Abstract

We carefully revisit the definitions of line rates, information rates, and spectral efficiencies in probabilistically shaped optical transmission systems. Generally accepted definitions for uniform quadrature amplitude modulation (QAM) systems are extended to more generally apply to systems with probabilistically shaped QAM, as well as to systems using pilot symbols of different QAM order than the information symbols. Based on the proper definitions, we correct erroneous claims in a recently reported work.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. F. Buchali, F. Steiner, G. Böcherer, 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]
  2. S. Chandrasekhar, B. Li, J. Cho, X. Chen, E. Burrows, G. Raybon, and P. J. Winzer, “High-spectral-efficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record rate-reach trade-offs,” in Proc. Eur. Conf. Opt. Commun. (2016) paper Th.3.C.1.
  3. J. Cho, X. Chen, S. Chandrasekhar, G. Raybon, R. Dar, L. Schmalen, E. Burrows, A. Adamiecki1, S. Corteselli, Y. Pan, D. Correa, B. McKay, S. Zsigmond, P. Winzer, and S. Grubb, “Trans-Atlantic field trial using probabilistically shaped 64-QAM at high spectral efficiencies and single-carrier real-time 250-Gb/s 16-QAM,” in Proc. Opt. Fiber Commun. Conf., 2017, paper Th5B.3.
  4. R. Maher, K. Croussore, M. Lauermann, R. Going, X. Xu, and J. Rahn, “Constellation shaped 66 GBd DP-1024QAM transceiver with 400 km transmission over standard SMF,” in Proc. Eur. Conf. Opt. Commun. (2017) paper Th.PDP.B.2.
  5. S. L. I. Olsson, J. Cho, S. Chandrasekhar, X. Chen, P. J. Winzer, and S. Makovejs, “Probabilistically shaped PDM 4096-QAM transmission over up to 200 km of fiber using standard intradyne detection,” Opt. Express 26(4), 4522–4530 (2018).
    [Crossref] [PubMed]
  6. S. L. I. Olsson, J. Cho, S. Chandrasekhar, X. Chen, E. Burrows, and P. J. Winzer, “Record-high 17.3-bit/s/Hz spectral efficiency transmission over 50 km using probabilistically shaped PDM 4096-QAM,” in Proc. Opt. Fiber Commun. Conf. (2018) paper Th4C.5.
    [Crossref]
  7. 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]
  8. X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P. I. Borel, and K. Carlson, “High spectral efficiency 400 Gb/s transmission using PDM time-domain hybrid 32-64 QAM and training-assisted carrier recovery,” J. Lightwave Technol. 31(7), 999–1005 (2013).
    [Crossref]
  9. J. Cho, S. Chandrasekhar, X. Chen, G. Raybon, and P. J. Winzer, “High spectral efficiency transmission with probabilistic shaping,” Proc. Eur. Conf. Opt. Commun. (2017) paper Th.1.E.1.
  10. P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
    [Crossref]
  11. A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems,” J. Lightwave Technol. 34(2), 707–721 (2016).
    [Crossref]
  12. J. Cho, L. Schmalen, and P. Winzer, “Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM,” in Proc. Eur. Conf. Opt. Commun. (2017) paper M.2.D.2.
  13. G. Böcherer, “Achievable rates for probabilistic shaping,” https://arxiv.org/abs/1707.01134 .
  14. P. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightwave Technol. 30(24), 3824–3835 (2012).
    [Crossref]

2018 (1)

2016 (3)

2015 (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]

2013 (1)

2012 (1)

Agrell, E.

Alvarado, A.

Bayvel, P.

Böcherer, G.

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

F. Buchali, F. Steiner, G. Böcherer, 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]

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]

Borel, P. I.

Buchali, F.

Carlson, K.

Chandrasekhar, S.

Chen, X.

Cho, J.

Idler, W.

Isaac, R.

Lavery, D.

Magill, P.

Maher, R.

Makovejs, S.

Nelson, L. E.

Olsson, S. L. I.

Peckham, D. W.

Schmalen, L.

Schulte, P.

F. Buchali, F. Steiner, G. Böcherer, 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]

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]

Steiner, F.

F. Buchali, F. Steiner, G. Böcherer, 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]

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]

Winzer, P.

Winzer, P. J.

Zhou, X.

Zhu, B.

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 (1)

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 (1)

Other (7)

S. L. I. Olsson, J. Cho, S. Chandrasekhar, X. Chen, E. Burrows, and P. J. Winzer, “Record-high 17.3-bit/s/Hz spectral efficiency transmission over 50 km using probabilistically shaped PDM 4096-QAM,” in Proc. Opt. Fiber Commun. Conf. (2018) paper Th4C.5.
[Crossref]

J. Cho, S. Chandrasekhar, X. Chen, G. Raybon, and P. J. Winzer, “High spectral efficiency transmission with probabilistic shaping,” Proc. Eur. Conf. Opt. Commun. (2017) paper Th.1.E.1.

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

J. Cho, X. Chen, S. Chandrasekhar, G. Raybon, R. Dar, L. Schmalen, E. Burrows, A. Adamiecki1, S. Corteselli, Y. Pan, D. Correa, B. McKay, S. Zsigmond, P. Winzer, and S. Grubb, “Trans-Atlantic field trial using probabilistically shaped 64-QAM at high spectral efficiencies and single-carrier real-time 250-Gb/s 16-QAM,” in Proc. Opt. Fiber Commun. Conf., 2017, paper Th5B.3.

R. Maher, K. Croussore, M. Lauermann, R. Going, X. Xu, and J. Rahn, “Constellation shaped 66 GBd DP-1024QAM transceiver with 400 km transmission over standard SMF,” in Proc. Eur. Conf. Opt. Commun. (2017) paper Th.PDP.B.2.

J. Cho, L. Schmalen, and P. Winzer, “Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM,” in Proc. Eur. Conf. Opt. Commun. (2017) paper M.2.D.2.

G. Böcherer, “Achievable rates for probabilistic shaping,” https://arxiv.org/abs/1707.01134 .

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Figures (4)

Fig. 1
Fig. 1 Block diagram defining (a) the rateR, and (b) the overhead OH.
Fig. 2
Fig. 2 Data flow within the PAS architecture.
Fig. 3
Fig. 3 (a) Rates, and (b) overheads of a PS QAM system and its subsystems, shown in a serially concatenated system model.
Fig. 4
Fig. 4 Rates of PS 8-PAM: (a) the effective code rates ρ c as a function of the true code rates R c with various R DM ,and (b) the overall system rates R Sys computed incorrectly by R Sh R c (dashed) and correctly by R Sh ρ c (solid).

Tables (2)

Tables Icon

Table 1 List of Symbols and Notation

Tables Icon

Table 2 Bit Rates within the PAS Architecture (cf. Figure 2)

Equations (12)

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

R DM = β m1 1.
R c = m1+γ m m1 m .
R Fr = m ρ Fr m ρ Fr +n(1 ρ Fr ) .
R Sys = β+γ m R Fr = ρ PAS R DM R c R Fr .
R Sys = R Sh ρ c R Fr ,
O H Sys =(1+O H Sh )(1+o h c )(1+O H Fr )1,
O H Sys =(1+O H DM + α PAS )(1+O H c )(1+O H Fr )1.
R Info =2vm R Sys r s b/s,
SE= R Info /F b/s/Hz.
R Line =v[ 2(X) R Fr +2( X Fr )(1 R Fr ) ] r s b/s,
R Line =v[ 2m R Fr +2n(1 R Fr ) ] r s b/s,
R Line =2vm r s b/s,

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