Abstract

For probabilistic amplitude shaping (PAS), we propose a super-symbol transmission method that improves fiber nonlinearity tolerance. A simple fiber nonlinearity low-pass filtering model, as well as its interaction with the spectral dip of signal’s intensity waveform, is provided to explain the origin of this nonlinear benefit. With 25-GHz-spaced, 26 × 22.5 GBaud dual-polarized PAS-64 quadrature amplitude modulation (QAM) signals transmitted over 12 spans of 80-km standard single mode fiber (SSMF), the proposed method is found to provide ∼0.15-dB gain over the previous finite-blocklength method with intra-DM pairing, ∼0.26-dB gain over finite-blocklength method with inter-DM pairing, and ∼0.44-dB benefit over the traditional method, all with a feasible blocklength at 200.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. ECOC, Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.
  2. J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.
  3. Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.
  4. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” 2014 IEEE International Symposium on Information Theory, Honolulu, HI, 2014, pp. 2794–2798.
  5. K. Roberts, M. O’Sullivan, M. Reimer, and M. Hubbard, “Nonlinear mitigation enabling next generation high speed optical transport beyond 100G,” in Optical Fiber Communication Conference (OFC) 2019, OSA Technical Digest (Optical Society of America, 2019), paper M3J.1.
  6. M. P. Yankov, K. J. Larsen, and S. Forchhammer, “Temporal probabilistic shaping for mitigation of nonlinearities in optical fiber systems,” J. Lightwave Technol. 35(10), 1803–1810 (2017).
    [Crossref]
  7. M. N. Tehrani, M. Torbatian, H. Sun, P. Mertz, and K. Wu, “A novel nonlinearity tolerant super-Gaussian distribution for probabilistically shaped modulation,” 2018 European Conference on Optical Communication (ECOC), Rome, 2018, pp. 1–3, doi: 10.1109/ECOC.2018.8535379.
  8. Q. Guo, W.-R. Peng, Y. Cui, and Y. Bai, “Multi-dimensional probabilistic shaping for higher fiber nonlinearity tolerance,” ECOC’19, Paper P70.
  9. A. Amari, S. Goossens, Y. C. Gultekin, O. Vassilieva, I. Kim, T. Ikeuchi, C. Okonkwo, F. M. J. Willems, and A. Alvarado, “Introducing enumerative sphere shaping for optical communication systems with short blocklengths,” J. Lightwave Technol. 37(23), 5926–5936 (2019).
    [Crossref]
  10. T. Fehenberger, H. Griesser, and J. Elbers, “Mitigating fiber nonlinearities by short-length probabilistic shaping,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper Th1I.2.
  11. T. Fehenberger, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, and H. Griesser, “Analysis of nonlinear fiber interactions for finite-length constant-composition sequences,” J. Lightwave Technol. 38(2), 457–465 (2020).
    [Crossref]
  12. W.-R Peng, Y. Cui, and Yusheng Bai, “Super-symbol signaling for optical communication,” filed for IP application, Oct. 2019.
  13. W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).
  14. G. Pierobon, “Codes for zero spectral density at zero frequency (Corresp.),” IEEE Trans. Inf. Theory 30(2), 435–439 (1984).
    [Crossref]
  15. Z. Tao, W. Yan, L. Li, L. Liu, S. Oda, T. Hoshida, and J. C. Rusmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
    [Crossref]
  16. R. Laroia, N. Farvardin, and S. A. Tretter, “On optimal shaping of multidimensional constellations,” J. Lightwave Technol. 40(4), 1044–1056 (1994).
    [Crossref]
  17. J. Cho, X. Chen, S. Chandrasekhar, and P. Winzer, “On line rates, information rates, and spectral efficiencies in probabilistically shaped QAM systems,” Opt. Express 26(8), 9784–9791 (2018).
    [Crossref]
  18. W. Peng, Zhihong Li, Fei Zhu, and Yusheng Bai, “Training-based determination of perturbation coefficients for fiber nonlinearity mitigation,” 2015 Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, 2015, Paper Th3D2.

2020 (1)

2019 (1)

2018 (1)

2017 (1)

2011 (1)

1994 (1)

R. Laroia, N. Farvardin, and S. A. Tretter, “On optimal shaping of multidimensional constellations,” J. Lightwave Technol. 40(4), 1044–1056 (1994).
[Crossref]

1984 (1)

G. Pierobon, “Codes for zero spectral density at zero frequency (Corresp.),” IEEE Trans. Inf. Theory 30(2), 435–439 (1984).
[Crossref]

Alvarado, A.

Amari, A.

Bai, Y.

Q. Guo, W.-R. Peng, Y. Cui, and Y. Bai, “Multi-dimensional probabilistic shaping for higher fiber nonlinearity tolerance,” ECOC’19, Paper P70.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

Bai, Yusheng

W.-R Peng, Y. Cui, and Yusheng Bai, “Super-symbol signaling for optical communication,” filed for IP application, Oct. 2019.

W. Peng, Zhihong Li, Fei Zhu, and Yusheng Bai, “Training-based determination of perturbation coefficients for fiber nonlinearity mitigation,” 2015 Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, 2015, Paper Th3D2.

Bocherer, G.

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. ECOC, Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.

Buchali, F.

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. ECOC, Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.

Chandrasekhar, S.

Chen, X.

Cho, J.

Chowdhury, S.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

Cui, Y.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

W.-R Peng, Y. Cui, and Yusheng Bai, “Super-symbol signaling for optical communication,” filed for IP application, Oct. 2019.

Q. Guo, W.-R. Peng, Y. Cui, and Y. Bai, “Multi-dimensional probabilistic shaping for higher fiber nonlinearity tolerance,” ECOC’19, Paper P70.

Dar, R.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” 2014 IEEE International Symposium on Information Theory, Honolulu, HI, 2014, pp. 2794–2798.

Dou, L.

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

Elbers, J.

T. Fehenberger, H. Griesser, and J. Elbers, “Mitigating fiber nonlinearities by short-length probabilistic shaping,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper Th1I.2.

Farvardin, N.

R. Laroia, N. Farvardin, and S. A. Tretter, “On optimal shaping of multidimensional constellations,” J. Lightwave Technol. 40(4), 1044–1056 (1994).
[Crossref]

Feder, M.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” 2014 IEEE International Symposium on Information Theory, Honolulu, HI, 2014, pp. 2794–2798.

Fehenberger, T.

T. Fehenberger, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, and H. Griesser, “Analysis of nonlinear fiber interactions for finite-length constant-composition sequences,” J. Lightwave Technol. 38(2), 457–465 (2020).
[Crossref]

T. Fehenberger, H. Griesser, and J. Elbers, “Mitigating fiber nonlinearities by short-length probabilistic shaping,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper Th1I.2.

Forchhammer, S.

Goossens, S.

Griesser, H.

T. Fehenberger, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, and H. Griesser, “Analysis of nonlinear fiber interactions for finite-length constant-composition sequences,” J. Lightwave Technol. 38(2), 457–465 (2020).
[Crossref]

T. Fehenberger, H. Griesser, and J. Elbers, “Mitigating fiber nonlinearities by short-length probabilistic shaping,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper Th1I.2.

Gultekin, Y. C.

Guo, Q.

Q. Guo, W.-R. Peng, Y. Cui, and Y. Bai, “Multi-dimensional probabilistic shaping for higher fiber nonlinearity tolerance,” ECOC’19, Paper P70.

Hoshida, T.

Z. Tao, W. Yan, L. Li, L. Liu, S. Oda, T. Hoshida, and J. C. Rusmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

Hubbard, M.

K. Roberts, M. O’Sullivan, M. Reimer, and M. Hubbard, “Nonlinear mitigation enabling next generation high speed optical transport beyond 100G,” in Optical Fiber Communication Conference (OFC) 2019, OSA Technical Digest (Optical Society of America, 2019), paper M3J.1.

Huo, X.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Idler, W.

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. ECOC, Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.

Ikeuchi, T.

Kan, C.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

Kim, I.

Koike-Akino, T.

Kojima, K.

Laroia, R.

R. Laroia, N. Farvardin, and S. A. Tretter, “On optimal shaping of multidimensional constellations,” J. Lightwave Technol. 40(4), 1044–1056 (1994).
[Crossref]

Larsen, K. J.

Li, A.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

Li, J.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Li, L.

Z. Tao, W. Yan, L. Li, L. Liu, S. Oda, T. Hoshida, and J. C. Rusmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

Li, Z.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

Li, Zhihong

W. Peng, Zhihong Li, Fei Zhu, and Yusheng Bai, “Training-based determination of perturbation coefficients for fiber nonlinearity mitigation,” 2015 Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, 2015, Paper Th3D2.

Liu, L.

Liu, X.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Mecozzi, A.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” 2014 IEEE International Symposium on Information Theory, Honolulu, HI, 2014, pp. 2794–2798.

Mertz, P.

M. N. Tehrani, M. Torbatian, H. Sun, P. Mertz, and K. Wu, “A novel nonlinearity tolerant super-Gaussian distribution for probabilistically shaped modulation,” 2018 European Conference on Optical Communication (ECOC), Rome, 2018, pp. 1–3, doi: 10.1109/ECOC.2018.8535379.

Millar, D. S.

O’Sullivan, M.

K. Roberts, M. O’Sullivan, M. Reimer, and M. Hubbard, “Nonlinear mitigation enabling next generation high speed optical transport beyond 100G,” in Optical Fiber Communication Conference (OFC) 2019, OSA Technical Digest (Optical Society of America, 2019), paper M3J.1.

Oda, S.

Z. Tao, W. Yan, L. Li, L. Liu, S. Oda, T. Hoshida, and J. C. Rusmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

Okonkwo, C.

Parsons, K.

Peng, W.

W. Peng, Zhihong Li, Fei Zhu, and Yusheng Bai, “Training-based determination of perturbation coefficients for fiber nonlinearity mitigation,” 2015 Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, 2015, Paper Th3D2.

Peng, W.-R

W.-R Peng, Y. Cui, and Yusheng Bai, “Super-symbol signaling for optical communication,” filed for IP application, Oct. 2019.

Peng, W.-R.

Q. Guo, W.-R. Peng, Y. Cui, and Y. Bai, “Multi-dimensional probabilistic shaping for higher fiber nonlinearity tolerance,” ECOC’19, Paper P70.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

Pierobon, G.

G. Pierobon, “Codes for zero spectral density at zero frequency (Corresp.),” IEEE Trans. Inf. Theory 30(2), 435–439 (1984).
[Crossref]

Qu, W.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Reimer, M.

K. Roberts, M. O’Sullivan, M. Reimer, and M. Hubbard, “Nonlinear mitigation enabling next generation high speed optical transport beyond 100G,” in Optical Fiber Communication Conference (OFC) 2019, OSA Technical Digest (Optical Society of America, 2019), paper M3J.1.

Roberts, K.

K. Roberts, M. O’Sullivan, M. Reimer, and M. Hubbard, “Nonlinear mitigation enabling next generation high speed optical transport beyond 100G,” in Optical Fiber Communication Conference (OFC) 2019, OSA Technical Digest (Optical Society of America, 2019), paper M3J.1.

Rusmussen, J. C.

Z. Tao, W. Yan, L. Li, L. Liu, S. Oda, T. Hoshida, and J. C. Rusmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

Schmalen, L.

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. ECOC, Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.

Schulte, P.

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. ECOC, Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.

Shtaif, M.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” 2014 IEEE International Symposium on Information Theory, Honolulu, HI, 2014, pp. 2794–2798.

Si, M.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Steiner, F.

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. ECOC, Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.

Sun, H.

M. N. Tehrani, M. Torbatian, H. Sun, P. Mertz, and K. Wu, “A novel nonlinearity tolerant super-Gaussian distribution for probabilistically shaped modulation,” 2018 European Conference on Optical Communication (ECOC), Rome, 2018, pp. 1–3, doi: 10.1109/ECOC.2018.8535379.

Tanimura, T.

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

Tao, Z.

Z. Tao, W. Yan, L. Li, L. Liu, S. Oda, T. Hoshida, and J. C. Rusmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

Tehrani, M. N.

M. N. Tehrani, M. Torbatian, H. Sun, P. Mertz, and K. Wu, “A novel nonlinearity tolerant super-Gaussian distribution for probabilistically shaped modulation,” 2018 European Conference on Optical Communication (ECOC), Rome, 2018, pp. 1–3, doi: 10.1109/ECOC.2018.8535379.

Torbatian, M.

M. N. Tehrani, M. Torbatian, H. Sun, P. Mertz, and K. Wu, “A novel nonlinearity tolerant super-Gaussian distribution for probabilistically shaped modulation,” 2018 European Conference on Optical Communication (ECOC), Rome, 2018, pp. 1–3, doi: 10.1109/ECOC.2018.8535379.

Tretter, S. A.

R. Laroia, N. Farvardin, and S. A. Tretter, “On optimal shaping of multidimensional constellations,” J. Lightwave Technol. 40(4), 1044–1056 (1994).
[Crossref]

Vassilieva, O.

Wang, J.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Wang, Y.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Willems, F. M. J.

Winzer, P.

Wu, K.

M. N. Tehrani, M. Torbatian, H. Sun, P. Mertz, and K. Wu, “A novel nonlinearity tolerant super-Gaussian distribution for probabilistically shaped modulation,” 2018 European Conference on Optical Communication (ECOC), Rome, 2018, pp. 1–3, doi: 10.1109/ECOC.2018.8535379.

Yan, W.

Z. Tao, W. Yan, L. Li, L. Liu, S. Oda, T. Hoshida, and J. C. Rusmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

Yang, Q.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Yankov, M. P.

Zhang, A.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Zhang, C.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Zhang, J.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Zhang, Z.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Zhu, Fei

W. Peng, Zhihong Li, Fei Zhu, and Yusheng Bai, “Training-based determination of perturbation coefficients for fiber nonlinearity mitigation,” 2015 Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, 2015, Paper Th3D2.

Zhu, Y.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

IEEE Trans. Inf. Theory (1)

G. Pierobon, “Codes for zero spectral density at zero frequency (Corresp.),” IEEE Trans. Inf. Theory 30(2), 435–439 (1984).
[Crossref]

J. Lightwave Technol. (5)

Opt. Express (1)

Other (11)

W. Peng, Zhihong Li, Fei Zhu, and Yusheng Bai, “Training-based determination of perturbation coefficients for fiber nonlinearity mitigation,” 2015 Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, 2015, Paper Th3D2.

W.-R Peng, Y. Cui, and Yusheng Bai, “Super-symbol signaling for optical communication,” filed for IP application, Oct. 2019.

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rusmussen, “Low-complexity digital perturbation back-propagation,” ECOC’11, Paper Tu3A2, (2011).

T. Fehenberger, H. Griesser, and J. Elbers, “Mitigating fiber nonlinearities by short-length probabilistic shaping,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper Th1I.2.

M. N. Tehrani, M. Torbatian, H. Sun, P. Mertz, and K. Wu, “A novel nonlinearity tolerant super-Gaussian distribution for probabilistically shaped modulation,” 2018 European Conference on Optical Communication (ECOC), Rome, 2018, pp. 1–3, doi: 10.1109/ECOC.2018.8535379.

Q. Guo, W.-R. Peng, Y. Cui, and Y. Bai, “Multi-dimensional probabilistic shaping for higher fiber nonlinearity tolerance,” ECOC’19, Paper P70.

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. ECOC, Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.

J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” OFC’17, Paper M3C1.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “On shaping gain in the nonlinear fiber-optic channel,” 2014 IEEE International Symposium on Information Theory, Honolulu, HI, 2014, pp. 2794–2798.

K. Roberts, M. O’Sullivan, M. Reimer, and M. Hubbard, “Nonlinear mitigation enabling next generation high speed optical transport beyond 100G,” in Optical Fiber Communication Conference (OFC) 2019, OSA Technical Digest (Optical Society of America, 2019), paper M3J.1.

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Figures (6)
Fig. 1.
Fig. 1. Four transmission methods for probabilistic amplitude shaping (PAS): (a) Traditional method (TRA): the shaped symbols from an amplitude shaper (AS) block are broken up due to the bit/symbol inter-leaver. (b) Previous finite-blocklength method with inter-AS paring (FBLwItr): each AS block is carried by one tributary and the four blocks over all tributaries are temporally-aligned. (c) Previous finite-blocklength method with intra-AS paring (FBLwIra): each AS block is divided into 2 subblocks carried by both tributaries of one polarization and the four subblocks across all tributaries are temporally-aligned. (c) Proposed super-symbol method (SUP): each AS block is divided into 4 subblocks carried by all the 4 tributaries and the four subblocks across all tributaries are temporally-aligned. A super symbol comprises all the shaped symbols from only a certain AS block. Note that for FBLwItr, FBLwIra, and SUP, the permutation caused by the bit/symbol inter-lever is assumed undone. A practical solution to undo this permutation is discussed in the end of Section 3.

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Fig. 2.
Fig. 2. Principle diagram of the resultant SPM power for (a) traditional method, (b) previous finite blocklength method with inter-AS pairing, (c) previous finite blocklength method with intra-AS pairing, (d) proposed super-symbol method. PSD: power spectral density, ${P_{xy}}$: intensity waveform of both polarizations, ${P_{avg}}:$ the average power of both polarizations, ${h_{spm}}$: the SPM filter, typically a low-pass filter. Note this principle diagram is also applicable to XPM by replacing ${P_{xy}}$, ${P_{avg}}$ and ${h_{xpm}}$ with ${P_{xy,u}}$, ${P_{avg,u}}$ and ${h_{xpm,u}}$, respectively, with u being the channel index of interfering channel.

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Fig. 3.
Fig. 3. (a) The measured power spectral density of the offset intensity waveform $[{{P_{xy}}(\textrm{t} )- {P_{avg}}} ]$ of the four methods with a block length at 40. (b) The passband power profiles of the SPM filter and the XPM filters with the 1st to 4th neighboring (interfering) channels. The labels on the XPM filters indicate the spacing between the probe and interfering channel. The spectral resolution is fixed at 10 MHz.

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Fig. 4.
Fig. 4. PSD at ∼DC frequencies with different blocklengths. (a) blocklength = 40, (b) 120, and (c) 200. Resolution bandwidth is 10 MHz.

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Fig. 5.
Fig. 5. The optical -signal-to-noise ratio (OSNR) margin to achieve BER = 2.1e-2 after transmission over 12 × 80 km SSMF, (a) single channel with a block length at 40. The inset depicts the respective constellation diagrams at ∼2 dBm without ASE loading. (b) 26 channels with a block length at 40, (c) 26 channels with a block length at 120, and (d) 26 channels with a block length at 200. The insets of (b)-(c) illustrate the respective constellation diagrams at −0.5 dBm without ASE loading.

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Fig. 6.
Fig. 6. One possible PAS architecture to accommodate the proposed SUP. This may applicable to both FBLs.

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Tables (1)

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Table 1. Level distribution of shell mapping with three block lengths at 40, 120, and 200.

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Equations (5)

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E x ′ ( t ) ≈ E x ( t ) ∗ exp { j κ [ | E x ( t ) | 2 + P x y ( t ) ] ⊗ h s p m ( t ) }
E y ′ ( t ) ≈ E y ( t ) ∗ exp { j κ [ | E y ( t ) | 2 + P x y ( t ) ] ⊗ h s p m ( t ) }
E x ′ ′ ( t ) ≈ E x ( t ) ∗ exp { j κ [ | E x , u ( t ) | 2 + P x y , u ( t ) ] ⊗ h x p m , u ( t ) }
E y ′ ′ ( t ) ≈ E y ( t ) ∗ exp { j κ [ | E y , u ( t ) | 2 + P x y , u ( t ) ] ⊗ h x p m , u ( t ) }
h s p m ( n ) = ∫ 0 L ⁡ d z f ( z ) ∫ d t | U ( z , t ) | 2 ∗ | U ( z , t − n T s ) | 2

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