Abstract

We prove that, under certain conditions, the capacity of an optical communication channel with in-line, nonlinear filtering (regeneration) elements can be higher than the Shannon capacity for the corresponding linear Gaussian white noise channel.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
  2. P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
    [CrossRef]
  3. E. Desurvire, J. Lightwave Technol. 24, 4697 (2006).
    [CrossRef]
  4. R.-J. Essiambre, G. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101 (2008).
    [CrossRef]
  5. A. D. Ellis, J. Zhao, and D. Cotter, J. Lightwave Technol. 28, 423 (2010).
    [CrossRef]
  6. D. J. Richardson, Science 330, 327 (2010).
    [CrossRef]
  7. R. Killey and C. Behrens, J. Mod. Opt. 58, 1 (2011).
    [CrossRef]
  8. A. Mecozzi and R.-J. Essiambre, J. Lightwave Technol. 30, 2011–2024 (2012).
    [CrossRef]
  9. E. Agrell, “The channel capacity increases with power,” http://arxiv.org/abs/1108.0391 (2011).
  10. K. Turitsyn, S. Derevyanko, I. Yurkevich, and S. Turitsyn, Phys. Rev. Lett. 91, 1 (2003).
    [CrossRef]
  11. M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
    [CrossRef]
  12. T. Lakoba and M. Vasilyev, Opt. Express 15, 10061 (2007).
    [CrossRef]

2012

2011

R. Killey and C. Behrens, J. Mod. Opt. 58, 1 (2011).
[CrossRef]

2010

2008

R.-J. Essiambre, G. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101 (2008).
[CrossRef]

2007

2006

2003

K. Turitsyn, S. Derevyanko, I. Yurkevich, and S. Turitsyn, Phys. Rev. Lett. 91, 1 (2003).
[CrossRef]

2001

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

1991

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

1948

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Agrell, E.

E. Agrell, “The channel capacity increases with power,” http://arxiv.org/abs/1108.0391 (2011).

Behrens, C.

R. Killey and C. Behrens, J. Mod. Opt. 58, 1 (2011).
[CrossRef]

Cotter, D.

Derevyanko, S.

K. Turitsyn, S. Derevyanko, I. Yurkevich, and S. Turitsyn, Phys. Rev. Lett. 91, 1 (2003).
[CrossRef]

Desurvire, E.

Ellis, A. D.

Essiambre, R.-J.

A. Mecozzi and R.-J. Essiambre, J. Lightwave Technol. 30, 2011–2024 (2012).
[CrossRef]

R.-J. Essiambre, G. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101 (2008).
[CrossRef]

Foschini, G.

R.-J. Essiambre, G. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101 (2008).
[CrossRef]

Killey, R.

R. Killey and C. Behrens, J. Mod. Opt. 58, 1 (2011).
[CrossRef]

Kramer, G.

R.-J. Essiambre, G. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101 (2008).
[CrossRef]

Kubota, H.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Lakoba, T.

Mecozzi, A.

Mitra, P. P.

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

Nakazawa, M.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Richardson, D. J.

D. J. Richardson, Science 330, 327 (2010).
[CrossRef]

Shannon, C. E.

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Stark, J. B.

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

Suzuki, K.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Turitsyn, K.

K. Turitsyn, S. Derevyanko, I. Yurkevich, and S. Turitsyn, Phys. Rev. Lett. 91, 1 (2003).
[CrossRef]

Turitsyn, S.

K. Turitsyn, S. Derevyanko, I. Yurkevich, and S. Turitsyn, Phys. Rev. Lett. 91, 1 (2003).
[CrossRef]

Vasilyev, M.

Winzer, P.

R.-J. Essiambre, G. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101 (2008).
[CrossRef]

Yamada, E.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Yurkevich, I.

K. Turitsyn, S. Derevyanko, I. Yurkevich, and S. Turitsyn, Phys. Rev. Lett. 91, 1 (2003).
[CrossRef]

Zhao, J.

Bell Syst. Tech. J.

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Electron. Lett.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

J. Lightwave Technol.

J. Mod. Opt.

R. Killey and C. Behrens, J. Mod. Opt. 58, 1 (2011).
[CrossRef]

Nature

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

Opt. Express

Phys. Rev. Lett.

K. Turitsyn, S. Derevyanko, I. Yurkevich, and S. Turitsyn, Phys. Rev. Lett. 91, 1 (2003).
[CrossRef]

R.-J. Essiambre, G. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101 (2008).
[CrossRef]

Science

D. J. Richardson, Science 330, 327 (2010).
[CrossRef]

Other

E. Agrell, “The channel capacity increases with power,” http://arxiv.org/abs/1108.0391 (2011).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1.
Fig. 1.

Schematic depiction of the modulation format and nonlinear transformation for K=5. Dashed lines represent the Voronoi diagram of the system, and also are the boundaries of the regions of attraction of ideal nonlinear filters.

Fig. 2.
Fig. 2.

Mutual information is shown as a function of SNR: the solid red (K=2) and green (K=5) lines are capacities of the linear discrete memoryless channels with K2 elements. The corresponding dashed lines depict the mutual information in the system with 10 regenerative nonlinear filters with the same alphabets of 4 and 25 elements. The solid blue line shows for comparison the classical Shannon capacity of the linear 2D AWGN channel.

Equations (4)

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

C=maxP(X)DXDYP(X,Y)log2P(X,Y)P(X)P(Y).
P(Y|X)=dXδ(YF(X))PC(X|X).
P(Y=Xk|X)=SkdXPC(X|X).
Wkl=12[erf(xkl+)erf(xkl)],

Metrics