Abstract

A novel, probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions is proposed in this paper. The proper geometric structural design of the star constellation, along with the probabilistic shaping, is able to achieve better improvement with regards to constellation figure of merit (CFM) and bit error rate (BER) performance. A 25-km standard single-mode fiber (SSMF) data transmission employing the proposed PS star-CAP modulation scheme is successfully demonstrated. Experiment results show that the proposed PS star-CAP-16 in C4,4,4,4 excels the traditional PS star-CAP-16 in C8,8 by 1.5 dB in receiver sensitivity at the BER of 1×103. At the same time, the novel PS star-CAP-32 with entropy of 4.4 bits/symbol defeats the uniform star-CAP-32 by 1.6 dB improvement under the same bit rate.

© 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. Y. Gao, Q. Zhuge, W. Wang, X. Xu, J. M. Buset, M. Qiu, M. Morsy-Osman, M. Chagnon, F. Li, L. Wang, C. Lu, A. P. T. Lau, and D. V. Plant, “40 Gb/s CAP32 short reach transmission over 80 km single mode fiber,” Opt. Express 23(9), 11412–11423 (2015).
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    [Crossref] [PubMed]
  3. S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Multidimensional PAM with Pseudo-Gray coding for flexible data center interconnects,” IEEE Photonics Technol. Lett. 30(12), 1143–1146 (2018).
    [Crossref]
  4. F. Li, X. Li, J. Zhang, and J. Yu, “Transmission of 100-Gb/s VSB DFT-spread DMT signal in short-reach optical communication systems,” IEEE Photonics J. 7(5), 1–7 (2015).
  5. F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental demonstration of four-channel WDM 560 Gbit/s 128QAM-DMT using IM/DD for 2-km optical interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
    [Crossref]
  6. G. Stepniak, “Comparison of efficiency of N-dimensional CAP modulations,” J. Lightwave Technol. 32(14), 2516–2523 (2014).
    [Crossref]
  7. L. Sun, J. Du, and Z. He, “Multiband three-dimensional carrierless amplitude phase modulation for short reach optical communications,” J. Lightwave Technol. 34(13), 3103–3109 (2016).
    [Crossref]
  8. J. Shi, J. Zhang, X. Li, N. Chi, Y. Zhang, Q. Zhang, and J. Yu, “Improved performance of high-order QAM OFDM based on probabilistically shaping in the datacom,” in Proc. OFC2018, paper W4G.6.
    [Crossref]
  9. C. Pan and F. R. Kschischang, “Probabilistic 16-QAM shaping in WDM systems,” J. Lightwave Technol. 34(18), 4285–4292 (2016).
    [Crossref]
  10. Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Proc. OFC2017, paper M3C.1.
    [Crossref]
  11. I. F. de Jauregui Ruiz, A. Ghazisaeidi, O. A. Sab, P. Plantady, A. Calsat, S. Dubost, L. Schmalen, V. Letellier, and J. Renaudier, “25.4-Tb/s transmission over transpacific distances using truncated probabilistically shaped PDM-64QAM,” J. Lightwave Technol. 36(6), 1354–1361 (2018).
    [Crossref]
  12. J. Shi, J. Zhang, N. Chi, Y. Cai, X. Li, Y. Zhang, Q. Zhang, and J. Yu, “Probabilistically shaped 1024-QAM OFDM transmission in an IM-DD system,” in Proc. OFC2018, paper W2A.44.
    [Crossref]
  13. X. Xu, B. Liu, X. Wu, L. Zhang, Y. Mao, J. Ren, Y. Zhang, L. Jiang, and X. Xin, “A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation,” Opt. Express 26(20), 26576–26589 (2018).
    [Crossref] [PubMed]
  14. S. Zhang and F. Yaman, “Constellation design with geometric and probabilistic shaping,” Opt. Commun. 409, 7–12 (2018).
    [Crossref]
  15. J.-X. Cai, H. G. Batshon, M. V. Mazurczyk, O. V. Sinkin, D. Wang, M. Paskov, W. W. Patterson, C. R. Davidson, P. C. Corbett, G. M. Wolter, T. E. Hammon, M. A. Bolshtyansky, D. G. Foursa, and A. N. Pilipetskii, “70.46 Tb/s over 7,600 km and 71.65 Tb/s over 6,970 km transmission in C+L band using coded modulation with hybrid constellation shaping and nonlinearity compensation,” J. Lightwave Technol. 36(1), 114–121 (2018).
    [Crossref]
  16. S. Zhang, Z. Qu, F. Yaman, E. Mateo, T. Inoue, K. Nakamura, Y. Inada, and I. B. Djordjevic, “Flex-rate transmission using hybrid probabilistic and geometric shaped 32QAM,” in Proc. OFC2018, paper M1G.3.
    [Crossref]
  17. B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
    [Crossref]
  18. G. D. Forney and L.-F. Wei, “Multidimensional constellations-part I: Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Comm. 7(6), 877–892 (1989).
    [Crossref]
  19. F. R. Kschischang and S. Pasupathy, “Optimal nonuniform signaling for Gaussian channels,” IEEE Trans. Inf. Theory 39(3), 913–929 (1993).
    [Crossref]
  20. G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
    [Crossref]
  21. P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
    [Crossref]
  22. K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018).
    [Crossref]

2018 (6)

S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Multidimensional PAM with Pseudo-Gray coding for flexible data center interconnects,” IEEE Photonics Technol. Lett. 30(12), 1143–1146 (2018).
[Crossref]

I. F. de Jauregui Ruiz, A. Ghazisaeidi, O. A. Sab, P. Plantady, A. Calsat, S. Dubost, L. Schmalen, V. Letellier, and J. Renaudier, “25.4-Tb/s transmission over transpacific distances using truncated probabilistically shaped PDM-64QAM,” J. Lightwave Technol. 36(6), 1354–1361 (2018).
[Crossref]

X. Xu, B. Liu, X. Wu, L. Zhang, Y. Mao, J. Ren, Y. Zhang, L. Jiang, and X. Xin, “A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation,” Opt. Express 26(20), 26576–26589 (2018).
[Crossref] [PubMed]

S. Zhang and F. Yaman, “Constellation design with geometric and probabilistic shaping,” Opt. Commun. 409, 7–12 (2018).
[Crossref]

J.-X. Cai, H. G. Batshon, M. V. Mazurczyk, O. V. Sinkin, D. Wang, M. Paskov, W. W. Patterson, C. R. Davidson, P. C. Corbett, G. M. Wolter, T. E. Hammon, M. A. Bolshtyansky, D. G. Foursa, and A. N. Pilipetskii, “70.46 Tb/s over 7,600 km and 71.65 Tb/s over 6,970 km transmission in C+L band using coded modulation with hybrid constellation shaping and nonlinearity compensation,” J. Lightwave Technol. 36(1), 114–121 (2018).
[Crossref]

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018).
[Crossref]

2017 (2)

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental demonstration of four-channel WDM 560 Gbit/s 128QAM-DMT using IM/DD for 2-km optical interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
[Crossref]

2016 (3)

2015 (4)

2014 (1)

1993 (1)

F. R. Kschischang and S. Pasupathy, “Optimal nonuniform signaling for Gaussian channels,” IEEE Trans. Inf. Theory 39(3), 913–929 (1993).
[Crossref]

1989 (1)

G. D. Forney and L.-F. Wei, “Multidimensional constellations-part I: Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Comm. 7(6), 877–892 (1989).
[Crossref]

Batshon, H. G.

Böcherer, G.

P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
[Crossref]

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

Bolshtyansky, M. A.

Buset, J. M.

Cai, J.-X.

Calsat, A.

Cao, Z.

Chagnon, M.

Chen, M.

Chen, W.

Corbett, P. C.

Davidson, C. R.

de Jauregui Ruiz, I. F.

Du, J.

Dubost, S.

Forney, G. D.

G. D. Forney and L.-F. Wei, “Multidimensional constellations-part I: Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Comm. 7(6), 877–892 (1989).
[Crossref]

Foursa, D. G.

Gao, Y.

Ghazisaeidi, A.

Gui, T.

Hammon, T. E.

He, Z.

Huo, J.

Jiang, L.

Kong, M.

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Kschischang, F. R.

C. Pan and F. R. Kschischang, “Probabilistic 16-QAM shaping in WDM systems,” J. Lightwave Technol. 34(18), 4285–4292 (2016).
[Crossref]

F. R. Kschischang and S. Pasupathy, “Optimal nonuniform signaling for Gaussian channels,” IEEE Trans. Inf. Theory 39(3), 913–929 (1993).
[Crossref]

Lau, A. P. T.

Letellier, V.

Li, F.

Li, X.

F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental demonstration of four-channel WDM 560 Gbit/s 128QAM-DMT using IM/DD for 2-km optical interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
[Crossref]

F. Li, X. Li, J. Zhang, and J. Yu, “Transmission of 100-Gb/s VSB DFT-spread DMT signal in short-reach optical communication systems,” IEEE Photonics J. 7(5), 1–7 (2015).

Liu, B.

X. Xu, B. Liu, X. Wu, L. Zhang, Y. Mao, J. Ren, Y. Zhang, L. Jiang, and X. Xin, “A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation,” Opt. Express 26(20), 26576–26589 (2018).
[Crossref] [PubMed]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Lu, C.

Man, J.

Mao, Y.

Mazurczyk, M. V.

Morsy-Osman, M.

Ohlendorf, S.

S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Multidimensional PAM with Pseudo-Gray coding for flexible data center interconnects,” IEEE Photonics Technol. Lett. 30(12), 1143–1146 (2018).
[Crossref]

Pachnicke, S.

S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Multidimensional PAM with Pseudo-Gray coding for flexible data center interconnects,” IEEE Photonics Technol. Lett. 30(12), 1143–1146 (2018).
[Crossref]

Pan, C.

Paskov, M.

Pasupathy, S.

F. R. Kschischang and S. Pasupathy, “Optimal nonuniform signaling for Gaussian channels,” IEEE Trans. Inf. Theory 39(3), 913–929 (1993).
[Crossref]

Patterson, W. W.

Pilipetskii, A. N.

Plant, D. V.

Plantady, P.

Qiu, M.

Ren, J.

Renaudier, J.

Rosenkranz, W.

S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Multidimensional PAM with Pseudo-Gray coding for flexible data center interconnects,” IEEE Photonics Technol. Lett. 30(12), 1143–1146 (2018).
[Crossref]

Sab, O. A.

Schmalen, L.

Schulte, P.

P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
[Crossref]

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

Sinkin, O. V.

Steiner, F.

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

Stepniak, G.

Sun, L.

Tao, L.

Tian, Q.

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Wang, D.

Wang, K.

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Wang, L.

Wang, W.

Wei, L.-F.

G. D. Forney and L.-F. Wei, “Multidimensional constellations-part I: Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Comm. 7(6), 877–892 (1989).
[Crossref]

Wolter, G. M.

Wu, X.

Xin, X.

X. Xu, B. Liu, X. Wu, L. Zhang, Y. Mao, J. Ren, Y. Zhang, L. Jiang, and X. Xin, “A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation,” Opt. Express 26(20), 26576–26589 (2018).
[Crossref] [PubMed]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Xu, X.

Yaman, F.

S. Zhang and F. Yaman, “Constellation design with geometric and probabilistic shaping,” Opt. Commun. 409, 7–12 (2018).
[Crossref]

Yu, C.

Yu, J.

F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental demonstration of four-channel WDM 560 Gbit/s 128QAM-DMT using IM/DD for 2-km optical interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
[Crossref]

F. Li, X. Li, J. Zhang, and J. Yu, “Transmission of 100-Gb/s VSB DFT-spread DMT signal in short-reach optical communication systems,” IEEE Photonics J. 7(5), 1–7 (2015).

Zeng, L.

Zhang, J.

F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental demonstration of four-channel WDM 560 Gbit/s 128QAM-DMT using IM/DD for 2-km optical interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
[Crossref]

F. Li, X. Li, J. Zhang, and J. Yu, “Transmission of 100-Gb/s VSB DFT-spread DMT signal in short-reach optical communication systems,” IEEE Photonics J. 7(5), 1–7 (2015).

Zhang, L.

X. Xu, B. Liu, X. Wu, L. Zhang, Y. Mao, J. Ren, Y. Zhang, L. Jiang, and X. Xin, “A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation,” Opt. Express 26(20), 26576–26589 (2018).
[Crossref] [PubMed]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Zhang, Q.

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Zhang, S.

S. Zhang and F. Yaman, “Constellation design with geometric and probabilistic shaping,” Opt. Commun. 409, 7–12 (2018).
[Crossref]

Zhang, Y.

X. Xu, B. Liu, X. Wu, L. Zhang, Y. Mao, J. Ren, Y. Zhang, L. Jiang, and X. Xin, “A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation,” Opt. Express 26(20), 26576–26589 (2018).
[Crossref] [PubMed]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Zhong, K.

Zhou, X.

Zhuge, Q.

IEEE J. Sel. Areas Comm. (1)

G. D. Forney and L.-F. Wei, “Multidimensional constellations-part I: Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Comm. 7(6), 877–892 (1989).
[Crossref]

IEEE Photonics J. (2)

F. Li, X. Li, J. Zhang, and J. Yu, “Transmission of 100-Gb/s VSB DFT-spread DMT signal in short-reach optical communication systems,” IEEE Photonics J. 7(5), 1–7 (2015).

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance comparison of PS star-16QAM and PS square-shaped 16QAM (square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (1)

S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Multidimensional PAM with Pseudo-Gray coding for flexible data center interconnects,” IEEE Photonics Technol. Lett. 30(12), 1143–1146 (2018).
[Crossref]

IEEE Trans. Commun. (1)

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

IEEE Trans. Inf. Theory (2)

P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
[Crossref]

F. R. Kschischang and S. Pasupathy, “Optimal nonuniform signaling for Gaussian channels,” IEEE Trans. Inf. Theory 39(3), 913–929 (1993).
[Crossref]

J. Lightwave Technol. (7)

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018).
[Crossref]

I. F. de Jauregui Ruiz, A. Ghazisaeidi, O. A. Sab, P. Plantady, A. Calsat, S. Dubost, L. Schmalen, V. Letellier, and J. Renaudier, “25.4-Tb/s transmission over transpacific distances using truncated probabilistically shaped PDM-64QAM,” J. Lightwave Technol. 36(6), 1354–1361 (2018).
[Crossref]

J.-X. Cai, H. G. Batshon, M. V. Mazurczyk, O. V. Sinkin, D. Wang, M. Paskov, W. W. Patterson, C. R. Davidson, P. C. Corbett, G. M. Wolter, T. E. Hammon, M. A. Bolshtyansky, D. G. Foursa, and A. N. Pilipetskii, “70.46 Tb/s over 7,600 km and 71.65 Tb/s over 6,970 km transmission in C+L band using coded modulation with hybrid constellation shaping and nonlinearity compensation,” J. Lightwave Technol. 36(1), 114–121 (2018).
[Crossref]

F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental demonstration of four-channel WDM 560 Gbit/s 128QAM-DMT using IM/DD for 2-km optical interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
[Crossref]

G. Stepniak, “Comparison of efficiency of N-dimensional CAP modulations,” J. Lightwave Technol. 32(14), 2516–2523 (2014).
[Crossref]

L. Sun, J. Du, and Z. He, “Multiband three-dimensional carrierless amplitude phase modulation for short reach optical communications,” J. Lightwave Technol. 34(13), 3103–3109 (2016).
[Crossref]

C. Pan and F. R. Kschischang, “Probabilistic 16-QAM shaping in WDM systems,” J. Lightwave Technol. 34(18), 4285–4292 (2016).
[Crossref]

Opt. Commun. (1)

S. Zhang and F. Yaman, “Constellation design with geometric and probabilistic shaping,” Opt. Commun. 409, 7–12 (2018).
[Crossref]

Opt. Express (3)

Other (4)

Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Proc. OFC2017, paper M3C.1.
[Crossref]

J. Shi, J. Zhang, X. Li, N. Chi, Y. Zhang, Q. Zhang, and J. Yu, “Improved performance of high-order QAM OFDM based on probabilistically shaping in the datacom,” in Proc. OFC2018, paper W4G.6.
[Crossref]

J. Shi, J. Zhang, N. Chi, Y. Cai, X. Li, Y. Zhang, Q. Zhang, and J. Yu, “Probabilistically shaped 1024-QAM OFDM transmission in an IM-DD system,” in Proc. OFC2018, paper W2A.44.
[Crossref]

S. Zhang, Z. Qu, F. Yaman, E. Mateo, T. Inoue, K. Nakamura, Y. Inada, and I. B. Djordjevic, “Flex-rate transmission using hybrid probabilistic and geometric shaped 32QAM,” in Proc. OFC2018, paper M1G.3.
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 (a) Constellation mapping rule and (b) principle of geometric structural design of the traditional star-CAP-16.
Fig. 2
Fig. 2 (a) Constellation mapping rule, (b) principle of geometric structural design, (c) honeycomb-like decision regions and (d) probability distribution with the entropy of 3.6 bits/symbol of the proposed novel PS star-CAP-16.
Fig. 3
Fig. 3 Comparison of CFM between traditional star-CAP-16 and novel star-CAP-16.
Fig. 4
Fig. 4 Theoretical MI vs. SNR curves of uniform star-CAP-16 in C 8 , 8 , PS star-CAP-16 in C 8 , 8 , uniform star-CAP-16 in C 4 , 4 , 4 , 4 and PS star-CAP-16 in C 4 , 4 , 4 , 4 .
Fig. 5
Fig. 5 (a) Constellation mapping rule, (b) principle of geometric structural design, (c) honeycomb-like decision regions and (d) probability distribution with the entropy of 4.6 bits/symbol of the proposed novel PS star-CAP-32.
Fig. 6
Fig. 6 Theoretical MI vs. SNR curves of uniform star-CAP-32 and PS star-CAP-32 with the entropy of 4.6 bits/symbol.
Fig. 7
Fig. 7 Experimental setup (AWG: arbitrary waveform generator; EA: electrical amplifier; MZM: Mach-Zehnder modulator; VOA: variable optical attenuator; PD: photodiode; MSO: mixed signal oscilloscope).
Fig. 8
Fig. 8 BER curves of uniform star-CAP-16 in C 8 , 8 and uniform star-CAP-16 in C 4 , 4 , 4 , 4 for b2b and 25 km transmission (b2b: back to back).
Fig. 9
Fig. 9 BER curves of uniform star-CAP-16 in C 8 , 8 , PS star-CAP-16 in C 8 , 8 , uniform star-CAP-16 in C 4 , 4 , 4 , 4 and PS star-CAP-16 in C 4 , 4 , 4 , 4 under the same bit rate after 25 km transmission.
Fig. 10
Fig. 10 BER curves of novel star-CAP-32 with different probability distributions under the same bit rate after 25 km transmission.

Tables (2)

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Table 1 Comparison between traditional star-CAP-16 and novel star-CAP-16

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Table 2 CFM performance of novel star-CAP-32 with different probability distributions

Equations (17)

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C F M ( C ) d min 2 ( C ) / P ( C ) .
Ξ = r ( l ) exp [ j ϕ ( i ) ] ,
r ( l ) = { 1.3066 ( i n n e r r i n g ) 2.3066 ( o u t e r r i n g ) ,
ϕ ( i ) = ( π / 4 ) i , i = 0 , 1 , , 7.
C F M ( C 8 , 8 ) = 1 ( 8 × 1.3066 2 + 8 × 2.3066 2 ) / 16 = 0.2846.
r ( l ) = { 0.7071 ( r i n g 1 ) 1.3660 ( r i n g 2 ) 1.7071 ( r i n g 3 ) 2.3660 ( r i n g 4 ) ,
ϕ ( i ) = { ( π / 2 ) i , i = 0 , 1 , 2 , 3 ( r i n g 1 , 3 ) ( π / 2 ) i + π / 4 , i = 0 , 1 , 2 , 3 ( r i n g 2 , 4 ) .
C F M ( C 4 , 4 , 4 , 4 ) = 1 ( 4 × 0.7071 2 + 4 × 1.3660 2 + 4 × 1.7071 2 + 4 × 2.3660 2 ) / 16 = 0.3677.
P ( x ) = A ν e ν x 2 ,
A ν = 1 x ' Ξ e ν x ' 2 .
r ( l ) = { 1 .3066 ( r i n g 1 ) 2 .0731 ( r i n g 2 ) 2 .5241 ( r i n g 3 ) 3 .0731 ( r i n g 4 ) ,
ϕ ( i ) = { ( π / 4 ) i , i = 0 , 1 , , 7 ( r i n g 1 , 3 ) ( π / 4 ) i + π / 8 , i = 0 , 1 , , 7 ( r i n g 2 , 4 ) .
h I ( t ) = g ( t ) cos ( 2 π f c t ) ,
h Q ( t ) = g ( t ) sin ( 2 π f c t ) ,
s ( t ) = n = [ x n h I ( t n T ) y n h Q ( t n T ) ] .
r I ( t ) = r ( t ) h I ( t ) ,
r Q ( t ) = r ( t ) h Q ( t ) .

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