Abstract

The relationship between modulation format and the performance of multi-channel digital back-propagation (MC-DBP) in ideal Nyquist-spaced optical communication systems is investigated. It is found that the nonlinear distortions behave independent of modulation format in the case of full-field DBP, in contrast to the cases of electronic dispersion compensation and partial-bandwidth DBP. It is shown that the minimum number of steps per span required for MC-DBP depends on the chosen modulation format. For any given target information rate, there exists a possible trade-off between modulation format and back-propagated bandwidth, which could be used to reduce the computational complexity requirement of MC-DBP.

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References

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2017 (1)

2016 (3)

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (2016).
[Crossref] [PubMed]

D. Rafique, “Fiber nonlinearity compensation: commercial applications and complexity analysis,” J. Lightwave Technol. 34(2), 544–553 (2016).
[Crossref]

M. Secondini, S. Rommel, G. Meloni, F. Fresi, E. Forestieri, and L. Potì, “Single-step digital backpropagation for nonlinearity mitigation,” Photonic Netw. Commun. 31(3), 493–502 (2016).
[Crossref]

2015 (6)

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]

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. Lightwave Technol. 33(2), 459–473 (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]

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 multi-channel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref] [PubMed]

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Opt. Express 23(7), 9183–9191 (2015).
[Crossref] [PubMed]

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
[Crossref] [PubMed]

2014 (7)

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

A. Napoli, Z. Maalej, V. A. J. M. Sleiffer, M. Kuschnerov, D. Rafique, E. Timmers, B. Spinnler, T. Rahman, L. D. Coelho, and N. Hanik, “Reduced complexity digital back-propagation methods for optical communication systems,” J. Lightwave Technol. 32(7), 1351–1362 (2014).
[Crossref]

G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
[Crossref] [PubMed]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part I-III: Numerical methods,” IEEE Trans. Inf. Theory 60(7), 4329–4345 (2014).
[Crossref]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Accumulation of nonlinear interference noise in fiber-optic systems,” Opt. Express 22(12), 14199–14211 (2014).
[Crossref] [PubMed]

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Express 22(13), 16335–16362 (2014).
[Crossref] [PubMed]

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. Lightwave Technol. 32(4), 694–721 (2014).
[Crossref]

2013 (5)

2012 (5)

2011 (1)

2010 (1)

2009 (1)

2008 (1)

2006 (1)

D. Arnold, H.-A. Loeliger, P. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory 52(8), 3498–3508 (2006).
[Crossref]

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

2000 (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Suppression of spurious tones induced by the split-step method in fiber systems simulation,” IEEE Photonics Technol. Lett. 12(5), 489–491 (2000).
[Crossref]

Agrell, E.

Alic, N.

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
[Crossref] [PubMed]

Alvarado, A.

Arnold, D.

D. Arnold, H.-A. Loeliger, P. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory 52(8), 3498–3508 (2006).
[Crossref]

Ataie, V.

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
[Crossref] [PubMed]

Bayvel, P.

D. Semrau, T. Xu, N. A. Shevchenko, M. Paskov, A. Alvarado, R. I. Killey, and P. Bayvel, “Achievable information rates estimates in optically amplified transmission systems using nonlinearity compensation and probabilistic shaping,” Opt. Lett. 42(1), 121–124 (2017).
[Crossref] [PubMed]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (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 multi-channel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref] [PubMed]

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Opt. Express 23(7), 9183–9191 (2015).
[Crossref] [PubMed]

G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
[Crossref] [PubMed]

Benedetto, S.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Suppression of spurious tones induced by the split-step method in fiber systems simulation,” IEEE Photonics Technol. Lett. 12(5), 489–491 (2000).
[Crossref]

Beygi, L.

Bononi, A.

Bosco, G.

Carena, A.

Cartledge, J. C.

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities,” Opt. Express (to appear).

Chandrasekhar, S.

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

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

Chraplyvy, A. R.

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

Coelho, L. D.

Curri, V.

Dar, R.

Ellis, A. D.

Essiambre, R.-J.

A. Mecozzi and R.-J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” J. Lightwave Technol. 30(12), 2011–2024 (2012).
[Crossref]

R.-J. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

Feder, M.

Fehenberger, T.

Fischer, J. K.

Forestieri, E.

M. Secondini, S. Rommel, G. Meloni, F. Fresi, E. Forestieri, and L. Potì, “Single-step digital backpropagation for nonlinearity mitigation,” Photonic Netw. Commun. 31(3), 493–502 (2016).
[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]

M. Secondini, S. Rommel, F. Fresi, E. Forestieri, G. Meloni, and L. Potì, “Coherent 100G nonlinear compensation with single-step digital backpropagation,” in Proceedings of International Conference on Optical Network Design and Modeling (ONDM), (Institute of Electrical and Electronics Engineers, 2015), pp. 63–67.
[Crossref]

Forghieri, F.

Fresi, F.

M. Secondini, S. Rommel, G. Meloni, F. Fresi, E. Forestieri, and L. Potì, “Single-step digital backpropagation for nonlinearity mitigation,” Photonic Netw. Commun. 31(3), 493–502 (2016).
[Crossref]

M. Secondini, S. Rommel, F. Fresi, E. Forestieri, G. Meloni, and L. Potì, “Coherent 100G nonlinear compensation with single-step digital backpropagation,” in Proceedings of International Conference on Optical Network Design and Modeling (ONDM), (Institute of Electrical and Electronics Engineers, 2015), pp. 63–67.
[Crossref]

Friberg, A. T.

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]

Gaudino, R.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Suppression of spurious tones induced by the split-step method in fiber systems simulation,” IEEE Photonics Technol. Lett. 12(5), 489–491 (2000).
[Crossref]

Guiomar, F. P.

F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express 20(2), 1360–1369 (2012).
[Crossref] [PubMed]

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities,” Opt. Express (to appear).

Hanik, N.

Ip, E. M.

Irukulapati, N. V.

Ishihara, K.

Jacobsen, G.

Jiang, Y.

Johannisson, P.

L. Beygi, N. V. Irukulapati, E. Agrell, P. Johannisson, M. Karlsson, H. Wymeersch, P. Serena, and A. Bononi, “On nonlinearly-induced noise in single-channel optical links with digital backpropagation,” Opt. Express 21(22), 26376–26386 (2013).
[Crossref] [PubMed]

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]

Kahn, J. M.

Karlsson, M.

L. Beygi, N. V. Irukulapati, E. Agrell, P. Johannisson, M. Karlsson, H. Wymeersch, P. Serena, and A. Bononi, “On nonlinearly-induced noise in single-channel optical links with digital backpropagation,” Opt. Express 21(22), 26376–26386 (2013).
[Crossref] [PubMed]

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]

Kavcic, A.

D. Arnold, H.-A. Loeliger, P. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory 52(8), 3498–3508 (2006).
[Crossref]

Killey, R. I.

D. Semrau, T. Xu, N. A. Shevchenko, M. Paskov, A. Alvarado, R. I. Killey, and P. Bayvel, “Achievable information rates estimates in optically amplified transmission systems using nonlinearity compensation and probabilistic shaping,” Opt. Lett. 42(1), 121–124 (2017).
[Crossref] [PubMed]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (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 multi-channel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref] [PubMed]

G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
[Crossref] [PubMed]

Kobayashi, T.

Kschischang, F. R.

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part I-III: Numerical methods,” IEEE Trans. Inf. Theory 60(7), 4329–4345 (2014).
[Crossref]

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities,” Opt. Express (to appear).

Kudo, R.

Kuo, B. P.-P.

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
[Crossref] [PubMed]

Kuschnerov, M.

Lavery, D.

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (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 multi-channel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref] [PubMed]

Li, J.

Liga, G.

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (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 multi-channel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref] [PubMed]

G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
[Crossref] [PubMed]

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities,” Opt. Express (to appear).

Liu, L.

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
[Crossref] [PubMed]

Liu, X.

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

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

Loeliger, H.-A.

D. Arnold, H.-A. Loeliger, P. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory 52(8), 3498–3508 (2006).
[Crossref]

Maalej, Z.

Maher, R.

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (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]

Mecozzi, A.

Meloni, G.

M. Secondini, S. Rommel, G. Meloni, F. Fresi, E. Forestieri, and L. Potì, “Single-step digital backpropagation for nonlinearity mitigation,” Photonic Netw. Commun. 31(3), 493–502 (2016).
[Crossref]

M. Secondini, S. Rommel, F. Fresi, E. Forestieri, G. Meloni, and L. Potì, “Coherent 100G nonlinear compensation with single-step digital backpropagation,” in Proceedings of International Conference on Optical Network Design and Modeling (ONDM), (Institute of Electrical and Electronics Engineers, 2015), pp. 63–67.
[Crossref]

Mitra, P. P.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Miyamoto, Y.

Myslivets, E.

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
[Crossref] [PubMed]

Napoli, A.

Nölle, M.

Paskov, M.

Pinto, A. N.

Poggiolini, P.

Popov, S.

Potì, L.

M. Secondini, S. Rommel, G. Meloni, F. Fresi, E. Forestieri, and L. Potì, “Single-step digital backpropagation for nonlinearity mitigation,” Photonic Netw. Commun. 31(3), 493–502 (2016).
[Crossref]

M. Secondini, S. Rommel, F. Fresi, E. Forestieri, G. Meloni, and L. Potì, “Coherent 100G nonlinear compensation with single-step digital backpropagation,” in Proceedings of International Conference on Optical Network Design and Modeling (ONDM), (Institute of Electrical and Electronics Engineers, 2015), pp. 63–67.
[Crossref]

Prati, G.

Radic, S.

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
[Crossref] [PubMed]

Rafique, D.

Rahman, T.

Reis, J. D.

Rommel, S.

M. Secondini, S. Rommel, G. Meloni, F. Fresi, E. Forestieri, and L. Potì, “Single-step digital backpropagation for nonlinearity mitigation,” Photonic Netw. Commun. 31(3), 493–502 (2016).
[Crossref]

M. Secondini, S. Rommel, F. Fresi, E. Forestieri, G. Meloni, and L. Potì, “Coherent 100G nonlinear compensation with single-step digital backpropagation,” in Proceedings of International Conference on Optical Network Design and Modeling (ONDM), (Institute of Electrical and Electronics Engineers, 2015), pp. 63–67.
[Crossref]

Sano, A.

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.

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 multi-channel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
[Crossref] [PubMed]

Schubert, C.

Secondini, M.

M. Secondini, S. Rommel, G. Meloni, F. Fresi, E. Forestieri, and L. Potì, “Single-step digital backpropagation for nonlinearity mitigation,” Photonic Netw. Commun. 31(3), 493–502 (2016).
[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]

M. Secondini, S. Rommel, F. Fresi, E. Forestieri, G. Meloni, and L. Potì, “Coherent 100G nonlinear compensation with single-step digital backpropagation,” in Proceedings of International Conference on Optical Network Design and Modeling (ONDM), (Institute of Electrical and Electronics Engineers, 2015), pp. 63–67.
[Crossref]

Semrau, D.

Serena, P.

Shevchenko, N. A.

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]

Shtaif, M.

Sleiffer, V. A. J. M.

Spinnler, B.

Stark, J. B.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Takatori, Y.

Tanimura, T.

Teixeira, A. L.

Temprana, E.

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
[Crossref] [PubMed]

Thomsen, B. C.

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 multi-channel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
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Timmers, E.

Tkach, R. W.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
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R.-J. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
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Vanin, E.

Vontobel, P.

D. Arnold, H.-A. Loeliger, P. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory 52(8), 3498–3508 (2006).
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Wang, K.

Winzer, P. J.

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
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X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Wymeersch, H.

Xu, T.

D. Semrau, T. Xu, N. A. Shevchenko, M. Paskov, A. Alvarado, R. I. Killey, and P. Bayvel, “Achievable information rates estimates in optically amplified transmission systems using nonlinearity compensation and probabilistic shaping,” Opt. Lett. 42(1), 121–124 (2017).
[Crossref] [PubMed]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (2016).
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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 multi-channel digital back-propagation,” Sci. Rep. 5, 13990 (2015).
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G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
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T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010).
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J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities,” Opt. Express (to appear).

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M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part I-III: Numerical methods,” IEEE Trans. Inf. Theory 60(7), 4329–4345 (2014).
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D. Arnold, H.-A. Loeliger, P. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory 52(8), 3498–3508 (2006).
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Zhang, Y.

IEEE Photonics Technol. Lett. (1)

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IEEE Signal Process. Mag. (1)

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IEEE Trans. Inf. Theory (2)

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D. Arnold, H.-A. Loeliger, P. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory 52(8), 3498–3508 (2006).
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Nat. Photonics (1)

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
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Nature (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
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Opt. Express (10)

F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express 20(2), 1360–1369 (2012).
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G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
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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).
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D. Rafique and A. D. 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).
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L. Beygi, N. V. Irukulapati, E. Agrell, P. Johannisson, M. Karlsson, H. Wymeersch, P. Serena, and A. Bononi, “On nonlinearly-induced noise in single-channel optical links with digital backpropagation,” Opt. Express 21(22), 26376–26386 (2013).
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T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010).
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Opt. Lett. (1)

Philos Trans A Math Phys Eng Sci (1)

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (2016).
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Photonic Netw. Commun. (1)

M. Secondini, S. Rommel, G. Meloni, F. Fresi, E. Forestieri, and L. Potì, “Single-step digital backpropagation for nonlinearity mitigation,” Photonic Netw. Commun. 31(3), 493–502 (2016).
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Proc. IEEE (1)

R.-J. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
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Sci. Rep. (2)

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).
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Science (1)

E. Temprana, E. Myslivets, B. P.-P. Kuo, L. Liu, V. Ataie, N. Alic, and S. Radic, “APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science 348(6242), 1445–1448 (2015).
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A. Bononi and P. Serena, “On the accuracy of the Gaussian nonlinear model for dispersion-unmanaged coherent links,” in Proceedings of European Conference on Optical Communication (ECOC), (Institute of Electrical and Electronics Engineers, 2013), paper Th.1.D.3.
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M. Secondini, S. Rommel, F. Fresi, E. Forestieri, G. Meloni, and L. Potì, “Coherent 100G nonlinear compensation with single-step digital backpropagation,” in Proceedings of International Conference on Optical Network Design and Modeling (ONDM), (Institute of Electrical and Electronics Engineers, 2015), pp. 63–67.
[Crossref]

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities,” Opt. Express (to appear).

P. Poggiolini, Y. Jiang, A. Carena, and F. Forghieri, “Analytical modeling of the impact of fiber non-linear propagation on coherent systems and networks,” Chapter 7 in Enabling Technologies for High Spectral-efficiency Coherent Optical Communication Networks, 247–309 (2016).

L. Szczecinski and A. Alvarado, Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design (John Wiley & Sons, Inc., 2015).

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Figures (10)

Fig. 1
Fig. 1 Schematic of the 9-channel Nyquist-spaced optical fibre communication system using EDC and MC-DBP. (NPS: Nyquist pulse shaping, PBS: polarisation beam splitter, PBC: polarisation beam combiner, LO: local oscillator, ADC: analogue-to-digital convertor, MI: mutual information)
Fig. 2
Fig. 2 Theoretical symbol-wise soft-decision MI versus SNR per symbol for dual-polarisation systems using different modulation formats under the assumption of a Gaussian channel law.
Fig. 3
Fig. 3 Simulation results of SNR versus optical launch power at different back-propagated bandwidths for different modulation formats.
Fig. 4
Fig. 4 Simulation results of SNR versus number of steps per span in MC-DBP at different back-propagated bandwidths for different modulation formats.
Fig. 5
Fig. 5 Simulation results of AIR versus number of steps per span in MC-DBP for different modulation formats. (a) 1-channel DBP (32 GHz), (b) 3-channel DBP (96 GHz), (c) 5-channel DBP (160 GHz), (d) 7-channel DBP (224 GHz), (e) 9-channel DBP (288 GHz).
Fig. 6
Fig. 6 Simulation results of AIR versus optical launch power at different back-propagated bandwidths for different modulation formats. The transmission distance is 2000 km.
Fig. 7
Fig. 7 Analytical and simulation results of AIRs (at optimum optical launch power) versus back-propagated number of channels for different modulation formats. Transmission distance is 2000 km. S: simulation results, T: theoretical model.
Fig. 8
Fig. 8 Analytical prediction of AIRs versus transmission distances at different back-propagated bandwidths for different modulation formats.
Fig. 9
Fig. 9 Simulation results of SNR versus optical launch power using 1-channel DBP for different modulation formats. (The transmission distance is 2000 km, and the 1-channel DBP is applied with 1 step/span).
Fig. 10
Fig. 10 Simulation results of AIR versus optical launch power using 1-channel DBP for different modulation formats. (The transmission distance is 2000 km, and the 1-channel DBP is applied with 1 step/span).

Tables (3)

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Table 1 Transmission System Parameters

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Table 2 Parameters in Analytical Model

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Table 3 Minimum required number of steps per span

Equations (11)

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SNR= P σ eff 2 P σ ASE 2 + σ SS 2 + σ SN 2 ,
σ ASE 2 = N s ( G1 ) F n h ν 0 R S ,
σ SS 2 = N s ε+1 η P 3 ,
σ SN 2 3ςη σ ASE 2 P 2 ,
ς= n=1 N s n ε+1 N s ε+1 2 + N s ε+2 ε+2 .
η( N ch ) η 0 ( N ch ) 80 81 κ γ 2 L eff 2 π| β 2 | L s R S 2 [ ψ( N ch +1 2 )+C+1 ],
η 0 ( N ch ) ( 2 3 ) 3 α γ 2 L eff 2 π| β 2 | R S 2 arsinh( π 2 2 | β 2 | L eff N ch 2 R S 2 ),
σ SS 2 = N s ε+1 [ η( N ch )η( N ch (DBP) ) ] P 3 ,
MI= 2 M xX C P Y|X ( y|x ) log 2 P Y|X ( y|x ) 1 M x X P Y|X ( y| x ) dy,
P Y|X ( y|x )= 1 π σ z 2 exp( | yx | 2 σ z 2 ).
AIR= N ch R S MI.

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