Abstract

In this paper, we implement an optical fiber communication system as an end-to-end deep neural network, including the complete chain of transmitter, channel model, and receiver. This approach enables the optimization of the transceiver in a single end-to-end process. We illustrate the benefits of this method by applying it to intensity modulation/direct detection (IM/DD) systems and show that we can achieve bit error rates below the 6.7% hard-decision forward error correction (HD-FEC) threshold. We model all componentry of the transmitter and receiver, as well as the fiber channel, and apply deep learning to find transmitter and receiver configurations minimizing the symbol error rate. We propose and verify in simulations a training method that yields robust and flexible transceivers that allow—without reconfiguration—reliable transmission over a large range of link dispersions. The results from end-to-end deep learning are successfully verified for the first time in an experiment. In particular, we achieve information rates of 42 Gb/s below the HD-FEC threshold at distances beyond 40 km. We find that our results outperform conventional IM/DD solutions based on two- and four-level pulse amplitude modulation with feedforward equalization at the receiver. Our study is the first step toward end-to-end deep learning based optimization of optical fiber communication systems.

© 2018 CCBY

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.
  2. F. Khan, C. Lu, and A. Lau, “Machine learning methods for optical communication systems,” in Proc. Adv. Photon. IPR, NOMA, Sensors, Netw., SPPCom, PS, OSA Tech. Dig., 2017, Paper SpW2F.3.
  3. J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.
  4. D. Zibar, M. Piels, R. Jones, and C. Schäffer, “Machine learning techniques in optical communication,” J. Lightw. Technol., vol. 34, no. 6, pp. 1442–1452, 2016.
  5. F. Khan, Y. Zhou, A. Lau, and C. Lu, “Modulation format identification in heterogeneous fiber-optic networks using artificial neural networks,” Opt. Express, vol. 20, no. 11, pp. 12422–12431, 2012.
  6. R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.
  7. K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw., vol. 2, no. 5, pp. 359–366, 1989.
  8. K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 40, no. 3, pp. 352–357, 2010.
  9. M. Ibnkahla, “Applications of neural networks to digital communications—A survey,” Elsevier Signal Process., vol. 80, no. 7, pp. 1185–1215, 2000.
  10. M. Jarajrehet al., “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett., vol. 27, no. 4, pp. 387–390, 2014.
  11. E. Giacoumidiset al., “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett., vol. 40, no. 21, pp. 5113–5116, 2015.
  12. T. 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.
  13. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning.Cambridge, MA, USA: MIT Press, 2016.
  14. C. Häger and H. Pfister, “Nonlinear interference mitigation via deep neural networks,” in Proc. Opt. Fiber Commun. Conf., OSA Tech. Dig., 2018, Paper W3A.4.
  15. E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, 2008.
  16. S. Gaiarinet al., “High speed PAM-8 optical interconnects with digital equalization based on neural network,” in Proc. Asia Commun. Photon. Conf., 2016, Paper AS1C-1.
  17. J. Estaránet al., “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proc. 42nd Eur. Conf. Opt. Commun., 2016, pp. 106–108.
  18. T. O'shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Trans. Cogn. Commun. Netw., vol. 3, no. 4, pp. 563–575, 2017.
  19. S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 1, 2018.
  20. M. Eiselt, N. Eiselt and A. Dochhan, “Direct detection solutions for 100G and beyond,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Tu3I.3.
  21. V. Nair and G. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proc. Int. Conf. Mach. Learn., 2010, pp. 807–814.
  22. D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 1986.
  23. D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 2014, arXiv:1412.6980.
  24. 2018. [Online]. Available: https://www.tensorflow.org/
  25. G. Agrawal, Fiber-Optic Communication systems,4th ed. Hoboken, NJ, USA: Wiley, 2010.
  26. A. Napoliet al., “Digital predistortion techniques for finite extinction ratio IQ Mach-Zehnder modulators,” J. Lightw. Technol., vol. 35, no. 19, pp. 4289–4296, 2017.
  27. C. Pearson, “High-speed, analog-to-digital converter basics,” Texas Instruments, Dallas, TX, USA, App. Rep. , 2011. [Online]. Available: http://www.ti.com/lit/an/slaa510/slaa510.pdf
  28. L. van der Maaten and G. Hinton, “Visualizing data using t-SNE,” J. Mach. Learn. Res., vol. 9, pp. 2579–2605, 2008.
  29. M. Grassl, “Bounds on the minimum distance of linear codes and quantum codes,” [Online]. Available: http://www.codetables.de. Accessed on: 11, 2018.

2018 (1)

S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 1, 2018.

2017 (5)

T. 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.

T. O'shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Trans. Cogn. Commun. Netw., vol. 3, no. 4, pp. 563–575, 2017.

A. Napoliet al., “Digital predistortion techniques for finite extinction ratio IQ Mach-Zehnder modulators,” J. Lightw. Technol., vol. 35, no. 19, pp. 4289–4296, 2017.

C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.

J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

2016 (1)

D. Zibar, M. Piels, R. Jones, and C. Schäffer, “Machine learning techniques in optical communication,” J. Lightw. Technol., vol. 34, no. 6, pp. 1442–1452, 2016.

2015 (1)

2014 (2)

M. Jarajrehet al., “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett., vol. 27, no. 4, pp. 387–390, 2014.

D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 2014, arXiv:1412.6980.

2012 (1)

2010 (2)

R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 40, no. 3, pp. 352–357, 2010.

2008 (2)

L. van der Maaten and G. Hinton, “Visualizing data using t-SNE,” J. Mach. Learn. Res., vol. 9, pp. 2579–2605, 2008.

E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, 2008.

2000 (1)

M. Ibnkahla, “Applications of neural networks to digital communications—A survey,” Elsevier Signal Process., vol. 80, no. 7, pp. 1185–1215, 2000.

1989 (1)

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw., vol. 2, no. 5, pp. 359–366, 1989.

1986 (1)

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 1986.

Agrawal, G.

G. Agrawal, Fiber-Optic Communication systems,4th ed. Hoboken, NJ, USA: Wiley, 2010.

Ba, J.

D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 2014, arXiv:1412.6980.

Bengio, Y.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning.Cambridge, MA, USA: MIT Press, 2016.

Brink, S. ten

S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 1, 2018.

Bülow, H.

T. 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.

Burse, K.

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 40, no. 3, pp. 352–357, 2010.

Cammerer, S.

S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 1, 2018.

Chen, K.-C.

C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.

Courville, A.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning.Cambridge, MA, USA: MIT Press, 2016.

Diniz, J. C. M.

J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

Dochhan, A.

M. Eiselt, N. Eiselt and A. Dochhan, “Direct detection solutions for 100G and beyond,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Tu3I.3.

Dörner, S.

S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 1, 2018.

Eiselt, M.

M. Eiselt, N. Eiselt and A. Dochhan, “Direct detection solutions for 100G and beyond,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Tu3I.3.

Eiselt, N.

M. Eiselt, N. Eiselt and A. Dochhan, “Direct detection solutions for 100G and beyond,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Tu3I.3.

Eriksson, T.

T. 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.

Essiambre, R.-J.

R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Estarán, J.

J. Estaránet al., “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proc. 42nd Eur. Conf. Opt. Commun., 2016, pp. 106–108.

Foschini, G.

R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Gaiarin, S.

S. Gaiarinet al., “High speed PAM-8 optical interconnects with digital equalization based on neural network,” in Proc. Asia Commun. Photon. Conf., 2016, Paper AS1C-1.

Giacoumidis, E.

Goebel, B.

R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Goodfellow, I.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning.Cambridge, MA, USA: MIT Press, 2016.

Grassl, M.

M. Grassl, “Bounds on the minimum distance of linear codes and quantum codes,” [Online]. Available: http://www.codetables.de. Accessed on: 11, 2018.

Häger, C.

C. Häger and H. Pfister, “Nonlinear interference mitigation via deep neural networks,” in Proc. Opt. Fiber Commun. Conf., OSA Tech. Dig., 2018, Paper W3A.4.

Han, Z.

C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.

Hanzo, L.

C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.

Hinton, G.

L. van der Maaten and G. Hinton, “Visualizing data using t-SNE,” J. Mach. Learn. Res., vol. 9, pp. 2579–2605, 2008.

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 1986.

V. Nair and G. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proc. Int. Conf. Mach. Learn., 2010, pp. 807–814.

Hornik, K.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw., vol. 2, no. 5, pp. 359–366, 1989.

Hoydis, J.

S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 1, 2018.

T. O'shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Trans. Cogn. Commun. Netw., vol. 3, no. 4, pp. 563–575, 2017.

Ibnkahla, M.

M. Ibnkahla, “Applications of neural networks to digital communications—A survey,” Elsevier Signal Process., vol. 80, no. 7, pp. 1185–1215, 2000.

Ip, E.

E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, 2008.

Jarajreh, M.

M. Jarajrehet al., “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett., vol. 27, no. 4, pp. 387–390, 2014.

Jiang, C.

C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.

Jones, R.

J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

D. Zibar, M. Piels, R. Jones, and C. Schäffer, “Machine learning techniques in optical communication,” J. Lightw. Technol., vol. 34, no. 6, pp. 1442–1452, 2016.

Kahn, J.

E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, 2008.

Khan, F.

F. Khan, Y. Zhou, A. Lau, and C. Lu, “Modulation format identification in heterogeneous fiber-optic networks using artificial neural networks,” Opt. Express, vol. 20, no. 11, pp. 12422–12431, 2012.

F. Khan, C. Lu, and A. Lau, “Machine learning methods for optical communication systems,” in Proc. Adv. Photon. IPR, NOMA, Sensors, Netw., SPPCom, PS, OSA Tech. Dig., 2017, Paper SpW2F.3.

Kingma, D.

D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 2014, arXiv:1412.6980.

Kramer, G.

R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Lau, A.

F. Khan, Y. Zhou, A. Lau, and C. Lu, “Modulation format identification in heterogeneous fiber-optic networks using artificial neural networks,” Opt. Express, vol. 20, no. 11, pp. 12422–12431, 2012.

F. Khan, C. Lu, and A. Lau, “Machine learning methods for optical communication systems,” in Proc. Adv. Photon. IPR, NOMA, Sensors, Netw., SPPCom, PS, OSA Tech. Dig., 2017, Paper SpW2F.3.

Leven, A.

T. 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.

Lu, C.

F. Khan, Y. Zhou, A. Lau, and C. Lu, “Modulation format identification in heterogeneous fiber-optic networks using artificial neural networks,” Opt. Express, vol. 20, no. 11, pp. 12422–12431, 2012.

F. Khan, C. Lu, and A. Lau, “Machine learning methods for optical communication systems,” in Proc. Adv. Photon. IPR, NOMA, Sensors, Netw., SPPCom, PS, OSA Tech. Dig., 2017, Paper SpW2F.3.

Nair, V.

V. Nair and G. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proc. Int. Conf. Mach. Learn., 2010, pp. 807–814.

Napoli, A.

A. Napoliet al., “Digital predistortion techniques for finite extinction ratio IQ Mach-Zehnder modulators,” J. Lightw. Technol., vol. 35, no. 19, pp. 4289–4296, 2017.

O'shea, T.

T. O'shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Trans. Cogn. Commun. Netw., vol. 3, no. 4, pp. 563–575, 2017.

Pearson, C.

C. Pearson, “High-speed, analog-to-digital converter basics,” Texas Instruments, Dallas, TX, USA, App. Rep. , 2011. [Online]. Available: http://www.ti.com/lit/an/slaa510/slaa510.pdf

Pfister, H.

C. Häger and H. Pfister, “Nonlinear interference mitigation via deep neural networks,” in Proc. Opt. Fiber Commun. Conf., OSA Tech. Dig., 2018, Paper W3A.4.

Piels, M.

J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

D. Zibar, M. Piels, R. Jones, and C. Schäffer, “Machine learning techniques in optical communication,” J. Lightw. Technol., vol. 34, no. 6, pp. 1442–1452, 2016.

Ren, Y.

C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.

Rumelhart, D.

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 1986.

Schäffer, C.

D. Zibar, M. Piels, R. Jones, and C. Schäffer, “Machine learning techniques in optical communication,” J. Lightw. Technol., vol. 34, no. 6, pp. 1442–1452, 2016.

Shrivastava, S.

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 40, no. 3, pp. 352–357, 2010.

Stinchcombe, M.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw., vol. 2, no. 5, pp. 359–366, 1989.

Thrane, J.

J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

van der Maaten, L.

L. van der Maaten and G. Hinton, “Visualizing data using t-SNE,” J. Mach. Learn. Res., vol. 9, pp. 2579–2605, 2008.

Wass, J.

J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

White, H.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw., vol. 2, no. 5, pp. 359–366, 1989.

Williams, R.

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 1986.

Winzer, P.

R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Yadav, R.

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 40, no. 3, pp. 352–357, 2010.

Zhang, H.

C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.

Zhou, Y.

Zibar, D.

J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

D. Zibar, M. Piels, R. Jones, and C. Schäffer, “Machine learning techniques in optical communication,” J. Lightw. Technol., vol. 34, no. 6, pp. 1442–1452, 2016.

Elsevier Signal Process. (1)

M. Ibnkahla, “Applications of neural networks to digital communications—A survey,” Elsevier Signal Process., vol. 80, no. 7, pp. 1185–1215, 2000.

IEEE J. Sel. Topics Signal Process. (1)

S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 1, 2018.

IEEE Photon. Technol. Lett. (2)

T. 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.

M. Jarajrehet al., “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett., vol. 27, no. 4, pp. 387–390, 2014.

IEEE Trans. Cogn. Commun. Netw. (1)

T. O'shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Trans. Cogn. Commun. Netw., vol. 3, no. 4, pp. 563–575, 2017.

IEEE Trans. Syst., Man, Cybern. C, Appl. Rev. (1)

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 40, no. 3, pp. 352–357, 2010.

IEEE Wireless Commun. (1)

C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, “Machine learning paradigms for next-generation wireless networks,” IEEE Wireless Commun., vol. 24, no. 2, pp. 98–105, 2017.

J. Lightw. Technol. (5)

J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

D. Zibar, M. Piels, R. Jones, and C. Schäffer, “Machine learning techniques in optical communication,” J. Lightw. Technol., vol. 34, no. 6, pp. 1442–1452, 2016.

R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, 2008.

A. Napoliet al., “Digital predistortion techniques for finite extinction ratio IQ Mach-Zehnder modulators,” J. Lightw. Technol., vol. 35, no. 19, pp. 4289–4296, 2017.

J. Mach. Learn. Res. (1)

L. van der Maaten and G. Hinton, “Visualizing data using t-SNE,” J. Mach. Learn. Res., vol. 9, pp. 2579–2605, 2008.

Nature (1)

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 1986.

Neural Netw. (1)

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw., vol. 2, no. 5, pp. 359–366, 1989.

Opt. Express (1)

Opt. Lett. (1)

Other (12)

F. Khan, C. Lu, and A. Lau, “Machine learning methods for optical communication systems,” in Proc. Adv. Photon. IPR, NOMA, Sensors, Netw., SPPCom, PS, OSA Tech. Dig., 2017, Paper SpW2F.3.

S. Gaiarinet al., “High speed PAM-8 optical interconnects with digital equalization based on neural network,” in Proc. Asia Commun. Photon. Conf., 2016, Paper AS1C-1.

J. Estaránet al., “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proc. 42nd Eur. Conf. Opt. Commun., 2016, pp. 106–108.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning.Cambridge, MA, USA: MIT Press, 2016.

C. Häger and H. Pfister, “Nonlinear interference mitigation via deep neural networks,” in Proc. Opt. Fiber Commun. Conf., OSA Tech. Dig., 2018, Paper W3A.4.

M. Eiselt, N. Eiselt and A. Dochhan, “Direct detection solutions for 100G and beyond,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Tu3I.3.

V. Nair and G. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proc. Int. Conf. Mach. Learn., 2010, pp. 807–814.

D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 2014, arXiv:1412.6980.

2018. [Online]. Available: https://www.tensorflow.org/

G. Agrawal, Fiber-Optic Communication systems,4th ed. Hoboken, NJ, USA: Wiley, 2010.

M. Grassl, “Bounds on the minimum distance of linear codes and quantum codes,” [Online]. Available: http://www.codetables.de. Accessed on: 11, 2018.

C. Pearson, “High-speed, analog-to-digital converter basics,” Texas Instruments, Dallas, TX, USA, App. Rep. , 2011. [Online]. Available: http://www.ti.com/lit/an/slaa510/slaa510.pdf

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.