Abstract

We apply the multicanonical Monte Carlo (MMC) method to compute the probability distribution of the received voltage in a chirped return-to-zero system. When computing the probabilities of very rare events, the MMC technique greatly enhances the efficiency of Monte Carlo simulations by biasing the noise realizations. Our results agree with the covariance matrix method over 20 orders of magnitude. The MMC method can be regarded as iterative importance sampling that automatically converges toward the optimal bias so that it requires less a priori knowledge of the simulated system than importance sampling requires. A second advantage is that the merging of different regions of a probability distribution function to obtain the entire function is not necessary in many cases.

© 2003 Optical Society of America

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  1. Y. Cai, J. M. Morris, T. Adali, and C. R. Menyuk, J. Lightwave Technol. 21, 727 (2003).
    [CrossRef]
  2. R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
    [CrossRef]
  3. R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
    [CrossRef]
  4. R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 15, 688 (2003).
    [CrossRef]
  5. B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).
    [CrossRef] [PubMed]
  6. P. M. Hahn and M. C. Jeruchim, IEEE Trans. Commun. 35, 706 (1987).
    [CrossRef]
  7. G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
    [CrossRef]
  8. D. Yevick, IEEE Photon. Technol. Lett. 15, 224 (2003).
    [CrossRef]
  9. B. A. Berg, Nucl. Phys. B. Proc. Suppl. 63, 982 (1998).
    [CrossRef]
  10. Pjk ∝ 1/ωj(k), where ωj(k) is Berg's9 weight. We choose to deal with Pjk rather than ωj(k), since we consider them to be more intuitive quantities.
  11. N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
    [CrossRef] [PubMed]

2003

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 15, 688 (2003).
[CrossRef]

D. Yevick, IEEE Photon. Technol. Lett. 15, 224 (2003).
[CrossRef]

Y. Cai, J. M. Morris, T. Adali, and C. R. Menyuk, J. Lightwave Technol. 21, 727 (2003).
[CrossRef]

2002

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
[CrossRef]

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

1998

B. A. Berg, Nucl. Phys. B. Proc. Suppl. 63, 982 (1998).
[CrossRef]

1992

B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).
[CrossRef] [PubMed]

1987

P. M. Hahn and M. C. Jeruchim, IEEE Trans. Commun. 35, 706 (1987).
[CrossRef]

1949

N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
[CrossRef] [PubMed]

Adali, T.

Berg, B. A.

B. A. Berg, Nucl. Phys. B. Proc. Suppl. 63, 982 (1998).
[CrossRef]

B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).
[CrossRef] [PubMed]

Biondini, G.

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

Cai, Y.

Grigoryan, V. S.

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 15, 688 (2003).
[CrossRef]

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
[CrossRef]

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

Hahn, P. M.

P. M. Hahn and M. C. Jeruchim, IEEE Trans. Commun. 35, 706 (1987).
[CrossRef]

Holzlöhner, R.

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 15, 688 (2003).
[CrossRef]

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
[CrossRef]

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

Jeruchim, M. C.

P. M. Hahn and M. C. Jeruchim, IEEE Trans. Commun. 35, 706 (1987).
[CrossRef]

Kath, W. L.

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 15, 688 (2003).
[CrossRef]

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
[CrossRef]

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

Menyuk, C. R.

Y. Cai, J. M. Morris, T. Adali, and C. R. Menyuk, J. Lightwave Technol. 21, 727 (2003).
[CrossRef]

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 15, 688 (2003).
[CrossRef]

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
[CrossRef]

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

Metropolis, N.

N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
[CrossRef] [PubMed]

Morris, J. M.

Neuhaus, T.

B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).
[CrossRef] [PubMed]

Ulam, S.

N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
[CrossRef] [PubMed]

Yevick, D.

D. Yevick, IEEE Photon. Technol. Lett. 15, 224 (2003).
[CrossRef]

IEEE Photon. Technol. Lett.

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

D. Yevick, IEEE Photon. Technol. Lett. 15, 224 (2003).
[CrossRef]

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

R. Holzlöhner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 15, 688 (2003).
[CrossRef]

IEEE Trans. Commun.

P. M. Hahn and M. C. Jeruchim, IEEE Trans. Commun. 35, 706 (1987).
[CrossRef]

J. Am. Stat. Assoc.

N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
[CrossRef] [PubMed]

J. Lightwave Technol.

Nucl. Phys. B. Proc. Suppl.

B. A. Berg, Nucl. Phys. B. Proc. Suppl. 63, 982 (1998).
[CrossRef]

Phys. Rev. Lett.

B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).
[CrossRef] [PubMed]

Other

Pjk ∝ 1/ωj(k), where ωj(k) is Berg's9 weight. We choose to deal with Pjk rather than ωj(k), since we consider them to be more intuitive quantities.

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Figures (1)

Fig. 1
Fig. 1

Pdfs of the low-pass-filtered received voltage for the marks and the spaces in the CRZ system. The circles and crosses represent results from the last iteration of MMC simulations with 55,000 and 100,000 samples, respectively; the solid line and curve represent the covariance matrix method.

Equations (7)

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

Pk=Γχkzρzdz,
Pk1Ni=1Nχkzi,
Pk=Γχkzρzρ*zρ*zdz1Ni=1Nχkz*,iρz*,iρ*z*,i,
ρ*,jz=ρzcjPkj,  zΓk.
πab=l=1dminρlzb,l*ρlza,l*,1minPkajPkbj,1.
Pk+1j+1=Pkj+1Pk+1jPkjHk+1*,jHk*,jgˆkj,
gˆkj=gkjl=1jgkl,  gkl=Hk*,lHk+1*,lHk*,l+Hk+1*,l,

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