Abstract

We propose an autoencoding sequence-based transceiver for communication over dispersive channels with intensity modulation and direct detection (IM/DD), designed as a bidirectional deep recurrent neural network (BRNN). The receiver uses a sliding window technique to allow for efficient data stream estimation. We find that this sliding window BRNN (SBRNN), based on end-to-end deep learning of the communication system, achieves a significant bit-error-rate reduction at all examined distances in comparison to previous block-based autoencoders implemented as feed-forward neural networks (FFNNs), leading to an increase of the transmission distance. We also compare the end-to-end SBRNN with a state-of-the-art IM/DD solution based on two level pulse amplitude modulation with an FFNN receiver, simultaneously processing multiple received symbols and approximating nonlinear Volterra equalization. Our results show that the SBRNN outperforms such systems at both 42 and 84 Gb/s, while training fewer parameters. Our novel SBRNN design aims at tailoring the end-to-end deep learning-based systems for communication over nonlinear channels with memory, such as the optical IM/DD fiber channel.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (Massachusetts Institute of Technology, 2016).
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  4. B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
    [Crossref]
  5. M. Chagnon, B. Karanov, and L. Schmalen, “Experimental demonstration of a dispersion tolerant end-to-end deep learning-based IM-DD transmission system,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.
  6. S. Li, C. Häger, N. Garcia, and H. Wymeersch, “Achievable information rates for nonlinear fiber communication via end-to-end autoencoder learning,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.
  7. R. Jones, T. A. Eriksson, M. P. Yankov, B. J. Puttnam, G. Rademacher, R. S. Luis, and D. Zibar, “Geometric constellation shaping for fiber optic communication systems via end-to-end learning,” ArXiv preprint arXiv:1810.00774 (2018).
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    [Crossref]
  9. D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
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  10. C. Ye and et al., “Recurrent neural network (RNN) based end-to-end nonlinear management for symmetrical 50Gbps NRZ PON with 29dB+ loss budget,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.
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  13. N. Farsad and A. Goldsmith, “Neural network detectors for molecular communication systems,” in Proceedings of 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–5.
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  22. T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photon. Technol. Lett. 29(23), 2091–2094 (2017).
    [Crossref]
  23. D.-U Lee, J. Villasenor, W. Luk, and P. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659 (2006).
    [Crossref]
  24. K. Lee, O. Levy, and L. Zettlemoyer, “Recurrent additive networks,” ArXiv preprint arXiv:1705.07393 (2017).
  25. E. Agrell and M. Secondini, “Information-theoretic tools for optical communication engineers,” in Proceedings of IEEE Photonics Conference (IPC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–5.

2018 (4)

S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process. 12(1), 132–143 (2018).
[Crossref]

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

N. Farsad and A. Goldsmith, “Neural network detection of data sequences in communication systems,” IEEE Trans. Signal Process. 66(21), 5663–5678 (2018).
[Crossref]

M. Ravanelli, P. Brakel, M. Omologo, and J. Bengio, “Light gated recurrent units for speech recognition,” IEEE Transactions on Emerging Topics in Computational Intelligence 2(2), 92–102 (2018).
[Crossref]

2017 (2)

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photon. Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

T. O’Shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Trans. Cogn. Commun. Netw. 3(4), 563–575 (2017).
[Crossref]

2006 (1)

D.-U Lee, J. Villasenor, W. Luk, and P. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659 (2006).
[Crossref]

1997 (2)

S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural Computation 9(8), 1735–1780 (1997).
[Crossref] [PubMed]

M. Schuster and K. Paliwal, “Bidirectional recurrent neural networks,” IEEE Trans. Signal Process. 45(11), 2673–2681 (1997).
[Crossref]

1986 (1)

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
[Crossref]

Agrawal, G.

G. Agrawal, Fiber-optic Communication Systems, 4th ed. (John Wiley & Sons, Inc., 2010).
[Crossref]

Agrell, E.

E. Agrell and M. Secondini, “Information-theoretic tools for optical communication engineers,” in Proceedings of IEEE Photonics Conference (IPC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–5.

Ba, J.

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

Bayvel, P.

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

Bengio, J.

M. Ravanelli, P. Brakel, M. Omologo, and J. Bengio, “Light gated recurrent units for speech recognition,” IEEE Transactions on Emerging Topics in Computational Intelligence 2(2), 92–102 (2018).
[Crossref]

Bengio, Y.

K. Cho, B. van Marrienboer, C. Gulcehre, D. Bhadanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN encoder-decoder for statistical machine translation,” in Proceedings of Conference on Empirical Methods in Natural Language Processing (Association for Computational Linguistics, 2014), pp. 1724–1734.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (Massachusetts Institute of Technology, 2016).

Bhadanau, D.

K. Cho, B. van Marrienboer, C. Gulcehre, D. Bhadanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN encoder-decoder for statistical machine translation,” in Proceedings of Conference on Empirical Methods in Natural Language Processing (Association for Computational Linguistics, 2014), pp. 1724–1734.

Bougares, F.

K. Cho, B. van Marrienboer, C. Gulcehre, D. Bhadanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN encoder-decoder for statistical machine translation,” in Proceedings of Conference on Empirical Methods in Natural Language Processing (Association for Computational Linguistics, 2014), pp. 1724–1734.

Brakel, P.

M. Ravanelli, P. Brakel, M. Omologo, and J. Bengio, “Light gated recurrent units for speech recognition,” IEEE Transactions on Emerging Topics in Computational Intelligence 2(2), 92–102 (2018).
[Crossref]

Bülow, H.

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photon. Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

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. 12(1), 132–143 (2018).
[Crossref]

Chagnon, M.

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

M. Chagnon, B. Karanov, and L. Schmalen, “Experimental demonstration of a dispersion tolerant end-to-end deep learning-based IM-DD transmission system,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.

Cho, K.

K. Cho, B. van Marrienboer, C. Gulcehre, D. Bhadanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN encoder-decoder for statistical machine translation,” in Proceedings of Conference on Empirical Methods in Natural Language Processing (Association for Computational Linguistics, 2014), pp. 1724–1734.

Chou, E.

V. Houtsma, E. Chou, and D. van Veen, “92 and 50 Gbps TDM-PON Using Neural Network Enabled Receiver Equalization Specialized for PON,” in Proceedings of Optical Fiber Communication Conference (OFC) (Optical Society of America, 2019), paper M2B.6.

Courville, A.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (Massachusetts Institute of Technology, 2016).

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. 12(1), 132–143 (2018).
[Crossref]

Eriksson, T. A.

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photon. Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

R. Jones, T. A. Eriksson, M. P. Yankov, B. J. Puttnam, G. Rademacher, R. S. Luis, and D. Zibar, “Geometric constellation shaping for fiber optic communication systems via end-to-end learning,” ArXiv preprint arXiv:1810.00774 (2018).

Farsad, N.

N. Farsad and A. Goldsmith, “Neural network detection of data sequences in communication systems,” IEEE Trans. Signal Process. 66(21), 5663–5678 (2018).
[Crossref]

N. Farsad and A. Goldsmith, “Neural network detectors for molecular communication systems,” in Proceedings of 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–5.

Garcia, N.

S. Li, C. Häger, N. Garcia, and H. Wymeersch, “Achievable information rates for nonlinear fiber communication via end-to-end autoencoder learning,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.

Goldsmith, A.

N. Farsad and A. Goldsmith, “Neural network detection of data sequences in communication systems,” IEEE Trans. Signal Process. 66(21), 5663–5678 (2018).
[Crossref]

N. Farsad and A. Goldsmith, “Neural network detectors for molecular communication systems,” in Proceedings of 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–5.

Goodfellow, I.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (Massachusetts Institute of Technology, 2016).

Gulcehre, C.

K. Cho, B. van Marrienboer, C. Gulcehre, D. Bhadanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN encoder-decoder for statistical machine translation,” in Proceedings of Conference on Empirical Methods in Natural Language Processing (Association for Computational Linguistics, 2014), pp. 1724–1734.

Häger, C.

S. Li, C. Häger, N. Garcia, and H. Wymeersch, “Achievable information rates for nonlinear fiber communication via end-to-end autoencoder learning,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.

Hinton, G.

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
[Crossref]

V. Nair and G. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proceedings of International Conference on Machine Learning (ICML) (International Machine Learning Society, 2010), pp. 807–814.

Hochreiter, S.

S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural Computation 9(8), 1735–1780 (1997).
[Crossref] [PubMed]

Houtsma, V.

V. Houtsma, E. Chou, and D. van Veen, “92 and 50 Gbps TDM-PON Using Neural Network Enabled Receiver Equalization Specialized for PON,” in Proceedings of Optical Fiber Communication Conference (OFC) (Optical Society of America, 2019), paper M2B.6.

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. 12(1), 132–143 (2018).
[Crossref]

T. O’Shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Trans. Cogn. Commun. Netw. 3(4), 563–575 (2017).
[Crossref]

Jones, R.

R. Jones, T. A. Eriksson, M. P. Yankov, B. J. Puttnam, G. Rademacher, R. S. Luis, and D. Zibar, “Geometric constellation shaping for fiber optic communication systems via end-to-end learning,” ArXiv preprint arXiv:1810.00774 (2018).

Karanov, B.

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

M. Chagnon, B. Karanov, and L. Schmalen, “Experimental demonstration of a dispersion tolerant end-to-end deep learning-based IM-DD transmission system,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.

Kingma, D.

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

Lavery, D.

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

Lee, D.-U

D.-U Lee, J. Villasenor, W. Luk, and P. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659 (2006).
[Crossref]

Lee, K.

K. Lee, O. Levy, and L. Zettlemoyer, “Recurrent additive networks,” ArXiv preprint arXiv:1705.07393 (2017).

Leong, P.

D.-U Lee, J. Villasenor, W. Luk, and P. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659 (2006).
[Crossref]

Leven, A.

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photon. Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

Levy, O.

K. Lee, O. Levy, and L. Zettlemoyer, “Recurrent additive networks,” ArXiv preprint arXiv:1705.07393 (2017).

Li, S.

S. Li, C. Häger, N. Garcia, and H. Wymeersch, “Achievable information rates for nonlinear fiber communication via end-to-end autoencoder learning,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.

Luis, R. S.

R. Jones, T. A. Eriksson, M. P. Yankov, B. J. Puttnam, G. Rademacher, R. S. Luis, and D. Zibar, “Geometric constellation shaping for fiber optic communication systems via end-to-end learning,” ArXiv preprint arXiv:1810.00774 (2018).

Luk, W.

D.-U Lee, J. Villasenor, W. Luk, and P. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659 (2006).
[Crossref]

Lyubomirsky, I.

I. Lyubomirsky, “Machine learning equalization techniques for high speed PAM4 fiber optic communication systems,” CS229 Final Project Report, Stanford University (2015). Accessed on: Mar. 13, 2019. [Online]. Available: http://cs229.stanford.edu/proj2015/232_report.pdf .

Nair, V.

V. Nair and G. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proceedings of International Conference on Machine Learning (ICML) (International Machine Learning Society, 2010), pp. 807–814.

O’Shea, T.

T. O’Shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Trans. Cogn. Commun. Netw. 3(4), 563–575 (2017).
[Crossref]

Omologo, M.

M. Ravanelli, P. Brakel, M. Omologo, and J. Bengio, “Light gated recurrent units for speech recognition,” IEEE Transactions on Emerging Topics in Computational Intelligence 2(2), 92–102 (2018).
[Crossref]

Paliwal, K.

M. Schuster and K. Paliwal, “Bidirectional recurrent neural networks,” IEEE Trans. Signal Process. 45(11), 2673–2681 (1997).
[Crossref]

Puttnam, B. J.

R. Jones, T. A. Eriksson, M. P. Yankov, B. J. Puttnam, G. Rademacher, R. S. Luis, and D. Zibar, “Geometric constellation shaping for fiber optic communication systems via end-to-end learning,” ArXiv preprint arXiv:1810.00774 (2018).

Rademacher, G.

R. Jones, T. A. Eriksson, M. P. Yankov, B. J. Puttnam, G. Rademacher, R. S. Luis, and D. Zibar, “Geometric constellation shaping for fiber optic communication systems via end-to-end learning,” ArXiv preprint arXiv:1810.00774 (2018).

Ravanelli, M.

M. Ravanelli, P. Brakel, M. Omologo, and J. Bengio, “Light gated recurrent units for speech recognition,” IEEE Transactions on Emerging Topics in Computational Intelligence 2(2), 92–102 (2018).
[Crossref]

Rumelhart, D.

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
[Crossref]

Schmalen, L.

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

M. Chagnon, B. Karanov, and L. Schmalen, “Experimental demonstration of a dispersion tolerant end-to-end deep learning-based IM-DD transmission system,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.

Schmidhuber, J.

S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural Computation 9(8), 1735–1780 (1997).
[Crossref] [PubMed]

Schuster, M.

M. Schuster and K. Paliwal, “Bidirectional recurrent neural networks,” IEEE Trans. Signal Process. 45(11), 2673–2681 (1997).
[Crossref]

Schwenk, H.

K. Cho, B. van Marrienboer, C. Gulcehre, D. Bhadanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN encoder-decoder for statistical machine translation,” in Proceedings of Conference on Empirical Methods in Natural Language Processing (Association for Computational Linguistics, 2014), pp. 1724–1734.

Secondini, M.

E. Agrell and M. Secondini, “Information-theoretic tools for optical communication engineers,” in Proceedings of IEEE Photonics Conference (IPC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–5.

ten Brink, S.

S. Dörner, S. Cammerer, J. Hoydis, and S. ten Brink, “Deep learning-based communication over the air,” IEEE J. Sel. Topics Signal Process. 12(1), 132–143 (2018).
[Crossref]

Thouin, F.

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightw. Technol. 36(20), 4843–4855 (2018).
[Crossref]

van Marrienboer, B.

K. Cho, B. van Marrienboer, C. Gulcehre, D. Bhadanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN encoder-decoder for statistical machine translation,” in Proceedings of Conference on Empirical Methods in Natural Language Processing (Association for Computational Linguistics, 2014), pp. 1724–1734.

van Veen, D.

V. Houtsma, E. Chou, and D. van Veen, “92 and 50 Gbps TDM-PON Using Neural Network Enabled Receiver Equalization Specialized for PON,” in Proceedings of Optical Fiber Communication Conference (OFC) (Optical Society of America, 2019), paper M2B.6.

Villasenor, J.

D.-U Lee, J. Villasenor, W. Luk, and P. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659 (2006).
[Crossref]

Williams, R.

D. Rumelhart, G. Hinton, and R. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
[Crossref]

Wymeersch, H.

S. Li, C. Häger, N. Garcia, and H. Wymeersch, “Achievable information rates for nonlinear fiber communication via end-to-end autoencoder learning,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.

Yankov, M. P.

R. Jones, T. A. Eriksson, M. P. Yankov, B. J. Puttnam, G. Rademacher, R. S. Luis, and D. Zibar, “Geometric constellation shaping for fiber optic communication systems via end-to-end learning,” ArXiv preprint arXiv:1810.00774 (2018).

Ye, C.

C. Ye and et al., “Recurrent neural network (RNN) based end-to-end nonlinear management for symmetrical 50Gbps NRZ PON with 29dB+ loss budget,” in Proceedings of 44th European Conference on Optical Communications (ECOC) (Institute of Electrical and Electronics Engineers, 2018), pp. 1–3.

Zettlemoyer, L.

K. Lee, O. Levy, and L. Zettlemoyer, “Recurrent additive networks,” ArXiv preprint arXiv:1705.07393 (2017).

Zibar, D.

R. Jones, T. A. Eriksson, M. P. Yankov, B. J. Puttnam, G. Rademacher, R. S. Luis, and D. Zibar, “Geometric constellation shaping for fiber optic communication systems via end-to-end learning,” ArXiv preprint arXiv:1810.00774 (2018).

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

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Figures (7)

Fig. 1
Fig. 1 Schematic of the IM/DD optical fiber communication system implemented as a bidirectional deep recurrent neural network. Optimization is performed between the stream of input messages and the outputs of the receiver, thus enabling end-to-end optimization via deep learning of the complete system. Inset figures show the transmitted signal spectrum both at the output of the neural network and before the DAC.
Fig. 2
Fig. 2 Bidirectional RNN schematic. The final transmitter/receiver outputs are obtained by merging the outputs of the forward and backward passes. The transmitter outputs are sent through the communication channel, while softmax is applied to the receiver outputs resulting in probability vectors pt, utilized in the sliding window estimation.
Fig. 3
Fig. 3 Schematic of: (a) a vanilla RNN cell, (b) an LSTM-GRU cell. Lines merge when their content is concatenated and diverge when it is copied.
Fig. 4
Fig. 4 Schematic of the sliding window sequence estimation technique in which the BRNN transceiver is operated. Note that W = 3 is chosen for illustration purposes.
Fig. 5
Fig. 5 PAM2 system with multi-symbol FFNN receiver as in [17].
Fig. 6
Fig. 6 BER as a function of transmission distance for the end-to-end vanilla and LSTM-GRU SBRNN systems compared to the end-to-end FFNN as well as the PAM2 system with multi-symbol FFNN receiver. The systems operate at (a) 42 Gb/s and (b) 84 Gb/s. (c) BER versus processing window for the 84 Gb/s vanilla and LSTM-GRU SBRNN at 30 km.
Fig. 7
Fig. 7 Cross entropy loss versus training step for the 42 Gb/s (a) vanilla and (b) LSTM-GRU SBRNN systems at 30 km.

Tables (2)

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Table 1 Simulations Parameters

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Table 2 Parameters of the Utilized Neural Networks

Equations (10)

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y i = exp ( x i ) j exp ( x j ) .
h t = α ( W ( x t T h t 1 T ) T + b ) ,
α Tx ( x ) = α ReLU ( x ) α ReLU ( x π 4 ) ,
g t a = α ( W 1 ( x t T h t 1 T ) T + b 1 ) ,
g t b = σ ( W 2 ( x t T h t 1 T ) T + b 2 ) ,
h t = ( 1 g t b ) h t 1 + g t b α ( W 3 ( x t T ( g t a h t 1 ) T ) T + b 3 ) ,
y i = 1 1 + exp ( x i ) .
p i = 1 i k = 1 i p i ( k ) , i = 1 , W ,
p i = 1 W k = i i + W 1 p i ( k W + 1 ) , i = W + 1 , T .
BLER = 1 | T | i T 𝟙 { m i argmax ( p i ) } ,

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