Abstract

We revisit the problem of estimating the nonlinear channel capacity of fiber-optic systems. By taking advantage of the fact that a large fraction of the nonlinear interference between different wavelength-division-multiplexed channels manifests itself as phase noise, and by accounting for the long temporal correlations of this noise, we show that the capacity is notably higher than what is currently assumed. This advantage translates into nearly doubling of the link distance for a fixed transmission rate.

© 2014 Optical Society of America

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References

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  1. P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
    [CrossRef]
  2. K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
    [CrossRef]
  3. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol. 28, 662 (2010).
    [CrossRef]
  4. A. D. Ellis, J. Zhao, and D. Cotter, J. Lightwave Technol. 28, 423 (2010).
    [CrossRef]
  5. G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, Opt. Express 19, B440 (2011).
    [CrossRef]
  6. A. Mecozzi and R.-J. Essiambre, J. Lightwave Technol. 30, 2011 (2012).
    [CrossRef]
  7. E. Agrell and M. Karlsson, in Optical Fiber Communication Conference 2013 (Optical Society of America, 2013), paper OTu3B.4.
  8. P. J. Winzer and G. J. Foschini, Opt. Express 19, 16680 (2011).
    [CrossRef]
  9. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, Opt. Express 21, 25685 (2013).
    [CrossRef]
  10. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).
  11. R. Dar, M. Shtaif, and M. Feder, in European Conference on Optical Communication 2013 (2013), paper P.4.16.
  12. With system parameters similar to those used for evaluating the capacity in [3] and assuming, for example, a 500 km link, the phase has been shown to be nearly constant on the scale of a few tens of symbol durations [9].

2013 (1)

2012 (1)

2011 (2)

2010 (2)

2003 (1)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

2001 (1)

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[CrossRef]

Agrell, E.

E. Agrell and M. Karlsson, in Optical Fiber Communication Conference 2013 (Optical Society of America, 2013), paper OTu3B.4.

Bosco, G.

Carena, A.

Cotter, D.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).

Curri, V.

Dar, R.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, Opt. Express 21, 25685 (2013).
[CrossRef]

R. Dar, M. Shtaif, and M. Feder, in European Conference on Optical Communication 2013 (2013), paper P.4.16.

Derevyanko, S. A.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

Ellis, A. D.

Essiambre, R.-J.

Feder, M.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, Opt. Express 21, 25685 (2013).
[CrossRef]

R. Dar, M. Shtaif, and M. Feder, in European Conference on Optical Communication 2013 (2013), paper P.4.16.

Forghieri, F.

Foschini, G. J.

Goebel, B.

Karlsson, M.

E. Agrell and M. Karlsson, in Optical Fiber Communication Conference 2013 (Optical Society of America, 2013), paper OTu3B.4.

Kramer, G.

Mecozzi, A.

Mitra, P. P.

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[CrossRef]

Poggiolini, P.

Shtaif, M.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, Opt. Express 21, 25685 (2013).
[CrossRef]

R. Dar, M. Shtaif, and M. Feder, in European Conference on Optical Communication 2013 (2013), paper P.4.16.

Stark, J. B.

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[CrossRef]

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).

Turitsyn, K. S.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

Turitsyn, S. K.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

Winzer, P. J.

Yurkevich, I. V.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

Zhao, J.

J. Lightwave Technol. (3)

Nature (1)

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (1)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

Other (4)

E. Agrell and M. Karlsson, in Optical Fiber Communication Conference 2013 (Optical Society of America, 2013), paper OTu3B.4.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).

R. Dar, M. Shtaif, and M. Feder, in European Conference on Optical Communication 2013 (2013), paper P.4.16.

With system parameters similar to those used for evaluating the capacity in [3] and assuming, for example, a 500 km link, the phase has been shown to be nearly constant on the scale of a few tens of symbol durations [9].

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Figures (3)

Fig. 1.
Fig. 1.

Numerically estimated σeff2 (normalized by T) versus block size in a 500 km link for input average power levels of 9, 7, and 5dBm. The red dashed line shows σASE2/T. Due to insufficient statistics for small values of N, the estimated σeff2 grows rapidly with block size. Then, when the accumulated statistics are sufficient, the growth is much slower, and this is due to the fact that phase fluctuations inflate the estimated σeff2.

Fig. 2.
Fig. 2.

(a) Capacity lower bound versus linear SNR for 500 km (red dots), 1000 km (blue squares), and 2000 km (green triangles). Dashed curves result from treating all the nonlinear noise as noise. Solid curves represent the new bounds derived here. The dotted curve represents the Shannon limit log2(1+SNR). (b) The maximum achievable transmission distance as a function of spectral efficiency with (solid) and without (dashed) phase noise cancellation.

Fig. 3.
Fig. 3.

Noise-to-signal ratio versus average input power in a 500 km link. The decreasing solid line shows σASE2/(PT), and the increasing solid line shows σθ2. The dashed line is the theoretical expression for σθ2 found in [6,9]. The dotted line is σNL2/(PT). Triangles and dots show σeff2/(PT) with and without phase noise cancellation, respectively.

Equations (5)

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yj=xjexp(iθj)+njNL+nj,
C=1NsuppX̲I(X̲;Y̲),
h(Y̲|X̲)=Ex̲(h(Y̲|X̲=x̲))12Ex̲(log2det(2πeQY^̲|X̲=x̲)),
det(QY^̲|X̲=x̲)=(σeff22)2N(1+2x̲2σeff2σc2)(1+2x̲2σeff2σs2),
Clog2(1+Pσeff2)12NEυ{log2(1+υσc2Pσeff2)}12NEυ{log2(1+υσs2Pσeff2)},

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