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Optica Publishing Group
  • Journal of Lightwave Technology
  • Vol. 39,
  • Issue 21,
  • pp. 6733-6745
  • (2021)

Transfer Learning for Neural Networks-Based Equalizers in Coherent Optical Systems

Open Access Open Access

Abstract

In this work, we address the question of the adaptability of artificial neural networks (NNs) used for impairments mitigation in optical transmission systems. We demonstrate that by using well-developed techniques based on the concept of transfer learning, we can efficaciously retrain NN-based equalizers to adapt to the changes in the transmission system, using just a fraction (down to 1%) of the initial training data or epochs. We evaluate the capability of transfer learning to adapt the NN to changes in the launch power, modulation format, symbol rate, or even fiber plants (different fiber types and lengths). The numerical examples utilize the recently introduced NN equalizer consisting of a convolutional layer coupled with bi-directional long-short term memory (biLSTM) recurrent NN element. Our analysis focuses on long-haul coherent optical transmission systems for two types of fibers: the standard single-mode fiber (SSMF) and the TrueWave Classic (TWC) fiber. We underline the specific peculiarities that occur when transferring the learning in coherent optical communication systems and draw the limits for the transfer learning efficiency. Our results demonstrate the effectiveness of transfer learning for the fast adaptation of NN architectures to different transmission regimes and scenarios, paving the way for engineering flexible and universal solutions for nonlinearity mitigation.

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2021 (6)

C. Häger and H. D. Pfister, “Physics-based deep learning for fiber-optic communication systems,” IEEE J. Sel. Areas Commun., vol. 39, no. 1, pp. 280–294, 2021.

P. J. Freire, “Complex-valued neural network design for mitigation of signal distortions in optical links,” J. Lightw. Technol., vol. 39, no. 6, pp. 1696–1705, 2021.

O. Sidelnikov, A. Redyuk, S. Sygletos, M. Fedoruk, and S. K. Turitsyn, “Advanced convolutional neural networks for nonlinearity mitigation in long-haul WDM transmission systems,” J. Lightw. Technol., vol. 39, no. 8, pp. 2397–2406, 2021.

O. Kotlyar, M. Kamalian-Kopae, M. Pankratova, A. Vasylchenkova, J. E. Prilepsky, and S. K. Turitsyn, “Convolutional long short-term memory neural network equalizer for nonlinear fourier transform-based optical transmission systems,” Opt. Exp., vol. 29, no. 7, pp. 11254–11267, 2021.

M. Sena, “Bayesian optimization for nonlinear system identification and pre-distortion in cognitive transmitters,” J. Lightw. Technol., vol. 39, no. 15, pp. 5008–5020, 2021.

X. Liu, Y. Wang, X. Wang, H. Xu, C. Li, and X. Xin, “Bi-directional gated recurrent unit neural network based nonlinear equalizer for coherent optical communication system,” Opt. Exp., vol. 29, no. 4, pp. 5923–5933, 2021.

2020 (8)

Z. Xu, C. Sun, T. Ji, J. H. Manton, and W. Shieh, “Feedforward and recurrent neural network-based transfer learning for nonlinear equalization in short-reach optical links,” J. Lightw. Technol., vol. 39, no. 2, pp. 475–480, 2020.

S. Deligiannidis, A. Bogris, C. Mesaritakis, and Y. Kopsinis, “Compensation of fiber nonlinearities in digital coherent systems leveraging long short-term memory neural networks,” J. Lightw. Technol., vol. 38, no. 21, pp. 5991–5999, 2020.

F. Qamar, M. K. Islam, R. Shahzadi, S. Z. Ali, and M. Ali, “128-QAM dual-polarization chaotic long-haul system performance evaluation,” J. Opt. Commun., 2020.

A. Ghazisaeidi, “Deep learning based digital backpropagation demonstrating SNR gain at low complexity in a 1200 km transmission link,” Opt. Exp., vol. 28, no. 20, pp. 29 318–29 334, 2020.

Y. Cheng, W. Zhang, S. Fu, M. Tang, and D. Liu, “Transfer learning simplified multi-task deep neural network for PDM-64QAM optical performance monitoring,” Opt. Exp., vol. 28, no. 5, pp. 7607–7617, 2020.

Z. Gao, “Ann-based multi-channel qot-prediction over a 563.4-km field-trial testbed,” J. Lightw. Technol., vol. 38, no. 9, pp. 2646–2655, 2020.

D. Zibar, F. Da Ros, G. Brajato, and U. C. de Moura, “Toward intelligence in photonic systems,” Opt. Photon. News, vol. 31, no. 3, pp. 34–41, 2020.

Q. Fan, G. Zhou, T. Gui, C. Lu, and A. P. T. Lau, “Advancing theoretical understanding and practical performance of signal processing for nonlinear optical communications through machine learning,” Nature Commun., vol. 11, no. 1, p. 3694, 2020.

2019 (5)

S. Zhang, “Field and lab experimental demonstration of nonlinear impairment compensation using neural networks,” Nature Commun., vol. 10, no. 1, pp. 1–8, 2019.

Q. Yao, H. Yang, A. Yu, and J. Zhang, “Transductive transfer learning-based spectrum optimization for resource reservation in seven-core elastic optical networks,” J. Lightw. Technol., vol. 37, no. 16, pp. 4164–4172, 2019.

J. Zhang, L. Xia, M. Zhu, S. Hu, B. Xu, and K. Qiu, “Fast remodeling for nonlinear distortion mitigation based on transfer learning,” Opt. Lett., vol. 44, no. 17, pp. 4243–4246, 2019.

L. Xia, J. Zhang, S. Hu, M. Zhu, Y. Song, and K. Qiu, “Transfer learning assisted deep neural network for OSNR estimation,” Opt. Exp., vol. 27, no. 14, pp. 19 398–19 406, 2019.

F. Musumeci, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surveys Tuts., vol. 21, no. 2, pp. 1383–1408, 2019.

2018 (3)

O. Sidelnikov, A. Redyuk, and S. Sygletos, “Equalization performance and complexity analysis of dynamic deep neural networks in long haul transmission systems,” Opt. Exp., vol. 26, no. 25, pp. 32 765–32 776, 2018.

A. Sarwar, F. Qamar, and M. Ahmad, “Performance analysis of 128-QAM dual polarization system for long haul optical communication,” Pakistan J. Sci., vol. 70, no. 4, p. 324, 2018. [Online]. Available: https://www.proquest.com/openview/0967b245cfa0cd11c1351860e82991d7/1?pq-origsite=gscholar&cbl=1616340

S. Gaiarin, A. M. Perego, E. P. daF. SilvaRos, and D. Zibar, “Dual-polarization nonlinear fourier transform-based optical communication system,” Optica, vol. 5, no. 3, pp. 263–270, 2018.

2017 (4)

G. Khanna “Single-carrier 400G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photon. Technol. Lett., vol. 29, no. 2, pp. 189–192, 2017.

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: Possible pitfalls,” IEEE Photon. Technol. Lett., vol. 29, no. 23, pp. 2091–2094, 2017.

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities,” Opt. Exp., vol. 25, no. 3, pp. 1916–1936, 2017.

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: Methods and potential gain,” J. Lightw. Technol., vol. 35, no. 4, pp. 903–930, 2017.

2015 (1)

A. Bakhshali, “Frequency-domain volterra-based equalization structures for efficient mitigation of intrachannel kerr nonlinearities,” J. Lightw. Technol., vol. 34, no. 8, pp. 1770–1777, 2015.

2010 (1)

S. J. Pan and Q. Yang, “A survey on transfer learning,” IEEE Trans. Knowl. data Eng., vol. 22, no. 10, pp. 1345–1359, 2010.

1998 (1)

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator,” ACM Trans. Model. Comput. Simul., vol. 8, no. 1, pp. 3–30, 1998.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. Boston: Academic Press, 2013. [Online]. Available: https://doi.org/10.1016/B978-0-12-397023-7.00002-4

Ahmad, M.

A. Sarwar, F. Qamar, and M. Ahmad, “Performance analysis of 128-QAM dual polarization system for long haul optical communication,” Pakistan J. Sci., vol. 70, no. 4, p. 324, 2018. [Online]. Available: https://www.proquest.com/openview/0967b245cfa0cd11c1351860e82991d7/1?pq-origsite=gscholar&cbl=1616340

Ali, M.

F. Qamar, M. K. Islam, R. Shahzadi, S. Z. Ali, and M. Ali, “128-QAM dual-polarization chaotic long-haul system performance evaluation,” J. Opt. Commun., 2020.

Ali, S. Z.

F. Qamar, M. K. Islam, R. Shahzadi, S. Z. Ali, and M. Ali, “128-QAM dual-polarization chaotic long-haul system performance evaluation,” J. Opt. Commun., 2020.

Bakhshali, A.

A. Bakhshali, “Frequency-domain volterra-based equalization structures for efficient mitigation of intrachannel kerr nonlinearities,” J. Lightw. Technol., vol. 34, no. 8, pp. 1770–1777, 2015.

Behbood, V.

J. Lu, V. Behbood, P. Hao, H. Zuo, S. Xue, and G. Zhang, “Transfer learning using computational intelligence: A survey,” Knowl.-Based Syst., vol. 80, pp. 14–23, 2015.

Bengio, Y.

R. Pascanu, T. Mikolov, and Y. Bengio, “On the difficulty of training recurrent neural networks,” in Proc. Int. Conf. Mach. Learn., 2013, pp. 1310–1318.

Bluemm, C.

M. Schaedler, F. Pittala, G. Böcherer, C. Bluemm, M. Kuschnerov, and S. Pachnicke, “Recurrent neural network soft-demapping for nonlinear isi in 800gbit/s DWDM coherent optical transmissions,” in Proc. 46th Eur. Conf. Opt. Commun., 2020, pp. 1–4, doi: .

Böcherer, G.

M. Schaedler, F. Pittala, G. Böcherer, C. Bluemm, M. Kuschnerov, and S. Pachnicke, “Recurrent neural network soft-demapping for nonlinear isi in 800gbit/s DWDM coherent optical transmissions,” in Proc. 46th Eur. Conf. Opt. Commun., 2020, pp. 1–4, doi: .

Bogris, A.

S. Deligiannidis, A. Bogris, C. Mesaritakis, and Y. Kopsinis, “Compensation of fiber nonlinearities in digital coherent systems leveraging long short-term memory neural networks,” J. Lightw. Technol., vol. 38, no. 21, pp. 5991–5999, 2020.

S. Deligiannidis, C. Mesaritakis, and A. Bogris, “Performance and complexity analysis of bi-directional recurrent neural network models vs. volterra nonlinear equalizers in digital coherent systems,” 2021, arXiv:2103.03832.

Brajato, G.

D. Zibar, F. Da Ros, G. Brajato, and U. C. de Moura, “Toward intelligence in photonic systems,” Opt. Photon. News, vol. 31, no. 3, pp. 34–41, 2020.

Bülow, H.

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: Possible pitfalls,” IEEE Photon. Technol. Lett., vol. 29, no. 23, pp. 2091–2094, 2017.

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. Exp., vol. 25, no. 3, pp. 1916–1936, 2017.

Cheng, Y.

Y. Cheng, W. Zhang, S. Fu, M. Tang, and D. Liu, “Transfer learning simplified multi-task deep neural network for PDM-64QAM optical performance monitoring,” Opt. Exp., vol. 28, no. 5, pp. 7607–7617, 2020.

Dar, R.

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: Methods and potential gain,” J. Lightw. Technol., vol. 35, no. 4, pp. 903–930, 2017.

de Moura, U. C.

D. Zibar, F. Da Ros, G. Brajato, and U. C. de Moura, “Toward intelligence in photonic systems,” Opt. Photon. News, vol. 31, no. 3, pp. 34–41, 2020.

Deligiannidis, S.

S. Deligiannidis, A. Bogris, C. Mesaritakis, and Y. Kopsinis, “Compensation of fiber nonlinearities in digital coherent systems leveraging long short-term memory neural networks,” J. Lightw. Technol., vol. 38, no. 21, pp. 5991–5999, 2020.

S. Deligiannidis, C. Mesaritakis, and A. Bogris, “Performance and complexity analysis of bi-directional recurrent neural network models vs. volterra nonlinear equalizers in digital coherent systems,” 2021, arXiv:2103.03832.

Dietterich, T. G.

M. T. Rosenstein, Z. Marx, L. P. Kaelbling, and T. G. Dietterich, “To transfer or not to transfer,” in NIPS Workshop Transfer Learn., vol. 898, 2005, pp. 1–4.

Eriksson, T. A.

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: Possible pitfalls,” IEEE Photon. Technol. Lett., vol. 29, no. 23, pp. 2091–2094, 2017.

Fan, F.-L

F.-L Fan, J. Xiong, M. Li, and G. Wang, “On interpretability of artificial neural networks: A survey,” IEEE Trans. Radiat. Plasma Med. Sci., early access, 2021, doi: .

Fan, Q.

Q. Fan, G. Zhou, T. Gui, C. Lu, and A. P. T. Lau, “Advancing theoretical understanding and practical performance of signal processing for nonlinear optical communications through machine learning,” Nature Commun., vol. 11, no. 1, p. 3694, 2020.

Fedoruk, M.

O. Sidelnikov, A. Redyuk, S. Sygletos, M. Fedoruk, and S. K. Turitsyn, “Advanced convolutional neural networks for nonlinearity mitigation in long-haul WDM transmission systems,” J. Lightw. Technol., vol. 39, no. 8, pp. 2397–2406, 2021.

Freire, P. J.

P. J. Freire, “Complex-valued neural network design for mitigation of signal distortions in optical links,” J. Lightw. Technol., vol. 39, no. 6, pp. 1696–1705, 2021.

P. J. Freire, “Performance versus complexity study of neural network equalizers in coherent optical systems,” J. Lightw. Technol., p. 1, 2021, doi: .

Fu, S.

Y. Cheng, W. Zhang, S. Fu, M. Tang, and D. Liu, “Transfer learning simplified multi-task deep neural network for PDM-64QAM optical performance monitoring,” Opt. Exp., vol. 28, no. 5, pp. 7607–7617, 2020.

Gaiarin, S.

Galdino, L.

L. Galdino, “The trade-off between transceiver capacity and symbol rate,” in Proc. Opt. Fiber Commun. Conf. Expo., 2018, pp. 1–3.

Gao, Z.

Z. Gao, “Ann-based multi-channel qot-prediction over a 563.4-km field-trial testbed,” J. Lightw. Technol., vol. 38, no. 9, pp. 2646–2655, 2020.

Ghazisaeidi, A.

A. Ghazisaeidi, “Deep learning based digital backpropagation demonstrating SNR gain at low complexity in a 1200 km transmission link,” Opt. Exp., vol. 28, no. 20, pp. 29 318–29 334, 2020.

Gui, T.

Q. Fan, G. Zhou, T. Gui, C. Lu, and A. P. T. Lau, “Advancing theoretical understanding and practical performance of signal processing for nonlinear optical communications through machine learning,” Nature Commun., vol. 11, no. 1, p. 3694, 2020.

Guiomar, F. P.

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities,” Opt. Exp., vol. 25, no. 3, pp. 1916–1936, 2017.

Gulli, A.

A. Gulli and S. Pal, Deep Learning With Keras. Packt Publishing Ltd, 2017.

Häger, C.

C. Häger and H. D. Pfister, “Physics-based deep learning for fiber-optic communication systems,” IEEE J. Sel. Areas Commun., vol. 39, no. 1, pp. 280–294, 2021.

C. Häger and H. D. Pfister, “Nonlinear interference mitigation via deep neural networks,” in Proc. Opt. Fiber Commun. Conf. Expo., 2018, pp. 1–3.

Hao, P.

J. Lu, V. Behbood, P. Hao, H. Zuo, S. Xue, and G. Zhang, “Transfer learning using computational intelligence: A survey,” Knowl.-Based Syst., vol. 80, pp. 14–23, 2015.

Hu, S.

L. Xia, J. Zhang, S. Hu, M. Zhu, Y. Song, and K. Qiu, “Transfer learning assisted deep neural network for OSNR estimation,” Opt. Exp., vol. 27, no. 14, pp. 19 398–19 406, 2019.

J. Zhang, L. Xia, M. Zhu, S. Hu, B. Xu, and K. Qiu, “Fast remodeling for nonlinear distortion mitigation based on transfer learning,” Opt. Lett., vol. 44, no. 17, pp. 4243–4246, 2019.

Islam, M. K.

F. Qamar, M. K. Islam, R. Shahzadi, S. Z. Ali, and M. Ali, “128-QAM dual-polarization chaotic long-haul system performance evaluation,” J. Opt. Commun., 2020.

Ji, T.

Z. Xu, C. Sun, T. Ji, J. H. Manton, and W. Shieh, “Feedforward and recurrent neural network-based transfer learning for nonlinear equalization in short-reach optical links,” J. Lightw. Technol., vol. 39, no. 2, pp. 475–480, 2020.

Jin, T.

W. Zhang, T. Jin, T. Xu, J. Zhang, and K. Qiu, “Nonlinear mitigation with TL-NN-NLC in coherent optical fiber communications,” in Proc. Asia Commun. Photon. Conf., 2020, Paper M 4A-321.

Kaelbling, L. P.

M. T. Rosenstein, Z. Marx, L. P. Kaelbling, and T. G. Dietterich, “To transfer or not to transfer,” in NIPS Workshop Transfer Learn., vol. 898, 2005, pp. 1–4.

Kamalian-Kopae, M.

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