Abstract

The past decade witnessed the stirring development of advanced optical modulations and digital signal processing, which have been pushing optical transmission systems towards the capacity limit. Recent research has sought to squeeze out the last few bits from bandwidth-limited optical channels. One straightforward path is to expand the signal spectrum beyond the bandwidth limit while keeping the single-carrier modulation, which inevitably induces huge inter-symbol interference. To cope with such penalty, sophisticated digital nonlinear equalization on single-carrier signals should be exploited to reduce the burden of the subsequent forward error corrections (FEC). On the other hand, a more instinctive capacity-approaching method for bandwidth-deficient channels is the well-known water-filling realized by multicarrier modulation. As its approximation, bit loading (BL) has been a well-established algorithm to maximize the bit rate of a discrete multitone (DMT) channel with fixed-rate FEC. Built on probabilistic constellation shaping (PCS), multicarrier entropy loading (EL) goes beyond BL by continuous source entropy adaptation and has proven its superiority over the single-carrier PCS counterpart. In this paper, we reveal the EL advantage over BL on both achievable information rate (AIR) and FEC, aiming to prove EL as the optimum capacity-approaching solution for bandwidth-limited channels with frequency-selective fading. In a 100G direct detection system with a bandwidth-deficient directly modulated laser, EL improves the AIR by 5%-10% over BL using identical FEC overhead. EL will be critical for short-reach interconnects dominated by low-cost optical components to squeeze out the last few bits from the bandwidth-constrained system.

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

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References

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2018 (2)

2017 (2)

2016 (4)

2015 (1)

2008 (1)

2006 (1)

A. Lozano, A. M. Tulino, and S. Verdu, “Optimum power allocation for parallel Gaussian channels with arbitrary input distributions,” IEEE Trans. Inf. Theory 52(7), 3033–3051 (2006).
[Crossref]

1995 (1)

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(234), 773–775 (1995).
[Crossref]

1991 (1)

G. D. Forney and M. V. Eyuboglu, “Combined equalization and coding using precoding,” IEEE Commun. Mag. 29(12), 25–34 (1991).
[Crossref]

1990 (1)

J. A. C. Bingham, “Multicarrier modulation for data transmission: an idea whose time has come,” IEEE Commun. Mag. 28(5), 5–14 (1990).
[Crossref]

Alvarado, A.

Antonelli, C.

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode kramers-kronig detection of 440-Gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (2017), PD1.
[Crossref]

Bingham, J. A. C.

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(234), 773–775 (1995).
[Crossref]

J. A. C. Bingham, “Multicarrier modulation for data transmission: an idea whose time has come,” IEEE Commun. Mag. 28(5), 5–14 (1990).
[Crossref]

Bocherer, G.

Böcherer, G.

Breyer, F.

Buchali, F.

F. Buchali, F. Steiner, G. Bocherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64- QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

W. Idler, F. Buchali, L. Schmalen, K. Schuh, and H. Buelow, “Hybrid modulation formats outperforming 16QAM and 8QAM in transmission distance and filtering with cascaded WSS,” in Optical Fiber Communication Conference (2015), M3G.4.
[Crossref]

Buelow, H.

W. Idler, F. Buchali, L. Schmalen, K. Schuh, and H. Buelow, “Hybrid modulation formats outperforming 16QAM and 8QAM in transmission distance and filtering with cascaded WSS,” in Optical Fiber Communication Conference (2015), M3G.4.
[Crossref]

Burrows, E.

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. Burrows, G. Raybon, and P. Winzer, “High-spectral-efficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in European Conference on Optical Communication (2016), Th.3.C.1.

Chandrasekhar, S.

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. Burrows, G. Raybon, and P. Winzer, “High-spectral-efficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in European Conference on Optical Communication (2016), Th.3.C.1.

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, B. Zhu, and D. Peckham, “Generation and FEC-decoding of a 231.5-Gb/s PDMOFDM signal with 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Optical Fiber Communication Conference (2012), PDP5B.3.
[Crossref]

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode kramers-kronig detection of 440-Gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (2017), PD1.
[Crossref]

Che, D.

D. Che and W. Shieh, “Approaching the capacity of colored-SNR optical channels by multicarrier entropy loading,” J. Lightwave Technol. 36(1), 68–78 (2018).
[Crossref]

D. Che, C. Sun, and W. Shieh, “Achievable Rate Comparison between Entropy and Bit Loading in a 100-Gb/s DM-DD DMT System,” in Optical Fiber Communication Conference (2019), W1F.3.

Chen, X.

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode kramers-kronig detection of 440-Gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (2017), PD1.
[Crossref]

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. Burrows, G. Raybon, and P. Winzer, “High-spectral-efficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in European Conference on Optical Communication (2016), Th.3.C.1.

Chen, Z.

Cho, J.

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. Burrows, G. Raybon, and P. Winzer, “High-spectral-efficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in European Conference on Optical Communication (2016), Th.3.C.1.

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode kramers-kronig detection of 440-Gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (2017), PD1.
[Crossref]

J. Cho, L. Schmalen, and P. Winzer, “Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM,” in European Conference on Optical Communication (2017), M.2.D.2.
[Crossref]

Chow, P. S.

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(234), 773–775 (1995).
[Crossref]

Cioffi, J. M.

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(234), 773–775 (1995).
[Crossref]

Clausen, D.

Corteselli, S.

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, B. Zhu, and D. Peckham, “Generation and FEC-decoding of a 231.5-Gb/s PDMOFDM signal with 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Optical Fiber Communication Conference (2012), PDP5B.3.
[Crossref]

Deng, L.

Djordjevic, I. B.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Downie, J. D.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Eyuboglu, M. V.

G. D. Forney and M. V. Eyuboglu, “Combined equalization and coding using precoding,” IEEE Commun. Mag. 29(12), 25–34 (1991).
[Crossref]

Fehenberger, T.

Forney, G. D.

G. D. Forney and M. V. Eyuboglu, “Combined equalization and coding using precoding,” IEEE Commun. Mag. 29(12), 25–34 (1991).
[Crossref]

Fu, S.

Hanik, N.

Haunstein, H.

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, B. Zhu, and D. Peckham, “Generation and FEC-decoding of a 231.5-Gb/s PDMOFDM signal with 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Optical Fiber Communication Conference (2012), PDP5B.3.
[Crossref]

He, Z.

Hoang, T. M.

M. Xiang, Q. Zhuge, X. Zhou, M. Qiu, F. Zhang, T. M. Hoang, M. Y. S. Sowailem, M. Tang, D. Liu, S. Fu, and D. V. Plant, “Filtering tolerant digital subcarrier multiplexing system with flexible bit and power loading,” in Optical Fiber Communication Conference (2017), W4A.7.
[Crossref]

Huang, Y.-K.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Hurley, J.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Idler, W.

F. Buchali, F. Steiner, G. Bocherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64- QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

W. Idler, F. Buchali, L. Schmalen, K. Schuh, and H. Buelow, “Hybrid modulation formats outperforming 16QAM and 8QAM in transmission distance and filtering with cascaded WSS,” in Optical Fiber Communication Conference (2015), M3G.4.
[Crossref]

Inada, Y.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Kai, Y.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. C. Rasmussen, “Discrete multi-tone for 100 Gb/s optical access networks,” in Optical Fiber Communication Conference (2014), M2I.1.
[Crossref]

Kanno, A.

K. Matsumoto, Y. Yoshida, A. Maruta, A. Kanno, N. Yamamoto, and K. Kitayama, “On the impact of Tomlinson-Harashima precoding in optical PAM transmissions for intra-DCN communication,” in Optical Fiber Communication Conference (2017), Th3D.7.
[Crossref]

Karinou, F.

Khrapko, R.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Kitayama, K.

K. Matsumoto, Y. Yoshida, A. Maruta, A. Kanno, N. Yamamoto, and K. Kitayama, “On the impact of Tomlinson-Harashima precoding in optical PAM transmissions for intra-DCN communication,” in Optical Fiber Communication Conference (2017), Th3D.7.
[Crossref]

Koonen, A. M. J.

Lee, S. C. J.

Li, B.

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. Burrows, G. Raybon, and P. Winzer, “High-spectral-efficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in European Conference on Optical Communication (2016), Th.3.C.1.

Li, L.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. C. Rasmussen, “Discrete multi-tone for 100 Gb/s optical access networks,” in Optical Fiber Communication Conference (2014), M2I.1.
[Crossref]

Li, X.

Liu, D.

C. Xie, Z. Chen, S. Fu, W. Liu, Z. He, L. Deng, M. Tang, and D. Liu, “Achievable information rate enhancement of visible light communication using probabilistically shaped OFDM modulation,” Opt. Express 26(1), 367–375 (2018).
[Crossref] [PubMed]

M. Xiang, Q. Zhuge, X. Zhou, M. Qiu, F. Zhang, T. M. Hoang, M. Y. S. Sowailem, M. Tang, D. Liu, S. Fu, and D. V. Plant, “Filtering tolerant digital subcarrier multiplexing system with flexible bit and power loading,” in Optical Fiber Communication Conference (2017), W4A.7.
[Crossref]

Liu, W.

Liu, X.

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, B. Zhu, and D. Peckham, “Generation and FEC-decoding of a 231.5-Gb/s PDMOFDM signal with 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Optical Fiber Communication Conference (2012), PDP5B.3.
[Crossref]

Lotz, T.

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, B. Zhu, and D. Peckham, “Generation and FEC-decoding of a 231.5-Gb/s PDMOFDM signal with 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Optical Fiber Communication Conference (2012), PDP5B.3.
[Crossref]

Lozano, A.

A. Lozano, A. M. Tulino, and S. Verdu, “Optimum power allocation for parallel Gaussian channels with arbitrary input distributions,” IEEE Trans. Inf. Theory 52(7), 3033–3051 (2006).
[Crossref]

Maruta, A.

K. Matsumoto, Y. Yoshida, A. Maruta, A. Kanno, N. Yamamoto, and K. Kitayama, “On the impact of Tomlinson-Harashima precoding in optical PAM transmissions for intra-DCN communication,” in Optical Fiber Communication Conference (2017), Th3D.7.
[Crossref]

Mateo, E.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Matsumoto, K.

K. Matsumoto, Y. Yoshida, A. Maruta, A. Kanno, N. Yamamoto, and K. Kitayama, “On the impact of Tomlinson-Harashima precoding in optical PAM transmissions for intra-DCN communication,” in Optical Fiber Communication Conference (2017), Th3D.7.
[Crossref]

Mecozzi, A.

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode kramers-kronig detection of 440-Gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (2017), PD1.
[Crossref]

Mishra, S.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Nazarov, V.

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

Nishihara, M.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. C. Rasmussen, “Discrete multi-tone for 100 Gb/s optical access networks,” in Optical Fiber Communication Conference (2014), M2I.1.
[Crossref]

Ohlendorf, S.

Pachnicke, S.

Peckham, D.

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, B. Zhu, and D. Peckham, “Generation and FEC-decoding of a 231.5-Gb/s PDMOFDM signal with 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Optical Fiber Communication Conference (2012), PDP5B.3.
[Crossref]

Plant, D. V.

M. Xiang, Q. Zhuge, X. Zhou, M. Qiu, F. Zhang, T. M. Hoang, M. Y. S. Sowailem, M. Tang, D. Liu, S. Fu, and D. V. Plant, “Filtering tolerant digital subcarrier multiplexing system with flexible bit and power loading,” in Optical Fiber Communication Conference (2017), W4A.7.
[Crossref]

Qiu, M.

M. Xiang, Q. Zhuge, X. Zhou, M. Qiu, F. Zhang, T. M. Hoang, M. Y. S. Sowailem, M. Tang, D. Liu, S. Fu, and D. V. Plant, “Filtering tolerant digital subcarrier multiplexing system with flexible bit and power loading,” in Optical Fiber Communication Conference (2017), W4A.7.
[Crossref]

Randel, S.

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W. Idler, F. Buchali, L. Schmalen, K. Schuh, and H. Buelow, “Hybrid modulation formats outperforming 16QAM and 8QAM in transmission distance and filtering with cascaded WSS,” in Optical Fiber Communication Conference (2015), M3G.4.
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X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode kramers-kronig detection of 440-Gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (2017), PD1.
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M. Xiang, Q. Zhuge, X. Zhou, M. Qiu, F. Zhang, T. M. Hoang, M. Y. S. Sowailem, M. Tang, D. Liu, S. Fu, and D. V. Plant, “Filtering tolerant digital subcarrier multiplexing system with flexible bit and power loading,” in Optical Fiber Communication Conference (2017), W4A.7.
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T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. C. Rasmussen, “Discrete multi-tone for 100 Gb/s optical access networks,” in Optical Fiber Communication Conference (2014), M2I.1.
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X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode kramers-kronig detection of 440-Gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (2017), PD1.
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J. Cho, L. Schmalen, and P. Winzer, “Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM,” in European Conference on Optical Communication (2017), M.2.D.2.
[Crossref]

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. Burrows, G. Raybon, and P. Winzer, “High-spectral-efficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in European Conference on Optical Communication (2016), Th.3.C.1.

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, B. Zhu, and D. Peckham, “Generation and FEC-decoding of a 231.5-Gb/s PDMOFDM signal with 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Optical Fiber Communication Conference (2012), PDP5B.3.
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Other (11)

D. Che, C. Sun, and W. Shieh, “Achievable Rate Comparison between Entropy and Bit Loading in a 100-Gb/s DM-DD DMT System,” in Optical Fiber Communication Conference (2019), W1F.3.

K. Matsumoto, Y. Yoshida, A. Maruta, A. Kanno, N. Yamamoto, and K. Kitayama, “On the impact of Tomlinson-Harashima precoding in optical PAM transmissions for intra-DCN communication,” in Optical Fiber Communication Conference (2017), Th3D.7.
[Crossref]

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. C. Rasmussen, “Discrete multi-tone for 100 Gb/s optical access networks,” in Optical Fiber Communication Conference (2014), M2I.1.
[Crossref]

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode kramers-kronig detection of 440-Gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (2017), PD1.
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J. Cho, L. Schmalen, and P. Winzer, “Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM,” in European Conference on Optical Communication (2017), M.2.D.2.
[Crossref]

S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. Burrows, G. Raybon, and P. Winzer, “High-spectral-efficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in European Conference on Optical Communication (2016), Th.3.C.1.

W. Idler, F. Buchali, L. Schmalen, K. Schuh, and H. Buelow, “Hybrid modulation formats outperforming 16QAM and 8QAM in transmission distance and filtering with cascaded WSS,” in Optical Fiber Communication Conference (2015), M3G.4.
[Crossref]

M. Xiang, Q. Zhuge, X. Zhou, M. Qiu, F. Zhang, T. M. Hoang, M. Y. S. Sowailem, M. Tang, D. Liu, S. Fu, and D. V. Plant, “Filtering tolerant digital subcarrier multiplexing system with flexible bit and power loading,” in Optical Fiber Communication Conference (2017), W4A.7.
[Crossref]

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, B. Zhu, and D. Peckham, “Generation and FEC-decoding of a 231.5-Gb/s PDMOFDM signal with 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Optical Fiber Communication Conference (2012), PDP5B.3.
[Crossref]

S. Zhang, F. Yaman, Y.-K. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishra, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz,” in Optical Fiber Communication Conference (2016), Th5C.2.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Relations between NGMI and SNR (i.e. look-up tables) for various modulation formats: (a) PCS 256-QAM; (b) discrete levels of QAM.
Fig. 2
Fig. 2 A 20-GHz DMT system: (a) SNR versus subcarrier frequency; (b) GMI versus NGMI. BL: bit loading; EL: entropy loading; EL-BG: entropy loading with bit loading subcarrier groups.
Fig. 3
Fig. 3 Channel capacity, bit/entropy loading map, and GMI versus frequency. (a-b) entropy loading (EL); (c-d) bit loading (BL); (e-f) EL with BL subcarrier groups (EL-BG); (g-h) GMI gaps to the channel capacity.
Fig. 4
Fig. 4 (a) SNR versus subcarrier frequency; (b) GMI versus NGMI. BL: bit loading; EL: entropy loading; B2B: back-to-back.
Fig. 5
Fig. 5 Channel capacity, bit/entropy loading map, and GMI versus frequency, in B2B systems. Both EL and BL has maximized the AIR with the NGMI shown in the left bottom corner.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

H(X)= i=1 M P( x i ) log 2 P( x i )
C= log 2 (1+SNR)
C= sup P(χ) I(X;Y)
I(X;Y)= 1 n i=1 n log 2 q( y i | x i ) x'χ P(x')q( y i |x')
NGMI=1[HGMI]/m
OH=(1NGMI)/NGMI
NGMI=1 E(H)E(GMI) E(m)

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