Abstract

A pruning method of artificial neural network based nonlinear equalizer (ANN-NLE) is proposed and validated for single-sideband 4-ary pulse amplitude modulation (SSB-PAM4) in IM/DD system. As a classifier, ANN is capable to form a complex nonlinear boundary among different classifications, which is considered as an appropriate way to mitigate the nonlinear impairments in optical communication system. In this paper, first, we introduce the operation principle of the traditional linear equalizer (LE) and NLE such as volterra equalizer (VE). Then we make an analogy among the LE, VE and ANN-NLE. After that, a novel pruning method is applied to reduce the complexity of ANN. The BER performance of ANN-NLE outperforms VE after fiber transmission. After 60 km fiber transmission, ANN-NLE decreases the BER by about one order of magnitude compared to VE. By implementing the proposed pruning method, the connections of ANN reduced by a factor of 10x while keeping the BER under the threshold of 3.8x10−3.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2017 (11)

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” Commun. ACM 60(6), 84–90 (2017).

Q. Zhang, N. Stojanovic, J. Wei, and C. Xie, “Single-lane 180 Gb/s DB-PAM-4-signal transmission over an 80 km DCF-free SSMF link,” Opt. Lett. 42(4), 883–886 (2017).
[PubMed]

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. Lightwave Technol. 35(4), 868–875 (2017).

Z. Li, M. S. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers–Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017).

M. Zhu, J. Zhang, X. Yi, Y. Song, B. Xu, X. Li, X. Du, and K. Qiu, “Hilbert superposition and modified signal-to-signal beating interference cancellation for single side-band optical NPAM-4 direct-detection system,” Opt. Express 25(11), 12622–12631 (2017).
[PubMed]

F. N. Khan, K. Zhong, X. Zhou, W. H. Al-Arashi, C. Yu, C. Lu, and A. P. T. Lau, “Joint OSNR monitoring and modulation format identification in digital coherent receivers using deep neural networks,” Opt. Express 25(15), 17767–17776 (2017).
[PubMed]

Z. Wang, M. Zhang, D. Wang, C. Song, M. Liu, J. Li, L. Lou, and Z. Liu, “Failure prediction using machine learning and time series in optical network,” Opt. Express 25(16), 18553–18565 (2017).
[PubMed]

Y. Cui, M. Zhang, D. Wang, S. Liu, Z. Li, and G. K. Chang, “Bit-based support vector machine nonlinear detector for millimeter-wave radio-over-fiber mobile fronthaul systems,” Opt. Express 25(21), 26186–26197 (2017).
[PubMed]

S. Liu, M. Xu, J. Wang, F. Lu, W. Zhang, H. Tian, and G. Chang, “A multilevel artificial neural network nonlinear equalizer for millimeter-wave mobile fronthaul systems,” J. Lightwave Technol. 35(20), 4406–4417 (2017).

Z. Wan, J. Li, L. Shu, S. Fu, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “64-Gb/s SSB-PAM4 transmission over 120-km dispersion-uncompensated SSMF with blind nonlinear equalization, adaptive noise-whitening postfilter and MLSD,” J. Lightwave Technol. 35(23), 5193–5200 (2017).

2016 (2)

2015 (1)

2014 (1)

2012 (1)

1998 (1)

1986 (1)

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

Al-Arashi, W. H.

Antonelli, C.

Arlunno, V.

Bayvel, P.

Bigo, S.

J. Estaran, R. Rios-Müller, M. A. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proceedings of European Conference on Optical Communication (ECOC)(2016), M.2.B.2.

Borkowski, R.

Brandt-Pearce, M.

Caballero, A.

Cartledge, J. C.

Chang, G.

Chang, G. K.

Chen, W.

Cui, Y.

Dai, Y.

Diniz, J. C. M.

Du, X.

Dupuy, J.-Y.

J. Estaran, R. Rios-Müller, M. A. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proceedings of European Conference on Optical Communication (ECOC)(2016), M.2.B.2.

Erkilinç, M. S.

Estaran, J.

J. Estaran, R. Rios-Müller, M. A. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proceedings of European Conference on Optical Communication (ECOC)(2016), M.2.B.2.

Fan, Y.

Franceschi, N.

Fu, S.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

Z. Wan, J. Li, L. Shu, S. Fu, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “64-Gb/s SSB-PAM4 transmission over 120-km dispersion-uncompensated SSMF with blind nonlinear equalization, adaptive noise-whitening postfilter and MLSD,” J. Lightwave Technol. 35(23), 5193–5200 (2017).

Galdino, L.

Gao, F.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

Gao, Y.

Gonzales, N. G.

Gui, T.

Hinton, G. E.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” Commun. ACM 60(6), 84–90 (2017).

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

Jones, R.

Jorge, F.

J. Estaran, R. Rios-Müller, M. A. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proceedings of European Conference on Optical Communication (ECOC)(2016), M.2.B.2.

Karar, A. S.

Khan, F. N.

Killey, R. I.

Konczykowska, A.

J. Estaran, R. Rios-Müller, M. A. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proceedings of European Conference on Optical Communication (ECOC)(2016), M.2.B.2.

Krizhevsky, A.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” Commun. ACM 60(6), 84–90 (2017).

Larsen, K. J.

Lau, A. P. T.

Li, J.

Li, X.

M. Zhu, J. Zhang, X. Yi, Y. Song, B. Xu, X. Li, X. Du, and K. Qiu, “Hilbert superposition and modified signal-to-signal beating interference cancellation for single side-band optical NPAM-4 direct-detection system,” Opt. Express 25(11), 12622–12631 (2017).
[PubMed]

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

Li, Z.

Liu, G. N.

Liu, M.

Liu, S.

Liu, Z.

Lou, L.

Lu, C.

Lu, F.

Man, J.

Mao, B.

Mao, Y.

Mardoyan, H.

J. Estaran, R. Rios-Müller, M. A. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proceedings of European Conference on Optical Communication (ECOC)(2016), M.2.B.2.

Mecozzi, A.

Mestre, M. A.

J. Estaran, R. Rios-Müller, M. A. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proceedings of European Conference on Optical Communication (ECOC)(2016), M.2.B.2.

Monroy, I. T.

Peddanarappagari, K. V.

Piels, M.

Qiu, K.

Rios-Müller, R.

J. Estaran, R. Rios-Müller, M. A. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems,” in Proceedings of European Conference on Optical Communication (ECOC)(2016), M.2.B.2.

Rumelhart, D. E.

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

Schmidt, M. N.

Shi, K.

Shtaif, M.

Shu, L.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

Z. Wan, J. Li, L. Shu, S. Fu, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “64-Gb/s SSB-PAM4 transmission over 120-km dispersion-uncompensated SSMF with blind nonlinear equalization, adaptive noise-whitening postfilter and MLSD,” J. Lightwave Technol. 35(23), 5193–5200 (2017).

Sillekens, E.

Song, C.

Song, Y.

Stojanovic, N.

Sutskever, I.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” Commun. ACM 60(6), 84–90 (2017).

Tao, L.

Thomsen, B. C.

Thrane, J.

Tian, H.

Wan, Z.

Z. Wan, J. Li, L. Shu, S. Fu, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “64-Gb/s SSB-PAM4 transmission over 120-km dispersion-uncompensated SSMF with blind nonlinear equalization, adaptive noise-whitening postfilter and MLSD,” J. Lightwave Technol. 35(23), 5193–5200 (2017).

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

Wang, D.

Wang, J.

Wang, Z.

Wass, J.

Wei, J.

Williams, R. J.

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

Winther, O.

Xie, C.

Xu, B.

Xu, K.

Z. Wan, J. Li, L. Shu, S. Fu, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “64-Gb/s SSB-PAM4 transmission over 120-km dispersion-uncompensated SSMF with blind nonlinear equalization, adaptive noise-whitening postfilter and MLSD,” J. Lightwave Technol. 35(23), 5193–5200 (2017).

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

Xu, M.

Xu, X.

Yang, Q.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

Ye, Y.

Yi, X.

Yin, F.

Yu, C.

Zeng, L.

Zhang, J.

Zhang, L.

Zhang, M.

Zhang, Q.

Zhang, W.

Zhong, K.

Zhou, E.

Zhou, X.

Zhou, Y.

Zhu, M.

Zibar, D.

Zuo, T.

Commun. ACM (1)

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” Commun. ACM 60(6), 84–90 (2017).

IEEE Photonics J. (1)

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers–Kronig detection over 80-km SSMF,” IEEE Photonics J. 9(6), 7204509 (2017).

J. Lightwave Technol. (7)

K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra series approach for optimizing fiber-optic communications system designs,” J. Lightwave Technol. 16(11), 2046–2055 (1998).

J. C. Cartledge and A. S. Karar, “100 Gb/s intensity modulation and direct detection,” J. Lightwave Technol. 32(16), 2809–2814 (2014).

L. Zhang, T. Zuo, Y. Mao, Q. Zhang, E. Zhou, G. N. Liu, and X. Xu, “Beyond 100-Gb/s transmission over 80-km SMF using direct-detection SSB-DMT at c-band,” J. Lightwave Technol. 34(2), 723–729 (2016).

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. Lightwave Technol. 35(4), 868–875 (2017).

Z. Li, M. S. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers–Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017).

S. Liu, M. Xu, J. Wang, F. Lu, W. Zhang, H. Tian, and G. Chang, “A multilevel artificial neural network nonlinear equalizer for millimeter-wave mobile fronthaul systems,” J. Lightwave Technol. 35(20), 4406–4417 (2017).

Z. Wan, J. Li, L. Shu, S. Fu, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “64-Gb/s SSB-PAM4 transmission over 120-km dispersion-uncompensated SSMF with blind nonlinear equalization, adaptive noise-whitening postfilter and MLSD,” J. Lightwave Technol. 35(23), 5193–5200 (2017).

Nature (1)

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

Opt. Express (6)

K. Zhong, X. Zhou, T. Gui, L. Tao, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “Experimental study of PAM-4, CAP-16, and DMT for 100 Gb/s short reach optical transmission systems,” Opt. Express 23(2), 1176–1189 (2015).
[PubMed]

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Figures (11)

Fig. 1
Fig. 1 (a) Schematic of LE. (b) Schematic of ANN based NLE. (c) Pure-linear function as activation function. (d) Rectified-Linear function as activation function. (e) Softmax function as activation function.
Fig. 2
Fig. 2 (a) Pipeline for ANN pruning. (b) Fully connected ANN. (c) Sparsely connected ANN.
Fig. 3
Fig. 3 Experimental setup of 112-Gb/s SSB-PAM4 transmission with DSP flows. (a) Impulse probe signal of AWG. (b) Received signal of DSO in optical B2B case when transmitting impulse probe signal. LE: linear equalizer; VE: Volterra equalizer; ANN-NLE: artificial neural network based nonlinear equalizer.
Fig. 4
Fig. 4 (a) Frequency response at Opt-B2B case including the bandwidth limitation of AWG and DSO. (b) Optical spectra of the SSB-PAM4 signal with and without pre-equalization.
Fig. 5
Fig. 5 BER versus the input optical power to PD at Opt-B2B case. pre-Equ: pre-equalization.
Fig. 6
Fig. 6 BER versus the launched optical power to 80-km dispersion-uncompensated SSMF.
Fig. 7
Fig. 7 BER versus fiber reach with the optimized launched optical power.
Fig. 8
Fig. 8 BER versus OSNR after 80 km dispersion uncompensated SSMF.
Fig. 9
Fig. 9 BER versus OSNR for different fiber reach. (a) with VE. (b) with ANN-NLE.
Fig. 10
Fig. 10 ANN pruning for different fiber reach. (a) Opt-B2B. (b) 20-km. (c) 40-km. (d) 60-km. (e) 80-km.
Fig. 11
Fig. 11 BER performance and connections versus fiber reach of fully-connected ANN-NLE and sparsely-connected ANN-NLE.

Equations (7)

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h w (n)= l=0 L1 w 1 ( l ) x( nl )
h w (n)= l 1 =0 L 1 1 w 1 ( l 1 ) x( n l 1 )+ l 1 =0 L 2 1 l 2 =0 l 1 w 2 ( l 1 , l 2 ) m=1 2 x ( n l m ) + l 1 =0 L 3 1 l 2 =0 l 1 l 3 =0 l 2 w 3 ( l 1 , l 2 , l 3 ) m=1 3 x( n l m ) + + l 1 =0 L k 1 l 2 =0 l 1 l k =0 l k1 w k ( l 1 , l 2 ,, l k ) m=1 k x( n l m )
h w ( x( n ) )=f( i w i x i )
J(w)= | y(n) h w ( x(n) ) | 2
w(n+1)=w(n)μ J(w) w(n) =w(n)+2μe(n) x * (n)
J(w)= k=1 K | y k (n) [ h w ( x(n) ) ] k | 2
w(n+1)=w(n)μ J(w) w(n)

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