Abstract

We introduce a novel probabilistic shaping (PS) scheme based on bit-weighted distribution matching (BWDM) into a discrete multi-tone wavelength division multiplexing passive optical network (DMT-WDM-PON) employing low-density parity-check-coded 16-ary quadrature amplitude modulation (16QAM). Unlike the prevailing arithmetic coding-class PS schemes with target symbol probability, such as arithmetic distribution matching and constant composition distribution matching, the proposed one realizes Gaussian-like symbol probability distribution emulation merely based on simple bit-class processing, having the advantage of much lower computational complexity. As the key operation in BWDM, the bit weight intervention is implemented in the process of PS-16QAM generation for elevated transmission probability of binary data ‘0’ by cascaded operations of weight bit labelling and bit reconstruction. The experimental results show that, compared with uniformly-distributed signal with the same net rate, significantly-improved receiver power sensitivity and system tolerance to optical fiber nonlinear effect can be obtained in the DMT-WDM-PON system. The proposed PS scheme can be considered as one of promising practical solutions for more available optical network units due to enlarged system power loss budget for the optical distribution network.

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

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References

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  1. J. Shi, J. Zhang, Y. Zhou, Y. Wang, N. Chi, and J. Yu, “Transmission Performance Comparison for 100-Gb/s PAM-4, CAP-16, and DFT-S OFDM with Direct Detection,” J. Lightwave Technol. 35(23), 5127–5133 (2017).
    [Crossref]
  2. Z. Dong, H. Chien, J. Yu, J. Zhang, L. Cheng, and G. Chang, “Very-High-Throughput Coherent Ultradense WDM-PON Based on Nyquist-ISB Modulation,” IEEE Photonics Technol. Lett. 27(7), 763–766 (2015).
    [Crossref]
  3. Q. Xiao, Y. Chen, S. Lin, H. He, X. Wu, J. You, Y. Zeng, L. Zhou, and Z. Dong, “DFT-Spread DMT-WDM-PON Employing LDPC-Coded Probabilistic Shaping 16 QAM,” J. Lightwave Technol. 38(4), 714–722 (2020).
    [Crossref]
  4. X. Wu, D. Zou, Z. Dong, X. Zhao, Y. Chen, and F. Li, “LDPC-coded DFT-Spread DMT Signal Transmission Employing Probabilistic Shaping 16/32QAM for Optical Interconnection,” Opt. Express 27(7), 9821–9828 (2019).
    [Crossref]
  5. G. P. Agrawal, Fiber-Optic Communication Systems, 222 (John Wiley & Sons, 2012).
  6. J. Ding, J. Zhang, and J. Yu, “Comparison of Geometrically Shaped and Probabilistically Shaped Bit-Loading DMT for Optical Interconnect System,” IEEE Photonics J. 12(2), 1–8 (2020).
    [Crossref]
  7. L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Rate-Adaptive Coded Modulation for Fiber-Optic Communications,” J. Lightwave Technol. 32(2), 333–343 (2014).
    [Crossref]
  8. L. Zhou, W. Huang, S. Peng, Y. Chen and, and Y. He, “An Improved Design of Gallager Mapping for LDPC-Coded BICM-ID System,” Electron. J. 20(1), 16–21 (2016).
    [Crossref]
  9. K. Wang, X. Li, M. Kong, P. Gou, W. Zhou, and J. Yu, “Probabilistically Shaped 16QAM Signal Transmission in a Photonics-Aided Wireless Terahertz-Wave System,” in Proc. OFC, San Diego, CA, USA, Mar. 2018, paper M4J.7.
  10. D. Raphaeli and A. Gurevitz, “Constellation Shaping for Pragmatic Turbo-Coded Modulation with High Spectral Efficiency,” IEEE Trans. Commun. Technol. 52(3), 341–345 (2004).
    [Crossref]
  11. M. P. Yankov, D. Zibar, K. J. Larsen, L. P. B. Christensen, and S. Forchhammer, “Constellation Shaping for Fiber-Optic Channels with QAM and High Spectral Efficiency,” IEEE Photonics Technol. Lett. 26(23), 2407–2410 (2014).
    [Crossref]
  12. S. Baur and G. Böcherer, “Arithmetic Distribution Matching,” in Proc. International ITG Conference on Systems, Communications and Coding (SCC), Hamburg, Germany, 2015, paper 1-6.
  13. P. Schulte and G. Böcherer, “Constant Composition Distribution Matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
    [Crossref]
  14. M. P. Yankov, F. D. Ros, E. P. da Silva, S. Forchhammer, K. J. Larsen, L. K. Oxenløwe, M. Galili, and D. Zibar, “Constellation Shaping for WDM Systems Using 256QAM/1024QAM with Probabilistic Optimization,” J. Lightwave Technol. 34(22), 5146–5156 (2016).
    [Crossref]
  15. Z. He, T. Bo, and H. Kim, “Probabilistically Shaped Coded Modulation for IM/DD System,” Opt. Express 27(9), 12126–12136 (2019).
    [Crossref]
  16. F. Li, X. Li, L. Chen, Y. Xia, C. Ge, and Y. Chen, “High-Level QAM OFDM System Using DML for Low-Cost Short Reach Optical Communications,” IEEE Photonics Technol. Lett. 26(9), 941–944 (2014).
    [Crossref]
  17. A. Bennatan and D. Burshtein, “On the Application of LDPC Codes to Arbitrary Discrete-memoryless channels,” IEEE Trans. Inf. Theory 50(3), 417–438 (2004).
    [Crossref]
  18. T. M. Cover and J. A. Thomas, “Elements of Information Theory,” John Wiley & Sons, (2006).

2020 (2)

Q. Xiao, Y. Chen, S. Lin, H. He, X. Wu, J. You, Y. Zeng, L. Zhou, and Z. Dong, “DFT-Spread DMT-WDM-PON Employing LDPC-Coded Probabilistic Shaping 16 QAM,” J. Lightwave Technol. 38(4), 714–722 (2020).
[Crossref]

J. Ding, J. Zhang, and J. Yu, “Comparison of Geometrically Shaped and Probabilistically Shaped Bit-Loading DMT for Optical Interconnect System,” IEEE Photonics J. 12(2), 1–8 (2020).
[Crossref]

2019 (2)

2017 (1)

2016 (3)

L. Zhou, W. Huang, S. Peng, Y. Chen and, and Y. He, “An Improved Design of Gallager Mapping for LDPC-Coded BICM-ID System,” Electron. J. 20(1), 16–21 (2016).
[Crossref]

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

M. P. Yankov, F. D. Ros, E. P. da Silva, S. Forchhammer, K. J. Larsen, L. K. Oxenløwe, M. Galili, and D. Zibar, “Constellation Shaping for WDM Systems Using 256QAM/1024QAM with Probabilistic Optimization,” J. Lightwave Technol. 34(22), 5146–5156 (2016).
[Crossref]

2015 (1)

Z. Dong, H. Chien, J. Yu, J. Zhang, L. Cheng, and G. Chang, “Very-High-Throughput Coherent Ultradense WDM-PON Based on Nyquist-ISB Modulation,” IEEE Photonics Technol. Lett. 27(7), 763–766 (2015).
[Crossref]

2014 (3)

L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Rate-Adaptive Coded Modulation for Fiber-Optic Communications,” J. Lightwave Technol. 32(2), 333–343 (2014).
[Crossref]

F. Li, X. Li, L. Chen, Y. Xia, C. Ge, and Y. Chen, “High-Level QAM OFDM System Using DML for Low-Cost Short Reach Optical Communications,” IEEE Photonics Technol. Lett. 26(9), 941–944 (2014).
[Crossref]

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. B. Christensen, and S. Forchhammer, “Constellation Shaping for Fiber-Optic Channels with QAM and High Spectral Efficiency,” IEEE Photonics Technol. Lett. 26(23), 2407–2410 (2014).
[Crossref]

2004 (2)

A. Bennatan and D. Burshtein, “On the Application of LDPC Codes to Arbitrary Discrete-memoryless channels,” IEEE Trans. Inf. Theory 50(3), 417–438 (2004).
[Crossref]

D. Raphaeli and A. Gurevitz, “Constellation Shaping for Pragmatic Turbo-Coded Modulation with High Spectral Efficiency,” IEEE Trans. Commun. Technol. 52(3), 341–345 (2004).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 222 (John Wiley & Sons, 2012).

Agrell, E.

Baur, S.

S. Baur and G. Böcherer, “Arithmetic Distribution Matching,” in Proc. International ITG Conference on Systems, Communications and Coding (SCC), Hamburg, Germany, 2015, paper 1-6.

Bennatan, A.

A. Bennatan and D. Burshtein, “On the Application of LDPC Codes to Arbitrary Discrete-memoryless channels,” IEEE Trans. Inf. Theory 50(3), 417–438 (2004).
[Crossref]

Beygi, L.

Bo, T.

Böcherer, G.

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

S. Baur and G. Böcherer, “Arithmetic Distribution Matching,” in Proc. International ITG Conference on Systems, Communications and Coding (SCC), Hamburg, Germany, 2015, paper 1-6.

Burshtein, D.

A. Bennatan and D. Burshtein, “On the Application of LDPC Codes to Arbitrary Discrete-memoryless channels,” IEEE Trans. Inf. Theory 50(3), 417–438 (2004).
[Crossref]

Chang, G.

Z. Dong, H. Chien, J. Yu, J. Zhang, L. Cheng, and G. Chang, “Very-High-Throughput Coherent Ultradense WDM-PON Based on Nyquist-ISB Modulation,” IEEE Photonics Technol. Lett. 27(7), 763–766 (2015).
[Crossref]

Chen, L.

F. Li, X. Li, L. Chen, Y. Xia, C. Ge, and Y. Chen, “High-Level QAM OFDM System Using DML for Low-Cost Short Reach Optical Communications,” IEEE Photonics Technol. Lett. 26(9), 941–944 (2014).
[Crossref]

Chen, Y.

Chen and, Y.

L. Zhou, W. Huang, S. Peng, Y. Chen and, and Y. He, “An Improved Design of Gallager Mapping for LDPC-Coded BICM-ID System,” Electron. J. 20(1), 16–21 (2016).
[Crossref]

Cheng, L.

Z. Dong, H. Chien, J. Yu, J. Zhang, L. Cheng, and G. Chang, “Very-High-Throughput Coherent Ultradense WDM-PON Based on Nyquist-ISB Modulation,” IEEE Photonics Technol. Lett. 27(7), 763–766 (2015).
[Crossref]

Chi, N.

Chien, H.

Z. Dong, H. Chien, J. Yu, J. Zhang, L. Cheng, and G. Chang, “Very-High-Throughput Coherent Ultradense WDM-PON Based on Nyquist-ISB Modulation,” IEEE Photonics Technol. Lett. 27(7), 763–766 (2015).
[Crossref]

Christensen, L. P. B.

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. B. Christensen, and S. Forchhammer, “Constellation Shaping for Fiber-Optic Channels with QAM and High Spectral Efficiency,” IEEE Photonics Technol. Lett. 26(23), 2407–2410 (2014).
[Crossref]

Cover, T. M.

T. M. Cover and J. A. Thomas, “Elements of Information Theory,” John Wiley & Sons, (2006).

da Silva, E. P.

Ding, J.

J. Ding, J. Zhang, and J. Yu, “Comparison of Geometrically Shaped and Probabilistically Shaped Bit-Loading DMT for Optical Interconnect System,” IEEE Photonics J. 12(2), 1–8 (2020).
[Crossref]

Dong, Z.

Forchhammer, S.

M. P. Yankov, F. D. Ros, E. P. da Silva, S. Forchhammer, K. J. Larsen, L. K. Oxenløwe, M. Galili, and D. Zibar, “Constellation Shaping for WDM Systems Using 256QAM/1024QAM with Probabilistic Optimization,” J. Lightwave Technol. 34(22), 5146–5156 (2016).
[Crossref]

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. B. Christensen, and S. Forchhammer, “Constellation Shaping for Fiber-Optic Channels with QAM and High Spectral Efficiency,” IEEE Photonics Technol. Lett. 26(23), 2407–2410 (2014).
[Crossref]

Galili, M.

Ge, C.

F. Li, X. Li, L. Chen, Y. Xia, C. Ge, and Y. Chen, “High-Level QAM OFDM System Using DML for Low-Cost Short Reach Optical Communications,” IEEE Photonics Technol. Lett. 26(9), 941–944 (2014).
[Crossref]

Gou, P.

K. Wang, X. Li, M. Kong, P. Gou, W. Zhou, and J. Yu, “Probabilistically Shaped 16QAM Signal Transmission in a Photonics-Aided Wireless Terahertz-Wave System,” in Proc. OFC, San Diego, CA, USA, Mar. 2018, paper M4J.7.

Gurevitz, A.

D. Raphaeli and A. Gurevitz, “Constellation Shaping for Pragmatic Turbo-Coded Modulation with High Spectral Efficiency,” IEEE Trans. Commun. Technol. 52(3), 341–345 (2004).
[Crossref]

He, H.

He, Y.

L. Zhou, W. Huang, S. Peng, Y. Chen and, and Y. He, “An Improved Design of Gallager Mapping for LDPC-Coded BICM-ID System,” Electron. J. 20(1), 16–21 (2016).
[Crossref]

He, Z.

Huang, W.

L. Zhou, W. Huang, S. Peng, Y. Chen and, and Y. He, “An Improved Design of Gallager Mapping for LDPC-Coded BICM-ID System,” Electron. J. 20(1), 16–21 (2016).
[Crossref]

Kahn, J. M.

Karlsson, M.

Kim, H.

Kong, M.

K. Wang, X. Li, M. Kong, P. Gou, W. Zhou, and J. Yu, “Probabilistically Shaped 16QAM Signal Transmission in a Photonics-Aided Wireless Terahertz-Wave System,” in Proc. OFC, San Diego, CA, USA, Mar. 2018, paper M4J.7.

Larsen, K. J.

M. P. Yankov, F. D. Ros, E. P. da Silva, S. Forchhammer, K. J. Larsen, L. K. Oxenløwe, M. Galili, and D. Zibar, “Constellation Shaping for WDM Systems Using 256QAM/1024QAM with Probabilistic Optimization,” J. Lightwave Technol. 34(22), 5146–5156 (2016).
[Crossref]

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. B. Christensen, and S. Forchhammer, “Constellation Shaping for Fiber-Optic Channels with QAM and High Spectral Efficiency,” IEEE Photonics Technol. Lett. 26(23), 2407–2410 (2014).
[Crossref]

Li, F.

X. Wu, D. Zou, Z. Dong, X. Zhao, Y. Chen, and F. Li, “LDPC-coded DFT-Spread DMT Signal Transmission Employing Probabilistic Shaping 16/32QAM for Optical Interconnection,” Opt. Express 27(7), 9821–9828 (2019).
[Crossref]

F. Li, X. Li, L. Chen, Y. Xia, C. Ge, and Y. Chen, “High-Level QAM OFDM System Using DML for Low-Cost Short Reach Optical Communications,” IEEE Photonics Technol. Lett. 26(9), 941–944 (2014).
[Crossref]

Li, X.

F. Li, X. Li, L. Chen, Y. Xia, C. Ge, and Y. Chen, “High-Level QAM OFDM System Using DML for Low-Cost Short Reach Optical Communications,” IEEE Photonics Technol. Lett. 26(9), 941–944 (2014).
[Crossref]

K. Wang, X. Li, M. Kong, P. Gou, W. Zhou, and J. Yu, “Probabilistically Shaped 16QAM Signal Transmission in a Photonics-Aided Wireless Terahertz-Wave System,” in Proc. OFC, San Diego, CA, USA, Mar. 2018, paper M4J.7.

Lin, S.

Oxenløwe, L. K.

Peng, S.

L. Zhou, W. Huang, S. Peng, Y. Chen and, and Y. He, “An Improved Design of Gallager Mapping for LDPC-Coded BICM-ID System,” Electron. J. 20(1), 16–21 (2016).
[Crossref]

Raphaeli, D.

D. Raphaeli and A. Gurevitz, “Constellation Shaping for Pragmatic Turbo-Coded Modulation with High Spectral Efficiency,” IEEE Trans. Commun. Technol. 52(3), 341–345 (2004).
[Crossref]

Ros, F. D.

Schulte, P.

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

Shi, J.

Thomas, J. A.

T. M. Cover and J. A. Thomas, “Elements of Information Theory,” John Wiley & Sons, (2006).

Wang, K.

K. Wang, X. Li, M. Kong, P. Gou, W. Zhou, and J. Yu, “Probabilistically Shaped 16QAM Signal Transmission in a Photonics-Aided Wireless Terahertz-Wave System,” in Proc. OFC, San Diego, CA, USA, Mar. 2018, paper M4J.7.

Wang, Y.

Wu, X.

Xia, Y.

F. Li, X. Li, L. Chen, Y. Xia, C. Ge, and Y. Chen, “High-Level QAM OFDM System Using DML for Low-Cost Short Reach Optical Communications,” IEEE Photonics Technol. Lett. 26(9), 941–944 (2014).
[Crossref]

Xiao, Q.

Yankov, M. P.

M. P. Yankov, F. D. Ros, E. P. da Silva, S. Forchhammer, K. J. Larsen, L. K. Oxenløwe, M. Galili, and D. Zibar, “Constellation Shaping for WDM Systems Using 256QAM/1024QAM with Probabilistic Optimization,” J. Lightwave Technol. 34(22), 5146–5156 (2016).
[Crossref]

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. B. Christensen, and S. Forchhammer, “Constellation Shaping for Fiber-Optic Channels with QAM and High Spectral Efficiency,” IEEE Photonics Technol. Lett. 26(23), 2407–2410 (2014).
[Crossref]

You, J.

Yu, J.

J. Ding, J. Zhang, and J. Yu, “Comparison of Geometrically Shaped and Probabilistically Shaped Bit-Loading DMT for Optical Interconnect System,” IEEE Photonics J. 12(2), 1–8 (2020).
[Crossref]

J. Shi, J. Zhang, Y. Zhou, Y. Wang, N. Chi, and J. Yu, “Transmission Performance Comparison for 100-Gb/s PAM-4, CAP-16, and DFT-S OFDM with Direct Detection,” J. Lightwave Technol. 35(23), 5127–5133 (2017).
[Crossref]

Z. Dong, H. Chien, J. Yu, J. Zhang, L. Cheng, and G. Chang, “Very-High-Throughput Coherent Ultradense WDM-PON Based on Nyquist-ISB Modulation,” IEEE Photonics Technol. Lett. 27(7), 763–766 (2015).
[Crossref]

K. Wang, X. Li, M. Kong, P. Gou, W. Zhou, and J. Yu, “Probabilistically Shaped 16QAM Signal Transmission in a Photonics-Aided Wireless Terahertz-Wave System,” in Proc. OFC, San Diego, CA, USA, Mar. 2018, paper M4J.7.

Zeng, Y.

Zhang, J.

J. Ding, J. Zhang, and J. Yu, “Comparison of Geometrically Shaped and Probabilistically Shaped Bit-Loading DMT for Optical Interconnect System,” IEEE Photonics J. 12(2), 1–8 (2020).
[Crossref]

J. Shi, J. Zhang, Y. Zhou, Y. Wang, N. Chi, and J. Yu, “Transmission Performance Comparison for 100-Gb/s PAM-4, CAP-16, and DFT-S OFDM with Direct Detection,” J. Lightwave Technol. 35(23), 5127–5133 (2017).
[Crossref]

Z. Dong, H. Chien, J. Yu, J. Zhang, L. Cheng, and G. Chang, “Very-High-Throughput Coherent Ultradense WDM-PON Based on Nyquist-ISB Modulation,” IEEE Photonics Technol. Lett. 27(7), 763–766 (2015).
[Crossref]

Zhao, X.

Zhou, L.

Q. Xiao, Y. Chen, S. Lin, H. He, X. Wu, J. You, Y. Zeng, L. Zhou, and Z. Dong, “DFT-Spread DMT-WDM-PON Employing LDPC-Coded Probabilistic Shaping 16 QAM,” J. Lightwave Technol. 38(4), 714–722 (2020).
[Crossref]

L. Zhou, W. Huang, S. Peng, Y. Chen and, and Y. He, “An Improved Design of Gallager Mapping for LDPC-Coded BICM-ID System,” Electron. J. 20(1), 16–21 (2016).
[Crossref]

Zhou, W.

K. Wang, X. Li, M. Kong, P. Gou, W. Zhou, and J. Yu, “Probabilistically Shaped 16QAM Signal Transmission in a Photonics-Aided Wireless Terahertz-Wave System,” in Proc. OFC, San Diego, CA, USA, Mar. 2018, paper M4J.7.

Zhou, Y.

Zibar, D.

M. P. Yankov, F. D. Ros, E. P. da Silva, S. Forchhammer, K. J. Larsen, L. K. Oxenløwe, M. Galili, and D. Zibar, “Constellation Shaping for WDM Systems Using 256QAM/1024QAM with Probabilistic Optimization,” J. Lightwave Technol. 34(22), 5146–5156 (2016).
[Crossref]

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. B. Christensen, and S. Forchhammer, “Constellation Shaping for Fiber-Optic Channels with QAM and High Spectral Efficiency,” IEEE Photonics Technol. Lett. 26(23), 2407–2410 (2014).
[Crossref]

Zou, D.

Electron. J. (1)

L. Zhou, W. Huang, S. Peng, Y. Chen and, and Y. He, “An Improved Design of Gallager Mapping for LDPC-Coded BICM-ID System,” Electron. J. 20(1), 16–21 (2016).
[Crossref]

IEEE Photonics J. (1)

J. Ding, J. Zhang, and J. Yu, “Comparison of Geometrically Shaped and Probabilistically Shaped Bit-Loading DMT for Optical Interconnect System,” IEEE Photonics J. 12(2), 1–8 (2020).
[Crossref]

IEEE Photonics Technol. Lett. (3)

Z. Dong, H. Chien, J. Yu, J. Zhang, L. Cheng, and G. Chang, “Very-High-Throughput Coherent Ultradense WDM-PON Based on Nyquist-ISB Modulation,” IEEE Photonics Technol. Lett. 27(7), 763–766 (2015).
[Crossref]

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. B. Christensen, and S. Forchhammer, “Constellation Shaping for Fiber-Optic Channels with QAM and High Spectral Efficiency,” IEEE Photonics Technol. Lett. 26(23), 2407–2410 (2014).
[Crossref]

F. Li, X. Li, L. Chen, Y. Xia, C. Ge, and Y. Chen, “High-Level QAM OFDM System Using DML for Low-Cost Short Reach Optical Communications,” IEEE Photonics Technol. Lett. 26(9), 941–944 (2014).
[Crossref]

IEEE Trans. Commun. Technol. (1)

D. Raphaeli and A. Gurevitz, “Constellation Shaping for Pragmatic Turbo-Coded Modulation with High Spectral Efficiency,” IEEE Trans. Commun. Technol. 52(3), 341–345 (2004).
[Crossref]

IEEE Trans. Inf. Theory (2)

A. Bennatan and D. Burshtein, “On the Application of LDPC Codes to Arbitrary Discrete-memoryless channels,” IEEE Trans. Inf. Theory 50(3), 417–438 (2004).
[Crossref]

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

J. Lightwave Technol. (4)

Opt. Express (2)

Other (4)

T. M. Cover and J. A. Thomas, “Elements of Information Theory,” John Wiley & Sons, (2006).

S. Baur and G. Böcherer, “Arithmetic Distribution Matching,” in Proc. International ITG Conference on Systems, Communications and Coding (SCC), Hamburg, Germany, 2015, paper 1-6.

G. P. Agrawal, Fiber-Optic Communication Systems, 222 (John Wiley & Sons, 2012).

K. Wang, X. Li, M. Kong, P. Gou, W. Zhou, and J. Yu, “Probabilistically Shaped 16QAM Signal Transmission in a Photonics-Aided Wireless Terahertz-Wave System,” in Proc. OFC, San Diego, CA, USA, Mar. 2018, paper M4J.7.

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Figures (6)

Fig. 1.
Fig. 1. (a) Principle of DMT-WDM-PON employing PS-16QAM based on BWDM, (b) PS-16QAM DMT generation based on BWDM, (c) DFT-S DMT modulation, (d) bit weight intervention (k = 4), (e) PS-16QAM mapping. Probability distribution of binary data ‘0’ in the four parallel sequences of PS-16QAM, b(I): before BWI, b(II): after BWI. PS DM: PS distribution matching, Map.: QAM mapping, DMT Mod.: DMT modulation, IM-E/O: intensity modulation-based electrical-to-optical conversion, DD-O/E: direct detection-based optical-to-electrical conversion.
Fig. 2.
Fig. 2. Probability distribution of binary data ‘0’ (k = 4 and v = 3/4) in the four input sequences (a) without and (b) with LDPC, SPD for ideal PS-16QAM (c) pre- and (d) post-LDPC cases, SPD for practical PS-16QAM (e) pre- and (f) post-LDPC cases.
Fig. 3.
Fig. 3. Channel capacity.
Fig. 4.
Fig. 4. Proof-of-concept experimental setup of DMT-WDM-PON employing LDPC-coded PS-16QAM based on BWDM.
Fig. 5.
Fig. 5. BER performance with the launch fiber power of 4 dBm, (a) versus ROP with k = 4 and LDPC v = 3/4, (b) versus ROP with k = 4, 9, 39, and LDPC v = 3/4 over 20-km SSMF transmission, (c) versus ROP with LDPC v = 1/2, 3/4, 5/6, and k = 4, (d) versus launch fiber power with k = 4 with the ROP of -17 dBm. Insets (I)-(III): constellation diagrams for PS-16QAM (k = 4, 9, 39 and v = 3/4) over 20-km SSMF transmission with the ROP of -17 dBm.
Fig. 6.
Fig. 6. Symbol probability distribution comparison with five k values.

Tables (1)

Tables Icon

Table 1. Look-up Table (based on pre-LDPC PS-16QAM SPDs with 5 k values)

Equations (6)

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

P [ D 1 ( d ) , D 2 ( d ) , D 3 ( d ) , D 4 ( d ) ] = P D 1 ( d ) P D 2 ( d ) P D 3 ( d ) P D 4 ( d ) , d [ 1 , 16200 v ]
{ P D 1 ( 0 ) = P D 2 ( 0 ) = 1 2 k ( t = k 2 k t + 1 k + 1 C k t + t = k 2 + 1 k t k + 1 C k t ) P D 3 ( 0 ) = P D 4 ( 0 ) = 1 2
P [ I 1 ( m ) , I 2 ( m ) , I 3 ( m ) , I 4 ( m ) ] = P I 1 ( m ) P I 2 ( m ) P I 3 ( m ) P I 4 ( m ) , m [ 1 , 16200 ]
{ P I 1 ( 0 ) = P I 2 ( 0 ) = 1 2 + v 2 [ 1 2 k 1 ( t = k 2 k t + 1 k + 1 C k t + t = k 2 + 1 k t k + 1 C k t ) 1 ] P I 3 ( 0 ) = P I 4 ( 0 ) = 1 2
I ( X ; Y ) = H ( Y ) H ( Y | X ) = H ( X + N ) H ( N ) = x X y Y p ( x , y ) log p ( x , y ) p ( x ) p ( y ) = x p ( x ) [ y p ( y | x ) log p ( y | x ) ] y log p ( y ) x p ( x , y ) = x p ( x ) H ( Y | X = x ) y log p ( y ) p ( y )  
C = max { I ( X ; Y ) }

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