Abstract

This paper investigates the impact of transceiver noise on the performance of digital back-propagation (DBP). A generalized expression to estimate the signal-to-noise ratio (SNR) obtained using DBP in the presence of transceiver noise is described. This new expression correctly accounts for the nonlinear beating between the transceiver noise and the signal in the optical fiber transmission link. The transceiver noise-signal nonlinear beating has been identified as the main reason for the discrepancy between predicted and practical performance of DBP; which has not been previously suggested. This nonlinear beating has been included in the GN model, allowing DBP gains in practical systems to be predicted analytically. Experiments and split-step simulations with and without polarization-mode dispersion (PMD) in the transmission link have been performed. The results show that the impact of transceiver noise greatly outweighs that of PMD, and the analytical expressions are confirmed by the numerical simulations.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  19. D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
    [Crossref]
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    [Crossref]
  21. P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightw. Technol. 32(4), 694–721 (2014).
    [Crossref]
  22. P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
    [Crossref]
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  24. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phased-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon. 7(7), 560–568 (2013).
    [Crossref]
  25. D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightw. Technol. 15(9), 1735–1746 (1997).
    [Crossref]
  26. T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
    [Crossref]
  27. S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

2016 (4)

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref] [PubMed]

R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” Photon. Technol. Lett. 28(11), 1253–1256 (2016).
[Crossref]

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
[Crossref]

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

2015 (5)

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

E. Temprana, E. Myslivets, L. Liu, V. Ataie, A. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Two-fold transmission reach enhancement enabled by transmitter-side digital backpropagation and optical frequency comb-derived information carriers,” Opt. Express 23(16), 20774–2783 (2015).
[Crossref] [PubMed]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
[Crossref]

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugates,” Opt. Express 20(16), 20381–20393 (2015).
[Crossref]

2014 (3)

2013 (1)

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phased-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon. 7(7), 560–568 (2013).
[Crossref]

2012 (2)

2011 (1)

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightw. Technol. 29(17), 2570–2576 (2011).
[Crossref]

2010 (1)

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightw. Technol. 28(6), 939–951 (2010).
[Crossref]

1997 (1)

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightw. Technol. 15(9), 1735–1746 (1997).
[Crossref]

Agrell, E.

G. Liga, C. B. Czegledi, T. Xu, E. Agrell, R. I. Killey, and P. Bayvel, “Ultra-wideband nonlinearity compensation performance in the presence of PMD,” in Proc. of European Conference on Optical Communication (ECOC), 794–796 (2016).

Alic, N.

E. Temprana, E. Myslivets, L. Liu, V. Ataie, A. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Two-fold transmission reach enhancement enabled by transmitter-side digital backpropagation and optical frequency comb-derived information carriers,” Opt. Express 23(16), 20774–2783 (2015).
[Crossref] [PubMed]

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

Al-Khateeb, M. A. Z.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugates,” Opt. Express 20(16), 20381–20393 (2015).
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

Alvarado, A.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
[Crossref]

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref] [PubMed]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Ataie, V.

E. Temprana, E. Myslivets, L. Liu, V. Ataie, A. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Two-fold transmission reach enhancement enabled by transmitter-side digital backpropagation and optical frequency comb-derived information carriers,” Opt. Express 23(16), 20774–2783 (2015).
[Crossref] [PubMed]

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

Awwad, E.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Bayvel, P.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
[Crossref]

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref] [PubMed]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

G. Liga, C. B. Czegledi, T. Xu, E. Agrell, R. I. Killey, and P. Bayvel, “Ultra-wideband nonlinearity compensation performance in the presence of PMD,” in Proc. of European Conference on Optical Communication (ECOC), 794–796 (2016).

Bosco, G.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightw. Technol. 32(4), 694–721 (2014).
[Crossref]

Brindel, P.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Burrows, E. C.

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

Carena, A.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightw. Technol. 32(4), 694–721 (2014).
[Crossref]

Chandrasekhar, S.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phased-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon. 7(7), 560–568 (2013).
[Crossref]

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

C. Lin, S. Chandrasekhar, and P. J. Winzer, “Experimental study of the limits of digital nonlinearity compensation in DWDM systems,” in Proc. of Optical Fiber Communication Conference (OFC), Th4D.4, (2016).

Xi Chen, S. Chandrasekhar, S. Randel, W. Gu, and P. Winzer, “Experimental Quantification of Implementation Penalties from Limited ADC Resolution for Nyquist Shaped Higher-Order QAM,” in Proc. of Optical Fiber Communication Conference (OFC), W.4.A.3 (2016).

Charlet, G.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Chen, X.

G. Gao, X. Chen, and W. Shieh, “Influence of PMD on fiber nonlinearity compensation using digital back propagation,” Opt. Express 20(13), 14406–14418 (2012).
[Crossref] [PubMed]

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

Chen, Xi

Xi Chen, S. Chandrasekhar, S. Randel, W. Gu, and P. Winzer, “Experimental Quantification of Implementation Penalties from Limited ADC Resolution for Nyquist Shaped Higher-Order QAM,” in Proc. of Optical Fiber Communication Conference (OFC), W.4.A.3 (2016).

Cho, J.

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

Chraplyvy, A. R.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phased-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon. 7(7), 560–568 (2013).
[Crossref]

Curri, V.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightw. Technol. 32(4), 694–721 (2014).
[Crossref]

Czegledi, C. B.

G. Liga, C. B. Czegledi, T. Xu, E. Agrell, R. I. Killey, and P. Bayvel, “Ultra-wideband nonlinearity compensation performance in the presence of PMD,” in Proc. of European Conference on Optical Communication (ECOC), 794–796 (2016).

Dangui, V.

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

Dar, R.

R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” Photon. Technol. Lett. 28(11), 1253–1256 (2016).
[Crossref]

Dou, L.

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightw. Technol. 29(17), 2570–2576 (2011).
[Crossref]

Ellis, A. D.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugates,” Opt. Express 20(16), 20381–20393 (2015).
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

Essiambre, R.-J.

R.-J. Essiambre and P. J. Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” in Proc. of European Conference on Optical Communication (ECOC), Tu.3.2.2 (2005).

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

Fischer, J. K.

Forestieri, E.

M. Secondini, D. Marsella, and E. Forestieri, “Enhanced split-step fourier method for digital backpropagation,” in Proc. of European Conference on Optical Communication (ECOC), We.3.3.5 (2014).

Forghieri, F.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightw. Technol. 32(4), 694–721 (2014).
[Crossref]

Galdino, L.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Gao, G.

Ghazisadeidi, A.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Ghazisaeidi, A.

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

Gu, W.

Xi Chen, S. Chandrasekhar, S. Randel, W. Gu, and P. Winzer, “Experimental Quantification of Implementation Penalties from Limited ADC Resolution for Nyquist Shaped Higher-Order QAM,” in Proc. of Optical Fiber Communication Conference (OFC), W.4.A.3 (2016).

Hoshida, T.

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightw. Technol. 29(17), 2570–2576 (2011).
[Crossref]

Ip, E.

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightw. Technol. 28(6), 939–951 (2010).
[Crossref]

Ives, D.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
[Crossref]

Jiang, Y.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightw. Technol. 32(4), 694–721 (2014).
[Crossref]

Killey, R. I.

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

G. Liga, C. B. Czegledi, T. Xu, E. Agrell, R. I. Killey, and P. Bayvel, “Ultra-wideband nonlinearity compensation performance in the presence of PMD,” in Proc. of European Conference on Optical Communication (ECOC), 794–796 (2016).

Kumar, S.

Kuo, B. P. P.

Kuo, B. P. -P.

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

Lavery, D.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
[Crossref]

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref] [PubMed]

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

Le, S. T.

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

Li, B.

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

Li, L.

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightw. Technol. 29(17), 2570–2576 (2011).
[Crossref]

Liang, X.

Liga, G.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
[Crossref]

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

G. Liga, C. B. Czegledi, T. Xu, E. Agrell, R. I. Killey, and P. Bayvel, “Ultra-wideband nonlinearity compensation performance in the presence of PMD,” in Proc. of European Conference on Optical Communication (ECOC), 794–796 (2016).

Lin, C.

C. Lin, S. Chandrasekhar, and P. J. Winzer, “Experimental study of the limits of digital nonlinearity compensation in DWDM systems,” in Proc. of Optical Fiber Communication Conference (OFC), Th4D.4, (2016).

Liu, L.

Liu, X.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phased-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon. 7(7), 560–568 (2013).
[Crossref]

Maher, R.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref] [PubMed]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Marcuse, D.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightw. Technol. 15(9), 1735–1746 (1997).
[Crossref]

Marsella, D.

M. Secondini, D. Marsella, and E. Forestieri, “Enhanced split-step fourier method for digital backpropagation,” in Proc. of European Conference on Optical Communication (ECOC), We.3.3.5 (2014).

McCarthy, M. E.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugates,” Opt. Express 20(16), 20381–20393 (2015).
[Crossref]

Menyuk, C. R.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightw. Technol. 15(9), 1735–1746 (1997).
[Crossref]

Myslivets, E.

E. Temprana, E. Myslivets, L. Liu, V. Ataie, A. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Two-fold transmission reach enhancement enabled by transmitter-side digital backpropagation and optical frequency comb-derived information carriers,” Opt. Express 23(16), 20774–2783 (2015).
[Crossref] [PubMed]

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

Nölle, M.

Poggiolini, P.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightw. Technol. 32(4), 694–721 (2014).
[Crossref]

Radic, S.

E. Temprana, E. Myslivets, L. Liu, V. Ataie, A. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Two-fold transmission reach enhancement enabled by transmitter-side digital backpropagation and optical frequency comb-derived information carriers,” Opt. Express 23(16), 20774–2783 (2015).
[Crossref] [PubMed]

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

Randel, S.

Xi Chen, S. Chandrasekhar, S. Randel, W. Gu, and P. Winzer, “Experimental Quantification of Implementation Penalties from Limited ADC Resolution for Nyquist Shaped Higher-Order QAM,” in Proc. of Optical Fiber Communication Conference (OFC), W.4.A.3 (2016).

Rasmussen, J. C.

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightw. Technol. 29(17), 2570–2576 (2011).
[Crossref]

Raybon, G.

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

Ruiz, I.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Sato, M.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Savory, S. J.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
[Crossref]

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Schmalen, L.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Schubert, C.

Secondini, M.

M. Secondini, D. Marsella, and E. Forestieri, “Enhanced split-step fourier method for digital backpropagation,” in Proc. of European Conference on Optical Communication (ECOC), We.3.3.5 (2014).

Shi, K.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Shieh, W.

Simonneau, C.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Sygletos, S.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugates,” Opt. Express 20(16), 20381–20393 (2015).
[Crossref]

Tanimura, T.

Tao, Z.

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightw. Technol. 29(17), 2570–2576 (2011).
[Crossref]

Temprana, E.

E. Temprana, E. Myslivets, L. Liu, V. Ataie, A. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Two-fold transmission reach enhancement enabled by transmitter-side digital backpropagation and optical frequency comb-derived information carriers,” Opt. Express 23(16), 20774–2783 (2015).
[Crossref] [PubMed]

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

Thomsen, B. C.

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Tkach, R. W.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phased-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon. 7(7), 560–568 (2013).
[Crossref]

Tran, P.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Turitsyn, S. K.

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

Uscumlic, B.

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

Vusirikala, V.

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

Wai, P. K. A.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightw. Technol. 15(9), 1735–1746 (1997).
[Crossref]

Wiberg, A.

Winzer, P.

Xi Chen, S. Chandrasekhar, S. Randel, W. Gu, and P. Winzer, “Experimental Quantification of Implementation Penalties from Limited ADC Resolution for Nyquist Shaped Higher-Order QAM,” in Proc. of Optical Fiber Communication Conference (OFC), W.4.A.3 (2016).

Winzer, P. J.

R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” Photon. Technol. Lett. 28(11), 1253–1256 (2016).
[Crossref]

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phased-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon. 7(7), 560–568 (2013).
[Crossref]

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

C. Lin, S. Chandrasekhar, and P. J. Winzer, “Experimental study of the limits of digital nonlinearity compensation in DWDM systems,” in Proc. of Optical Fiber Communication Conference (OFC), Th4D.4, (2016).

R.-J. Essiambre and P. J. Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” in Proc. of European Conference on Optical Communication (ECOC), Tu.3.2.2 (2005).

Xu, T.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

G. Liga, C. B. Czegledi, T. Xu, E. Agrell, R. I. Killey, and P. Bayvel, “Ultra-wideband nonlinearity compensation performance in the presence of PMD,” in Proc. of European Conference on Optical Communication (ECOC), 794–796 (2016).

Yan, W.

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightw. Technol. 29(17), 2570–2576 (2011).
[Crossref]

J. Lightw. Technol. (6)

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightw. Technol. 28(6), 939–951 (2010).
[Crossref]

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightw. Technol. 29(17), 2570–2576 (2011).
[Crossref]

A. Ghazisadeidi, I. Ruiz, L. Schmalen, P. Tran, C. Simonneau, E. Awwad, B. Uscumlic, P. Brindel, and G. Charlet, “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol. 34(8), 1886–1895 (2016).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightw. Technol. 32(4), 694–721 (2014).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol. 33(2), 459–473 (2015).
[Crossref]

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightw. Technol. 15(9), 1735–1746 (1997).
[Crossref]

Nature Photon. (1)

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phased-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon. 7(7), 560–568 (2013).
[Crossref]

Opt. Express (6)

Photon. Technol. Lett. (2)

R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” Photon. Technol. Lett. 28(11), 1253–1256 (2016).
[Crossref]

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single channel optical fiber communications,” Photon. Technol. Lett. 28(17), 1803–1806 (2016).
[Crossref]

Sci. Rep. (3)

T. Xu, G. Liga, D. Lavery, B. C. Thomsen, S. J. Savory, R. I. Killey, and P. Bayvel, “Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multichannel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref] [PubMed]

Other (9)

Xi Chen, S. Chandrasekhar, S. Randel, W. Gu, and P. Winzer, “Experimental Quantification of Implementation Penalties from Limited ADC Resolution for Nyquist Shaped Higher-Order QAM,” in Proc. of Optical Fiber Communication Conference (OFC), W.4.A.3 (2016).

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

M. Secondini, D. Marsella, and E. Forestieri, “Enhanced split-step fourier method for digital backpropagation,” in Proc. of European Conference on Optical Communication (ECOC), We.3.3.5 (2014).

G. Liga, C. B. Czegledi, T. Xu, E. Agrell, R. I. Killey, and P. Bayvel, “Ultra-wideband nonlinearity compensation performance in the presence of PMD,” in Proc. of European Conference on Optical Communication (ECOC), 794–796 (2016).

R.-J. Essiambre and P. J. Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” in Proc. of European Conference on Optical Communication (ECOC), Tu.3.2.2 (2005).

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit: the difference between optical and electrical phase conjugation,” in Proc. of IEEE Summer Topicals Meeting Series, 209–210 (2015).

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. C. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission on PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. of European Conference on Optical Communication (ECOC), postdeadline paper Th.3.C.1, (2016).

C. Lin, S. Chandrasekhar, and P. J. Winzer, “Experimental study of the limits of digital nonlinearity compensation in DWDM systems,” in Proc. of Optical Fiber Communication Conference (OFC), Th4D.4, (2016).

E. Temprana, E. Myslivets, V. Ataie, B. P. -P. Kuo, N. Alic, V. Vusirikala, V. Dangui, and S. Radic, “Demonstration of coherent transmission reach tripling by frequency-referenced nonlinearity pre-compensation in EDFA-only SMF link,” in Proc. of European Conference on Optical Communication (ECOC), p376, (2016).

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Figures (9)

Fig. 1
Fig. 1 Nonlinear signal-noise interactions accumulation along transmission link for (a) receiver-side DBP and (b) transmitter-side DBP. The colored lines show (1) nonlinear transmitter noise-signal beating, cancelled after DBP, (2) nonlinear receiver noise-signal beating, generated after DBP as: 3ηξ2κRP3, and (3) nonlinear transmitter noise-signal beating, generated in transmission as: 3ηξ2κTP3.
Fig. 2
Fig. 2 Experimental configuration.
Fig. 3
Fig. 3 BTB measurements (a) SNR vs. OSNR for single channel and each subcarrier of the superchannel; (b) maximum archivable SNR for each subcarrier.
Fig. 4
Fig. 4 Received SNR vs. subcarrier launch power over 5,000 km transmission (a) without transceiver noise and (b) with transceiver noise.
Fig. 5
Fig. 5 DBP gain over EDC for each subcarrier of the superchannel after 5,000 km of optical fiber transmission.
Fig. 6
Fig. 6 SNR vs. distance at optimum subcarrier launch power(a) without transceiver noise and (b) with transceiver noise.
Fig. 7
Fig. 7 SNR gais over EDC vs. number of backpropagated channels for transceiver SNR of 24 dB and transmission distance over (a) 1,000 km (b) 10,000 km.
Fig. 8
Fig. 8 The SNR gain for receiver-side FF-DBP (red line) and transmitter-side DBP (blue line) with respect to EDC as a function of the transceiver noise ratio between the transmitter and receiver.
Fig. 9
Fig. 9 SNR gains over EDC for different transceiver SNR’s for transmission distance over (a) 1,000 km and (b) 10,000 km. The vertical lines show the true solution (dashed line) together with its approximation (dotted line) from Inequality (11) for the transceiver SNR where the ASE signal beating is equals the receiver noise-signal beating is shown by the vertical lines.

Equations (17)

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σ EDC 2 = σ NLI 2 + σ ASE 2 + σ TR 2 ,
σ TR 2 = σ T 2 + σ R 2 .
SNR EDC = P N 1 + η P 3 + κ P + N P ASE ,
max P ( SNR EDC ) = 1 κ + 27 4 P ASE 2 η N 3 + 3 .
SNR = P ( N 1 + η N 1 + NLC η NLC ) P 3 + κ P + N P ASE + 3 η ( ξ 1 P ASE + ξ 2 κ R P ) P 2 ,
SNR FF DBP = P κ P + N P ASE + 3 η ( ξ 1 P ASE + ξ 2 κ R P ) P 2 .
P opt = ξ 1 P ASE ϕ 6 ξ 2 κ R ,
max P ( SNR FF DBP ) = ξ 1 ϕ ( ϕ + 6 ) ϕ 2 ξ 1 3 P ASE 2 η 12 κ R N 1 + + 6 κ R N 2 + + ξ 1 κ ϕ ,
ϕ = 2 cosh [ 1 3 a cosh ( Γ ) ] 1 ,
Γ = 18 N 3 + 2 κ R 2 ξ 1 3 P ASE 2 η 1 .
max P ( SNR EDC , ideal ) [ dB ] 2 3 SNR TR [ dB ] 4.5 dB ,
max P ( SNR EDC , ideal ) [ dB ] 2 3 SNR TR [ dB ] 4.5 dB .
P opt ( P ASE 6 N κ R η ) 1 3 ξ 1 P ASE 6 N 1 + κ R .
ξ 1 P ASE N 1 + κ R P opt .
( 7 ξ 1 ) 3 P ASE 2 η 36 N 3 + 2 κ R 2 .
( 4 27 P ASE 2 η N 3 ) 1 3 7 6 ( 3 κ R ) 2 3 ,
SNR EDC , ideal 7 6 5 3 SNR TR 2 3 .

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