise waveform,” J. Lightwave Technol. 33(10), 2011–2018 (2015).
[Crossref]

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
[Crossref]

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightwave Technol. 31(23), 3839–3852 (2013).
[Crossref]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: modeling and mitigation,” J. Lightwave Technol. 33(5), 1044–1053 (2015).
[Crossref]

M. Secondini, E. Forestieri, and C. R. Menyuk, “A combined regular-logarithmic perturbation method for signal-noise interaction in amplified optical systems”, J. Lightwave Technol. 27(16), 3358–3369 (2009).
[Crossref]

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers”, J. Lightwave Technol. 15(12), 2232–2241 (1997).
[Crossref]

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightwave Technol. 32(16), 2862–2876 (2014).
[Crossref]

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

E. E. Narimanov and P. Mitra, “The channel capacity of a fiber optics communication system: perturbation theory,” J. Lightwave Technol. 20(3), 530–537 (2002).
[Crossref]

Journal of Optics (1)

M. Secondini, chapter in “Roadmap of optical communications,” by E. Agrell et al. Journal of Optics 18 (6), 063002 (2016).
[Crossref]

Nat. Commun. (1)

M. A. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
[Crossref] [PubMed]

Nature (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027–1030 (2001).
[Crossref] [PubMed]

Opt. Express (3)

Optics and Photonics News (1)

P. J. Winzer, “Scaling optical fiber networks: challenges and solutions,” Optics and Photonics News,  26, 28–35 (2015).
[Crossref]

Optics Letters (1)

R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Optics Letters 39, 398–401 (2014).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[Crossref] [PubMed]

Phys. Rev. Letters (1)

K. S. Turitsyn, S.A. Derevyanko, I.V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Letters 91, 203901 (2003).
[Crossref]

Science (2)

D. J. Richardson, “Filling the light pipe,” Science 330, 327–328 (2010).
[Crossref] [PubMed]

E. Temprana, E. Myslivets, B.P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348, 1445–1448 (2015).
[Crossref] [PubMed]

Other (15)

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” Tech. Digest of European Conference on Optical Communication paper MoC2.4. (1993).

M. Sorokina, A. Ellis, and S. Turitsyn, “Optical information capacity processing,” chapter in All-Optical Signal Processing325–354 (2015).

E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiberoptic channels: A primer,” IEEE Information Theory Workshop (2015).

C. Pan and F. R. Kschischang, “Probabilistic 16-QAM Shaping in WDM Systems,” Journal of Lightwave Technology (in press).

I. B. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. Optical Fiber Communication Conference, Los Angeles, CA, Mar. 2010, p. OMK2

M. Secondini and E. Forestieri, “Scope and limitations of the nonlinear Shannon limit,” online version of 24.10.2016 http://ieeexplore.ieee.org/document/7637002/ .

M. Sorokina, S. Sygletos, and S. K. Turitsyn, “Shannon capacity of nonlinear communication channels,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper SM3F.4.

M. Sorokina, S. Sygletos, and S. K. Turitsyn, “Ripple distribution for nonlinear fiber-optic channels,” https://arxiv.org/abs/1610.06937

M. Shtaif, R. Dar, A. Mecozzi, and M. Feder, “Nonlinear interference noise in WDM systems and approaches for its cancelation,” in Optical Communication (ECOC 2014), 39th European Conference and Exhibition on Optical Communications, paper We1.3.1.

M. Schetzen, “The Volterra and Wiener theories of nonlinear systems”. (Krieger, 2006).

A. Amari, P. Ciblat, and Y. Jaouen, “Fifth-order Volterra series based nonlinear equalizer for long-haul high data rate optical fiber communications,” Asilomar Conference ACSSC (2014).

Z. Li, W.-R. Peng, F. Zhu, and Y. Bai, “Optimum quantization of perturbation coefficients for perturbative fiber nonlinearity mitigation,” Tech. Digest of European Conference on Optical Communication paper We.1.3.4. (2014).

A. Ghazisaeidi and R.-J. Essiambre, “Calculation of coefficients of perturbative nonlinear pre-compensation for Nyquist pulses,” Tech. Digest of European Conference on Optical Communication paper We.1.3.3. (2014).

E. Agrell and M. Karlsson, “Satellite constellations: towards the nonlinear channel capacity,” 25th IEEE Photonics Conference pp. 316–317 (2012).

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA, July 2014.

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Figures (3)

Fig. 1
Fig. 1 Fiber-optic communication system. a) The fundamental building blocks of a communication system where data is coded to a discrete set of symbols Xk (panel b) and transformed into continuous time form E(t, 0) (panel c) to be transmitted via the fiber channel. During transmission the signal is governed by the NLSE (panel d), which results in distortions: dispersion, nonlinearity, noise (panel e), which are reflected in the conditional pdf P(Y|X), which we can use to optimize constellation and coding (panel f), to receive the maximum achievable transmission rate – channel capacity C. The received signal E(t, L) is processed and sampled Yk and, finally, decoded to receive the data (panel g).
Fig. 2
Fig. 2 Coupling matrix. For various transmission distances a) L = 100 km, b) L = 500 km, c) L = 1000 km and the corresponding received constellation diagrams below (for input power 6dBm and span length 100km). We see that the coupling matrix reflects the strength of the inter symbol interaction and its effect on the signal distortion.
Fig. 3
Fig. 3 Capacity and ripple distribution. a) Capacity lower bounds for uncompensated signal-signal (S-S) distortions ISS (GN model (red, dotted) and the proposed model (green)) and compensated deterministic distortions with account of signal-noise (S-N) interference. Previous lower bound (denoted by I0) decreases to zero, whereas ripple distribution as input pdf (Eq. (15)) allows to achieve higher monotonically increasing bounds, denoted by I1 and I2 for the increased number of ripples in an input pdf as shown in panels b) and c) correspondingly (Gaussian pdf is shown in red dashed lines for comparison).

Tables (2)

Tables Icon

Table 1 Review of previous channel models

Tables Icon

Table 2: Statistical properties of ripple distribution

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

E z = α 2 E i β 2 2 2 E 2 t + i γ | E | 2 E + η ( t , z ) ,
Y k = L d L η k + ε V [ Y ] k , V [ Y ] k = Ψ s ( ξ ) m , n = M M Y k + m ( ξ ) Y k + n ( ξ ) Y k + m + n * ( ξ ) C ˜ m n ( ξ )
C ˜ m n = i d ω d ω 1 d ω 2 e i ω 1 ω 2 β 2 L d ξ i ω 1 m T i ω 2 n T × f * ( ω ) f ( ω 1 + ω ) f ( ω 2 + ω ) f * ( ω 1 + ω 2 + ω )
Y = X ^ + M ζ + L ζ * , ζ = d ξ η ( ξ )
Y k = X ^ k + m M k , m ζ m + L k , m ζ m *
X ^ k = Y k ( 0 ) + N o = 1 ε N o Y k ( N o ) , Y k ( 0 ) = X k
Y k ( N o ) = i , j , l = 0 i + j + l = N o 1 N o 1 m , n C m n Y k + n ( i ) Y k + m ( j ) ( Y k + n + m ( l ) ) *
M k , m = δ k , m + ε n K n , m k ( X ^ k + n X ^ m + n * + X ^ m + n X ^ k + n * ) ,
L k , m = ε n K n , m k n X ^ k + n X ^ m n
K m n = d z Ψ n ( z ) Ψ s ( z ) C ˜ m n ( z )
Y k θ = X ^ k θ + m , α M k θ m α ζ m α + L k θ m α ζ m α *
C = lim d = dim ( X ) sup 1 d I ( X , Y )
P ( Y | X ) = ( π ) d ( | Γ | | P | ) 1 / 2 exp [ 1 2 [ ( y x ^ ) H , ( y x ^ ) T ] ( Γ ϒ ϒ H Γ * ) 1 ( y x ^ y * x ^ * ) ]
Γ = E [ ( Y X ^ ) ( Y X ^ ) H ] , ϒ = E [ ( Y X ^ ) ( Y X ^ ) T ] P = Γ * ϒ H Γ 1 ϒ
Γ = ( M M H + L L H ) , ϒ = ( M L T + L M T )
P X = i = 1 d P X i , P X i ( x i = { r i , φ i } ) = α = 1 q r i p α π σ α e r i 2 + ρ α 2 S α I 0 ( 2 r i ρ α σ α )
P X = i = 1 d r i π σ 1 e r i 2 σ 1
I 0 = log 2 ( 1 + σ 1 2 + C nl σ 1 2 )
1 = d x P x p 1 d + d p 1 d 1 p 2 d = d x x 2 P x d p 1 d σ 1 + d p 1 d 1 p 2 ( ( d 1 ) σ 1 + σ 2 + ρ 2 )
I 1 = lim δ 0 d p 1 d log 2 ( 1 + σ 1 2 + 6 ε 2 2 m , n | K m n | 2 σ 1 2 ) p 1 d log 2 p 1 p 0 d 1 p 2 log 2 ( p 1 d 1 p 2 ) + p 1 d 1 p 2 d l = d / 2 d / 2 [ log 2 ( 2 π ρ 2 σ 2 2 + 6 ε 2 2 m , n l | K m n | 2 σ 1 2 + 12 ε 2 2 m | K m l | 2 σ 1 ( σ 2 + ρ 2 ) + 6 ε 2 2 | K l l | 2 ( σ 2 + ρ 2 ) 2 ) + ( d 1 ) log 2 ( 1 + σ 1 2 + 6 ε 2 2 m , n l | K m n | 2 σ 1 2 + 12 ε 2 2 m | K m l | 2 σ 1 ( σ 2 + ρ 2 ) + 6 ε 2 2 | K l l | 2 ( σ 2 + ρ 2 ) 2 ) ]
I 1 = ( 1 δ ) log 2 ( 1 + 1 2 1 C nl ) + δ log 2 ( 2 π ρ 2 σ 2 σ 1 ) + δ log 2 e δ log 2 δ δ ( σ 2 + ρ 2 σ 1 ) 1 C nl 1 / 2 log 2 e
I 1 = log 2 ( 1 + 1 2 C nl ) + 2 π ρ 2 1 C nl 1 / 2 e ρ 2 1 C nl 1 / 2 log 2 e

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