Abstract

For decades, advanced modulation techniques have been proposed to increase the capacity for intensity-modulation and direct-detection (IM-DD) optical fiber interconnection systems. Typically, the frequency-resolved discrete multi-tone (DMT) modulation was proposed by loading modulations with different bit numbers to fit the channel’s frequency response. Capacity can thus be better improved through finer use of the signal-to-noise-ratio (SNR) distribution in the frequency domain. For conventional DMT, the constellations loaded on individual subcarriers are all equip probability distributed. In this work, we propose a probabilistically shaped DMT (PS-DMT) modulation with adaptively loaded entropies referring to channel frequency response for short-reach optical interconnects. Achievable information rate (AIR) improvements of PS-DMT with both Maxwell-Boltzmann and dyadic distribution are investigated based on generalized mutual information (GMI). Moreover, the proposed PS-DMT has been realized experimentally over a multimode optical link using vertical-cavity surface-emitting lasers (VCSELs) with 100-m-long multimode fiber (MMF) transmission. This method can significantly improve the signaling capacity since two significant benefits are simultaneously utilized: 1) the shaping gain of PS at limited SNR condition and 2) the frequency-resolved continuous entropy loading for better fitting to the channel frequency response. Improved capacity, in terms of AIR, can thus be expected for a practical channel when using PS-DMT. This method can potentially be extended to a wide range of application scenarios, including both multimode and single-mode IM-DD fiber-optic communications.

© 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 (4)

2017 (1)

2016 (4)

2015 (2)

2014 (1)

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. 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]

2012 (1)

2010 (1)

2008 (1)

2004 (1)

J. M. Kahn and K. P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 259–272 (2004).
[Crossref]

2003 (1)

J. Garcia-Frias and W. Zhong, “Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix,” IEEE Commun. Lett. 7(6), 266–268 (2003).
[Crossref]

2001 (1)

S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001).
[Crossref]

2000 (1)

S. Ten Brink, “Rate one-half code for approaching the Shannon limit by 0.1 dB,” Electron. Lett. 36(15), 1293–1294 (2000).
[Crossref]

1998 (2)

A. J. Goldsmith and S. G. Chua, “Adaptive coded modulation for fading channels,” IEEE Trans. Commun. 46(5), 595–602 (1998).
[Crossref]

G. D. Forney and G. Ungerboeck, “Modulation and coding for linear Gaussian channels,” IEEE J. Sel. Areas Comm. 44, 2384–2415 (1998).

1996 (1)

D. J. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes,” Electron. Lett. 32(18), 1645–1646 (1996).
[Crossref]

1995 (1)

P. S. Chow, J. M. Cioffi, and J. A. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2/3/4), 773–775 (1995).
[Crossref]

Agrell, E.

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 Photonics Conference (IEEE, 2017), pp. 1–2.
[Crossref]

Armstrong, J.

Bai, Y.

Y. Zhu, A. Li, W. R. Peng, C. Kan, Z. Li, S. Chowdhury, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper M3C.1.
[Crossref]

Bayvel, P.

Bergano, N. S.

Berrou, C.

C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes,” in Proceedings of International Conference on Communications (IEEE, 1993), pp. 1064–1070.
[Crossref]

Bingham, J. A.

P. S. Chow, J. M. Cioffi, and J. A. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2/3/4), 773–775 (1995).
[Crossref]

Bocherer, G.

G. Bocherer and R. Mathar, “Matching dyadic distributions to channels,” in Proceedings of the 2011 Data Compression Conference (AMC, 2011), pp. 23–32.
[Crossref]

Böcherer, G.

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

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On probabilistic shaping of quadrature amplitude modulation for the nonlinear fiber channel,” J. Lightwave Technol. 34(21), 5063–5073 (2016).
[Crossref]

G. Böcherer, “On Joint Design of Probabilistic Shaping and Forward Error Correction for Optical Systems,” in Proceedings of the Optical Fiber Communication Conference (Optical Society of America, 2018), paper M4E.1.
[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 Proceedings of European Conference on Optical Communications (IEEE, 2011), pp.1–3.

Cai, J. X.

Cai, Y.

Cao, G.

Chandrasekhar, S.

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 Photonics Conference (IEEE, 2017), pp. 1–2.
[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 Proceedings of European Conference on Optical Communications (IEEE, 2011), pp.1–3.

Chen, B.

Chen, J.

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 Photonics Conference (IEEE, 2017), pp. 1–2.
[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 Proceedings of European Conference on Optical Communications (IEEE, 2011), pp.1–3.

Chen, Z.

Cho, J.

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 Photonics Conference (IEEE, 2017), pp. 1–2.
[Crossref]

J. Cho, L. Schmalen, and P. J. Winzer, “Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM,” in Proceedings of European Conference on Optical Communications (IEEE, 2017), pp. 1–3.
[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 Proceedings of European Conference on Optical Communications (IEEE, 2011), pp.1–3.

Chow, P. S.

P. S. Chow, J. M. Cioffi, and J. A. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2/3/4), 773–775 (1995).
[Crossref]

Chowdhury, S.

Y. Zhu, A. Li, W. R. Peng, C. Kan, Z. Li, S. Chowdhury, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper M3C.1.
[Crossref]

Christensen, L. P.

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. 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]

Chua, S. G.

A. J. Goldsmith and S. G. Chua, “Adaptive coded modulation for fading channels,” IEEE Trans. Commun. 46(5), 595–602 (1998).
[Crossref]

Chung, S. Y.

S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001).
[Crossref]

Cioffi, J. M.

P. S. Chow, J. M. Cioffi, and J. A. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2/3/4), 773–775 (1995).
[Crossref]

Deng, L.

Di, C.

Du, J.

Ellis, A.

A. Ellis, “Modulation formats which approach the Shannon limit,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper OMM4.

Engenhardt, K. M.

Fehenberger, T.

Fischer, R. F.

R. F. Fischer and J. B. Huber, “A new loading algorithm for discrete multitone transmission,” in Global Telecommunications Conference (IEEE, 1996), pp. 724–728.
[Crossref]

Forchhammer, S.

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. 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]

Forney, G. D.

S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001).
[Crossref]

G. D. Forney and G. Ungerboeck, “Modulation and coding for linear Gaussian channels,” IEEE J. Sel. Areas Comm. 44, 2384–2415 (1998).

Fu, S.

Garcia-Frias, J.

J. Garcia-Frias and W. Zhong, “Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix,” IEEE Commun. Lett. 7(6), 266–268 (2003).
[Crossref]

Glavieux, A.

C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes,” in Proceedings of International Conference on Communications (IEEE, 1993), pp. 1064–1070.
[Crossref]

Goldsmith, A. J.

A. J. Goldsmith and S. G. Chua, “Adaptive coded modulation for fading channels,” IEEE Trans. Commun. 46(5), 595–602 (1998).
[Crossref]

Guo, C.

Hanik, N.

He, Z.

Ho, K. P.

J. M. Kahn and K. P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 259–272 (2004).
[Crossref]

Hong, X.

Hu, W.

Huber, J. B.

R. F. Fischer and J. B. Huber, “A new loading algorithm for discrete multitone transmission,” in Global Telecommunications Conference (IEEE, 1996), pp. 724–728.
[Crossref]

Jacobsen, G.

Kahn, J. M.

J. M. Kahn and K. P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 259–272 (2004).
[Crossref]

Kan, C.

Y. Zhu, A. Li, W. R. Peng, C. Kan, Z. Li, S. Chowdhury, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper M3C.1.
[Crossref]

Killey, R. I.

Kschischang, F. R.

Larsen, K. J.

M. P. Yankov, D. Zibar, K. J. Larsen, L. P. 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]

Lau, A. P. T.

Lavery, D.

Li, A.

Y. Zhu, A. Li, W. R. Peng, C. Kan, Z. Li, S. Chowdhury, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper M3C.1.
[Crossref]

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 Proceedings of European Conference on Optical Communications (IEEE, 2011), pp.1–3.

Li, Z.

Y. Zhu, A. Li, W. R. Peng, C. Kan, Z. Li, S. Chowdhury, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper M3C.1.
[Crossref]

Liu, D.

Liu, W.

Lowery, A.

Lu, C.

MacKay, D. J.

D. J. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes,” Electron. Lett. 32(18), 1645–1646 (1996).
[Crossref]

Maher, R.

Mathar, R.

G. Bocherer and R. Mathar, “Matching dyadic distributions to channels,” in Proceedings of the 2011 Data Compression Conference (AMC, 2011), pp. 23–32.
[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 Photonics Conference (IEEE, 2017), pp. 1–2.
[Crossref]

Mohs, G.

Neal, R. M.

D. J. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes,” Electron. Lett. 32(18), 1645–1646 (1996).
[Crossref]

Nordwall, F.

Ozolins, O.

Pan, C.

Pang, X.

Paskov, M.

Peng, W. R.

Y. Zhu, A. Li, W. R. Peng, C. Kan, Z. Li, S. Chowdhury, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper M3C.1.
[Crossref]

Pilipetskii, A.

Popov, S.

Raybon, G.

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 Proceedings of European Conference on Optical Communications (IEEE, 2011), pp.1–3.

Richardson, T. J.

S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001).
[Crossref]

Schatz, R.

Schmalen, L.

J. Cho, L. Schmalen, and P. J. Winzer, “Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM,” in Proceedings of European Conference on Optical Communications (IEEE, 2017), pp. 1–3.
[Crossref]

Schmidt, B.

Schulte, P.

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

Semrau, D.

Shannon, C. E.

C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, 1963).

Shevchenko, N. A.

Shtaif, M.

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 Photonics Conference (IEEE, 2017), pp. 1–2.
[Crossref]

Sun, L.

Tang, M.

Ten Brink, S.

S. Ten Brink, “Rate one-half code for approaching the Shannon limit by 0.1 dB,” Electron. Lett. 36(15), 1293–1294 (2000).
[Crossref]

Thitimajshima, P.

C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes,” in Proceedings of International Conference on Communications (IEEE, 1993), pp. 1064–1070.
[Crossref]

Udalcovs, A.

Ungerboeck, G.

G. D. Forney and G. Ungerboeck, “Modulation and coding for linear Gaussian channels,” IEEE J. Sel. Areas Comm. 44, 2384–2415 (1998).

Urbanke, R.

S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001).
[Crossref]

Weaver, W.

C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, 1963).

Westergren, U.

Willems, F. M.

William, S.

Winzer, P.

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 Proceedings of European Conference on Optical Communications (IEEE, 2011), pp.1–3.

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 Photonics Conference (IEEE, 2017), pp. 1–2.
[Crossref]

Winzer, P. J.

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Figures (12)

Fig. 1
Fig. 1 AIR (in terms of GMI) gain by PS-DMT. (a) Frequency responses for ideal (green line) and practical channels (orange curve); (b) AIR with respect to SNR for the uniform distribution and a non-uniform distribution, along with the Shannon limit; (c) Corresponding AIR-frequency responses for the ideal (green) and practical (orange) channels. The solid curves indicate the Shannon limit. The dotted and dashed curves represent the AIR curves for the uniform distribution and adaptive non-uniform distribution, respectively.
Fig. 2
Fig. 2 (a) Conventional DMT using discrete bit loading and power allocation; (b) PS-DMT using entropy loading.
Fig. 3
Fig. 3 Bit loading metrologies of conventional DMT and proposed PS-DMT schemes.
Fig. 4
Fig. 4 (a) Simulated channel SNR response (blue line), adapted channel response using power allocation (red line), and entropy loading results by PS-DMT; (b) The probability distribution of 60th subcarrier for PS-DMT.
Fig. 5
Fig. 5 (a) Loaded entropy of conventional DMT (red circles), PS-DMT (MB) (blue triangles) and PS-DMT (dyadic) (black circles), and corresponding GMI; (b) The GMI-to-SNR curve for the 60th subcarrier.
Fig. 6
Fig. 6 AIR gain versus varying SNR and bandwidth: (a), PS-DMT (MB); (b), PS-DMT (dyadic).
Fig. 7
Fig. 7 Experimental setup of VCSEL-MMF optical link.
Fig. 8
Fig. 8 Experimental bit loading results for DMT and PS-DMT in the optical B2B case: (a) Bit-loading results for conventional DMT (red dots), PS-DMT (blue dots) and PS-DMT (dyadic) (blue line). (b) Shaped probability distributions of two typical subcarriers (12th and 66th subcarriers) for PS-DMT.
Fig. 9
Fig. 9 Experimental bit loading results for DMT and PS-DMT after 100-m transmission: (a) Bit-loading results for conventional DMT (red dots), PS-DMT (blue dots) and PS-DMT (dyadic) (blue line). (b) Shaped probability distributions of two typical subcarriers (12th and 66th subcarriers) for PS-DMT.
Fig. 10
Fig. 10 Constellations of 12th and 66th subcarriers for optical B2B case (3.5-dBm received power) and after 100-m OM3 fiber transmission (3.3-dBm received power).
Fig. 11
Fig. 11 Generalized Mutual information (GMI) values: (a) Conventional DMT and PS-DMT for the optical B2B case, with received optical power of 3.5 dBm; (b) Conventional DMT and PS-DMT after 100-m OM3 MMF transmission, with received optical power of 3.3 dBm.
Fig. 12
Fig. 12 Experimental NGMI values and data rate of reliable communication under various received optical powers.

Equations (7)

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B i = B total + log 2 N i M log 2 N i
min μ (P log 2 P B i 2 ) s.t. P= e -μ| x |
min μ (P log 2 P2) s.t. P= e -μ| x |
GM I i = k=1 m I( B k i ; L k i )
F(f)=SN R f=0 e 2.54 f 2 B W 3dB 2
p'={ p m1 , 2 p m1 p m , if if p m1 4 p m p m1 <4 p m
L k = log 2 e ( (x X k 1 ) 2 σ x 2 + (y Y k 1 ) 2 σ y 2 ) e ( (x X k 0 ) 2 σ x 2 + (y Y k 0 ) 2 σ y 2 )

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