Abstract

Two-dimensional eight-level pulse amplitude modulation with trellis-coded modulation (2D-TCM-PAM8) is proposed to overcome the bandwidth limitation for high-speed signal transmission due to its high spectral efficiency. However, the high coding gain of the TCM can only be achieved in bandlimited additive white Gaussian noise (AWGN) channels and cannot be achieved in nonlinear channels without any equalizers. In the directly modulated laser and direct detection (DML-DD) transmission system, the transceiver nonlinearities and the interaction between DML chirp and fiber dispersion will introduce nonlinear distortion. To compensate for the nonlinear distortion, we propose a computationally efficient piecewise linear (PWL)-Volterra equalizer. In this equalizer, we first use the PWL to correct the skewed eye diagram and then employ a simple 2nd order Volterra to compensate for the residual nonlinear distortions. By using the PWL-Volterra equalizer prior to the Viterbi decoder, the high coding gain of TCM can be achieved. In the experiment, a 104 Gb/s 8-state 2D-TCM-PAM8 signal generated in a ∼ 20 GHz DML is successfully transmitted over 10 km standard single-mode fiber (SSMF) in C band, with the bit error ratio (BER) below the HD-FEC limit of 3.8 × 10−3. Compared to only using the conventional 2nd order Volterra equalizer with a similar BER performance, the PWL-Volterra equalizer shows 29% computational complexity reduction.

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

Full Article  |  PDF Article

Corrections

4 March 2020: A typographical correction was made to the author affiliations.


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References

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2020 (1)

2019 (4)

2018 (4)

2017 (2)

N. Stojanovic, F. Karinou, Z. Qiang, and C. Prodaniuc, “Volterra and Wiener equalizers for short-reach 100G PAM-4 applications,” J. Lightwave Technol. 35(21), 4583–4594 (2017).
[Crossref]

Y. Fu, M. Bi, D. Feng, X. Miao, H. He, and W. Hu, “Spectral efficiency improved 2D-PAM8 trellis coded modulation for short reach optical system,” IEEE Photonics J. 9(4), 1–8 (2017).
[Crossref]

2016 (3)

2015 (2)

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit ethernet using advanced modulation formats: performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

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 PAM4, CAP-16, and DMT for 100 Gb/s short reach optical transmission systems,” Opt. Express 23(2), 1176–1189 (2015).
[Crossref]

1987 (1)

G. Ungerboeck, “Trellis-coded modulation with redundant signal sets part II: state of the art,” IEEE Commun. Mag. 25(2), 5–11 (1987).
[Crossref]

Amiralizadeh, S.

Bae, S. H.

Bi, M.

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for DML based PAM-4 signal transmission over a dispersion uncompensated link,” J. Lightwave Technol. 38(3), 654–660 (2020).
[Crossref]

Y. Fu, M. Bi, D. Feng, X. Miao, H. He, and W. Hu, “Spectral efficiency improved 2D-PAM8 trellis coded modulation for short reach optical system,” IEEE Photonics J. 9(4), 1–8 (2017).
[Crossref]

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for 56 Gbit/s PAM4 signal transmission using DML with large adiabatic chirp,” 2019 Eur. Conf. Opt. Commun.Tu.2.B.5 (2019).

Buchali, F.

Bülow, H.

Chagnon, M.

Chen, W.

Cheng, M.

D. Li, L. Deng, Y. Ye, Y. Zhang, M. Cheng, S. Fu, M. Tang, and D. Liu, “4 × 96 Gbit/s PAM8 for short-reach applications employing low-cost DML without pre-equalization,” in Optical Fiber Communication Conference, W2A. 33 (2019).

Cheng, Q.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit ethernet using advanced modulation formats: performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

Chung, Y. C.

Cunningham, D. G.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit ethernet using advanced modulation formats: performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

Deng, L.

D. Li, L. Deng, Y. Ye, Y. Zhang, M. Cheng, S. Fu, M. Tang, and D. Liu, “4 × 96 Gbit/s PAM8 for short-reach applications employing low-cost DML without pre-equalization,” in Optical Fiber Communication Conference, W2A. 33 (2019).

Diamantopoulos, N. P.

El-Fiky, E.

Feng, D.

Y. Fu, M. Bi, D. Feng, X. Miao, H. He, and W. Hu, “Spectral efficiency improved 2D-PAM8 trellis coded modulation for short reach optical system,” IEEE Photonics J. 9(4), 1–8 (2017).
[Crossref]

Fu, S.

D. Li, L. Deng, Y. Ye, Y. Zhang, M. Cheng, S. Fu, M. Tang, and D. Liu, “4 × 96 Gbit/s PAM8 for short-reach applications employing low-cost DML without pre-equalization,” in Optical Fiber Communication Conference, W2A. 33 (2019).

Fu, Y.

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for DML based PAM-4 signal transmission over a dispersion uncompensated link,” J. Lightwave Technol. 38(3), 654–660 (2020).
[Crossref]

Y. Fu, M. Bi, D. Feng, X. Miao, H. He, and W. Hu, “Spectral efficiency improved 2D-PAM8 trellis coded modulation for short reach optical system,” IEEE Photonics J. 9(4), 1–8 (2017).
[Crossref]

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for 56 Gbit/s PAM4 signal transmission using DML with large adiabatic chirp,” 2019 Eur. Conf. Opt. Commun.Tu.2.B.5 (2019).

Gao, Y.

Gui, T.

Hashimoto, T.

He, H.

K. Zhang, H. He, H. Xin, W. Hu, S. Liang, D. Lu, and L. Zhao, “Chirp-aided power fading mitigation for upstream 100 km full-range long reach PON with DBR DML,” Opt. Commun. 407, 63–68 (2018).
[Crossref]

Y. Fu, M. Bi, D. Feng, X. Miao, H. He, and W. Hu, “Spectral efficiency improved 2D-PAM8 trellis coded modulation for short reach optical system,” IEEE Photonics J. 9(4), 1–8 (2017).
[Crossref]

H. Xin, K. Zhang, Q. Zhuge, L. Yi, H. He, W. Hu, and D. V. Plant, “Transmission of 100Gb/s PAM4 Signals Over 15 km Dispersion-Unmanaged SSMF Using a Directly Modulated Laser in C-Band,” 2018 Eur. Conf. Opt. Commun., We2.33 (2018).

Hu, H.

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for DML based PAM-4 signal transmission over a dispersion uncompensated link,” J. Lightwave Technol. 38(3), 654–660 (2020).
[Crossref]

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for 56 Gbit/s PAM4 signal transmission using DML with large adiabatic chirp,” 2019 Eur. Conf. Opt. Commun.Tu.2.B.5 (2019).

Hu, Q.

Hu, R.

C. Yang, R. Hu, M. Luo, Q. Yang, C. Li, H. Li, and S. Yu, “IM/DD-based 112-Gb/s/lambda PAM-4 transmission using 18-Gbps DML,” IEEE Photonics J. 8(3), 1–7 (2016).
[Crossref]

Hu, W.

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for DML based PAM-4 signal transmission over a dispersion uncompensated link,” J. Lightwave Technol. 38(3), 654–660 (2020).
[Crossref]

K. Zhang, H. He, H. Xin, W. Hu, S. Liang, D. Lu, and L. Zhao, “Chirp-aided power fading mitigation for upstream 100 km full-range long reach PON with DBR DML,” Opt. Commun. 407, 63–68 (2018).
[Crossref]

K. Zhang, Q. Zhuge, H. Xin, W. Hu, and D. V. Plant, “Performance comparison of DML, EML and MZM in dispersion-unmanaged short reach transmissions with digital signal processing,” Opt. Express 26(26), 34288–34304 (2018).
[Crossref]

Y. Fu, M. Bi, D. Feng, X. Miao, H. He, and W. Hu, “Spectral efficiency improved 2D-PAM8 trellis coded modulation for short reach optical system,” IEEE Photonics J. 9(4), 1–8 (2017).
[Crossref]

H. Xin, K. Zhang, Q. Zhuge, L. Yi, H. He, W. Hu, and D. V. Plant, “Transmission of 100Gb/s PAM4 Signals Over 15 km Dispersion-Unmanaged SSMF Using a Directly Modulated Laser in C-Band,” 2018 Eur. Conf. Opt. Commun., We2.33 (2018).

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for 56 Gbit/s PAM4 signal transmission using DML with large adiabatic chirp,” 2019 Eur. Conf. Opt. Commun.Tu.2.B.5 (2019).

Ida, M.

Jia, S.

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for DML based PAM-4 signal transmission over a dispersion uncompensated link,” J. Lightwave Technol. 38(3), 654–660 (2020).
[Crossref]

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for 56 Gbit/s PAM4 signal transmission using DML with large adiabatic chirp,” 2019 Eur. Conf. Opt. Commun.Tu.2.B.5 (2019).

Kakitsuka, T.

Karinou, F.

Kim, H.

Kobayashi, W.

Kong, D.

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for DML based PAM-4 signal transmission over a dispersion uncompensated link,” J. Lightwave Technol. 38(3), 654–660 (2020).
[Crossref]

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for 56 Gbit/s PAM4 signal transmission using DML with large adiabatic chirp,” 2019 Eur. Conf. Opt. Commun.Tu.2.B.5 (2019).

Kong, M.

Lau, A. P. T.

Li, C.

C. Yang, R. Hu, M. Luo, Q. Yang, C. Li, H. Li, and S. Yu, “IM/DD-based 112-Gb/s/lambda PAM-4 transmission using 18-Gbps DML,” IEEE Photonics J. 8(3), 1–7 (2016).
[Crossref]

Li, D.

D. Li, L. Deng, Y. Ye, Y. Zhang, M. Cheng, S. Fu, M. Tang, and D. Liu, “4 × 96 Gbit/s PAM8 for short-reach applications employing low-cost DML without pre-equalization,” in Optical Fiber Communication Conference, W2A. 33 (2019).

Li, H.

C. Yang, R. Hu, M. Luo, Q. Yang, C. Li, H. Li, and S. Yu, “IM/DD-based 112-Gb/s/lambda PAM-4 transmission using 18-Gbps DML,” IEEE Photonics J. 8(3), 1–7 (2016).
[Crossref]

Li, X.

Liang, S.

K. Zhang, H. He, H. Xin, W. Hu, S. Liang, D. Lu, and L. Zhao, “Chirp-aided power fading mitigation for upstream 100 km full-range long reach PON with DBR DML,” Opt. Commun. 407, 63–68 (2018).
[Crossref]

Liu, B.

Liu, D.

D. Li, L. Deng, Y. Ye, Y. Zhang, M. Cheng, S. Fu, M. Tang, and D. Liu, “4 × 96 Gbit/s PAM8 for short-reach applications employing low-cost DML without pre-equalization,” in Optical Fiber Communication Conference, W2A. 33 (2019).

Llorente, R.

Lu, C.

Lu, D.

K. Zhang, H. He, H. Xin, W. Hu, S. Liang, D. Lu, and L. Zhao, “Chirp-aided power fading mitigation for upstream 100 km full-range long reach PON with DBR DML,” Opt. Commun. 407, 63–68 (2018).
[Crossref]

Luo, M.

C. Yang, R. Hu, M. Luo, Q. Yang, C. Li, H. Li, and S. Yu, “IM/DD-based 112-Gb/s/lambda PAM-4 transmission using 18-Gbps DML,” IEEE Photonics J. 8(3), 1–7 (2016).
[Crossref]

Man, J.

Matsuo, S.

Miao, X.

Y. Fu, M. Bi, D. Feng, X. Miao, H. He, and W. Hu, “Spectral efficiency improved 2D-PAM8 trellis coded modulation for short reach optical system,” IEEE Photonics J. 9(4), 1–8 (2017).
[Crossref]

Miyamoto, Y.

Morsy-Osman, M.

Nagatani, M.

Nakamura, M.

Nishi, H.

Nosaka, H.

Ogiso, Y.

Pan, X.

Penty, R. V.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit ethernet using advanced modulation formats: performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

Plant, D. V.

Prodaniuc, C.

Qiang, Z.

Rusch, L. A.

Schuh, K.

Stojanovic, N.

Takeda, K.

Tang, M.

D. Li, L. Deng, Y. Ye, Y. Zhang, M. Cheng, S. Fu, M. Tang, and D. Liu, “4 × 96 Gbit/s PAM8 for short-reach applications employing low-cost DML without pre-equalization,” in Optical Fiber Communication Conference, W2A. 33 (2019).

Tao, L.

Ungerboeck, G.

G. Ungerboeck, “Trellis-coded modulation with redundant signal sets part II: state of the art,” IEEE Commun. Mag. 25(2), 5–11 (1987).
[Crossref]

Wakita, H.

Wang, K.

Wei, J.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit ethernet using advanced modulation formats: performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

Wei, Y.

White, I. H.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit ethernet using advanced modulation formats: performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

Xiang, M.

Xin, H.

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for DML based PAM-4 signal transmission over a dispersion uncompensated link,” J. Lightwave Technol. 38(3), 654–660 (2020).
[Crossref]

K. Zhang, H. He, H. Xin, W. Hu, S. Liang, D. Lu, and L. Zhao, “Chirp-aided power fading mitigation for upstream 100 km full-range long reach PON with DBR DML,” Opt. Commun. 407, 63–68 (2018).
[Crossref]

K. Zhang, Q. Zhuge, H. Xin, W. Hu, and D. V. Plant, “Performance comparison of DML, EML and MZM in dispersion-unmanaged short reach transmissions with digital signal processing,” Opt. Express 26(26), 34288–34304 (2018).
[Crossref]

H. Xin, K. Zhang, Q. Zhuge, L. Yi, H. He, W. Hu, and D. V. Plant, “Transmission of 100Gb/s PAM4 Signals Over 15 km Dispersion-Unmanaged SSMF Using a Directly Modulated Laser in C-Band,” 2018 Eur. Conf. Opt. Commun., We2.33 (2018).

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for 56 Gbit/s PAM4 signal transmission using DML with large adiabatic chirp,” 2019 Eur. Conf. Opt. Commun.Tu.2.B.5 (2019).

Xin, X.

Xing, Z.

Yamazaki, H.

Yang, C.

C. Yang, R. Hu, M. Luo, Q. Yang, C. Li, H. Li, and S. Yu, “IM/DD-based 112-Gb/s/lambda PAM-4 transmission using 18-Gbps DML,” IEEE Photonics J. 8(3), 1–7 (2016).
[Crossref]

Yang, Q.

C. Yang, R. Hu, M. Luo, Q. Yang, C. Li, H. Li, and S. Yu, “IM/DD-based 112-Gb/s/lambda PAM-4 transmission using 18-Gbps DML,” IEEE Photonics J. 8(3), 1–7 (2016).
[Crossref]

Ye, Y.

D. Li, L. Deng, Y. Ye, Y. Zhang, M. Cheng, S. Fu, M. Tang, and D. Liu, “4 × 96 Gbit/s PAM8 for short-reach applications employing low-cost DML without pre-equalization,” in Optical Fiber Communication Conference, W2A. 33 (2019).

Yekani, A.

Yi, L.

H. Xin, K. Zhang, Q. Zhuge, L. Yi, H. He, W. Hu, and D. V. Plant, “Transmission of 100Gb/s PAM4 Signals Over 15 km Dispersion-Unmanaged SSMF Using a Directly Modulated Laser in C-Band,” 2018 Eur. Conf. Opt. Commun., We2.33 (2018).

Yu, J.

Yu, S.

C. Yang, R. Hu, M. Luo, Q. Yang, C. Li, H. Li, and S. Yu, “IM/DD-based 112-Gb/s/lambda PAM-4 transmission using 18-Gbps DML,” IEEE Photonics J. 8(3), 1–7 (2016).
[Crossref]

Zeng, L.

Zhang, J.

Zhang, K.

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for DML based PAM-4 signal transmission over a dispersion uncompensated link,” J. Lightwave Technol. 38(3), 654–660 (2020).
[Crossref]

K. Zhang, H. He, H. Xin, W. Hu, S. Liang, D. Lu, and L. Zhao, “Chirp-aided power fading mitigation for upstream 100 km full-range long reach PON with DBR DML,” Opt. Commun. 407, 63–68 (2018).
[Crossref]

K. Zhang, Q. Zhuge, H. Xin, W. Hu, and D. V. Plant, “Performance comparison of DML, EML and MZM in dispersion-unmanaged short reach transmissions with digital signal processing,” Opt. Express 26(26), 34288–34304 (2018).
[Crossref]

H. Xin, K. Zhang, Q. Zhuge, L. Yi, H. He, W. Hu, and D. V. Plant, “Transmission of 100Gb/s PAM4 Signals Over 15 km Dispersion-Unmanaged SSMF Using a Directly Modulated Laser in C-Band,” 2018 Eur. Conf. Opt. Commun., We2.33 (2018).

Y. Fu, D. Kong, H. Xin, S. Jia, K. Zhang, M. Bi, W. Hu, and H. Hu, “Piecewise linear equalizer for 56 Gbit/s PAM4 signal transmission using DML with large adiabatic chirp,” 2019 Eur. Conf. Opt. Commun.Tu.2.B.5 (2019).

Zhang, Y.

D. Li, L. Deng, Y. Ye, Y. Zhang, M. Cheng, S. Fu, M. Tang, and D. Liu, “4 × 96 Gbit/s PAM8 for short-reach applications employing low-cost DML without pre-equalization,” in Optical Fiber Communication Conference, W2A. 33 (2019).

Zhao, L.

J. Zhang, J. Yu, X. Li, Y. Wei, K. Wang, L. Zhao, W. Zhao, M. Kong, X. Pan, B. Liu, and X. Xin, “100 Gbit/s VSB-PAM-n IM/DD transmission system based on 10 GHz DML with optical filtering and joint nonlinear equalization,” Opt. Express 27(5), 6098–6105 (2019).
[Crossref]

K. Zhang, H. He, H. Xin, W. Hu, S. Liang, D. Lu, and L. Zhao, “Chirp-aided power fading mitigation for upstream 100 km full-range long reach PON with DBR DML,” Opt. Commun. 407, 63–68 (2018).
[Crossref]

Zhao, W.

Zhong, K.

Zhou, X.

Zhuge, Q.

IEEE Commun. Mag. (2)

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Figures (6)

Fig. 1.
Fig. 1. (a) Configuration of transmitter DSP: generation process of 2D-TCM-PAM8 signal, (b) Constellation mapper: set partitioning rule of 2D-TCM-PAM8, (c) Receiver DSP consists of a PWL-Volterra equalizer (PWL equalizer and 2nd order Volterra equalizer with small taps) and an 8-state Viterbi decoder, and (d) Procedures for PWL equalizer.
Fig. 2.
Fig. 2. Experimental setups of 2D-TCM-PAM8 signal in DML-DD transmission. Convolutional encoder, constellation mapper, and Viterbi decoder are specific procedures for 2D-TCM-PAM8.
Fig. 3.
Fig. 3. (a) 3D colormap surface of SER performance versus threshold sets ${\lambda _1}$ and ${\lambda _2}$ of PWL equalizer, (i) and (ii) correspond to threshold decompositions schematic diagrams and eye diagrams in 104 Gb/s over 10 km transmission for PWL equalizer with threshold sets: $\{ - 10,10\}$ , and $\{ 1, - 3\}$ , respectively.
Fig. 4.
Fig. 4. (a) SER and (b) BER performance comparisons of 104 Gb/s 2D-TCM-PAM8 over 10 km without equalizers, with FFE(164), with PWL(51), with Volterra(81, 7), and with PWL(51)-Volterra(81, 7), respectively, (c) SER and BER performances of 104 Gb/s 2D-TCM-PAM8 in the case of BtB and after 10 km transmission.
Fig. 5.
Fig. 5. (a) BER comparisons of PWL-Volterra and classical Volterra equalizers with 11 2nd taps, (b) BER and (c) computational complexity comparisons of PWL-Volterra and classical 2nd order Volterra when varying the number of 2nd order taps of classical 2nd order Volterra equalizer.
Fig. 6.
Fig. 6. (a) SER and (b) BER performance comparisons of 56 Gb/s, 72 Gb/s, 88 Gb/s, and 104 Gb/s 2D-TCM-PAM8 over 10 km with PWL(51)-Volterra(81, 7), respectively, (c) electrical spectra of 56 Gb/s, 72 Gb/s, 88 Gb/s, and 104 Gb/s 2D-TCM-PAM8 over 10 km transmission.

Tables (1)

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Table 1. The computational complexities in terms of the number of required multiplexers.

Equations (1)

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y ( k ) = l 1 = 0 L 2 1 l 2 = 0 l 1 h 2 ( l 1 , l 2 ) m = 1 2 x ( k l m ) + l 1 = 0 L 1 1 h 1 ( l 1 ) x ( k l 1 ) .

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