Abstract

We introduce several easily programmed techniques that enhance the accuracy of multicanonical sampling. With minor modifications to the standard technique, our methods achieve equivalent or enhanced accuracy compared with existing, often far more complex, algorithmic refinements. Despite their simple formulation, these procedures have been previously overlooked because of the low cost of additional realizations in numerical calculations. When applied in the context of our recently introduced experimental multicanonical measurements, however, significant time savings can result.

© 2006 Optical Society of America

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  1. T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, "An experimental approach to multicanonical sampling," IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
    [CrossRef]
  2. T. Lu, D. Yevick, L. Yan, and A. E. Willner, "Experimental realization of multi-canonical sampling," in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics (Optical Society of America, 2004), Vol. 1, pp. 1012-1014.
  3. T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, and M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
    [CrossRef]
  4. L. Yan, T. Lu, B. Zhang, C. Yu, D. Yevick, and A. Willner, "Fiber transmission system application and limitation of multicanonical sampling in PMD emulation," in Optical Fiber Communications Conference (OFC), Postconference Digest, 2005), paper OThT4.
  5. T. Lu and D. Yevick, "Biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 1420-1422 (2005).
    [CrossRef]
  6. B. A. Berg, "Introduction to multicanonical Monte Carlo simulations," Fields Inst. Commun. 26, 1-24 (2000).
  7. D. Yevick, A First Course in Computational Physics and Object-Oriented Programming with C++ (Cambrige U. Press, 2005), Chap. 22.
  8. D. Yevick, "The accuracy of multicanonical system models," IEEE Photon. Technol. Lett. 15, 224-226 (2003).
    [CrossRef]
  9. D. Yevick, "Multicanonical evaluation of joint probability density functions in communication system modeling," IEEE Photon. Technol. Lett. 15, 1540-1542 (2003).
    [CrossRef]
  10. D. Yevick, A First Course in Computational Physics and Object-Oriented Programming with C++ (Cambrige U. Press, 2005).
  11. T. Lu,W. Huang, D. Yevick, M. O'Sullivan, and M. Reimer, "Multicanonical comparison of polarization-mode dispersion compensator performance," J. Opt. Soc. Am. A 22, 2804-2809 (2005).
    [CrossRef]
  12. O. V. Sinkin, R. Holzlohner, V. S. Grigoryan, J. Zweck, and C. R. Menyuk, "Probabilistic description of the nonlinear penalties in WDM RZ systems using multicanonical Monte Carlo simulations," in The Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS (IEEE, 2003), Vol. 2, p. ThI5.
  13. Y. Yadin, M. Shtaif, and M. Orenstein, "Bit-error rate of optical DPSK in fiber systems by multicanonical Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1355-1357 (2005).
    [CrossRef]
  14. A. Bilenca and G. Eisenstein, "Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier," IEEE J. Quantum Electron. 41, 36-44 (2005).
    [CrossRef]
  15. A. Bilenca and G. Eisenstein, "Fokker-Planck and Langevin analyses of noise accompanying the amplification of optical pulses in semiconductor optical amplifiers," J. Opt. Soc. Am. B 22, 1632-1639 (2005).
    [CrossRef]
  16. T. Kamalakis, D. Varoutas, and T. Sphicopoulos, "Statistical study of in-band crosstalk noise using the multicanonical Monte Carlo method," IEEE Photon. Technol. Lett. 16, 2242-2244 (2004).
    [CrossRef]
  17. I. Neokosmidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, "Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method," Opt. Lett. 30, 11-13 (2005).
    [CrossRef] [PubMed]
  18. R. Holzlöhner and C. R. Menyuk, "Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems," Opt. Lett. 28, 1894-1896 (2003).
    [CrossRef] [PubMed]
  19. J. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath, and C. R. Menyuk, "Analysis of PMD compensators with fixed DGD using importance sampling," IEEE Photon. Technol. Lett. 14, 627-629 (2002).
    [CrossRef]
  20. T. Lu and D. O. Yevick, "Efficient multicanonical algorithms," IEEE Photon. Technol. Lett. 17, 861-863 (2005).
    [CrossRef]
  21. W. Janke, "Statistical analysis of simulations: data correlations and error estimation," in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, Lecture Notes, J.Grotendorst, D.Marx, and A.Muramatsu, eds., Vol. 10 of the John von Neumann Institute for Computing Series (John von Neumann Institute for Computing, 2002), pp. 423-445.
  22. A. O. Lima, J. Ivan, T. Lima, and C. R. Menyuk, "Error estimation in multicanonical Monte Carlo simulations with applications to polarization-mode-dispersion emulators," J. Lightwave Technol. 23, 3781-3789 (2005).
    [CrossRef]
  23. R. Holzlöhner, A. Mahadevan, C. R. Menyuk, J. M. Morris, and J. Zweck, "Evaluation of the very low BER of FEC codes using dual adaptive importance sampling," IEEE Commun. Lett. 9, 163-165 (2005).
    [CrossRef]
  24. M. Karlsson, "Probability density functions of the differential group delay in optical fiber communication systems," J. Lightwave Technol. 19, 324-331 (2001).
    [CrossRef]

2005 (10)

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, and M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
[CrossRef]

T. Lu and D. Yevick, "Biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 1420-1422 (2005).
[CrossRef]

T. Lu,W. Huang, D. Yevick, M. O'Sullivan, and M. Reimer, "Multicanonical comparison of polarization-mode dispersion compensator performance," J. Opt. Soc. Am. A 22, 2804-2809 (2005).
[CrossRef]

Y. Yadin, M. Shtaif, and M. Orenstein, "Bit-error rate of optical DPSK in fiber systems by multicanonical Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1355-1357 (2005).
[CrossRef]

A. Bilenca and G. Eisenstein, "Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier," IEEE J. Quantum Electron. 41, 36-44 (2005).
[CrossRef]

A. Bilenca and G. Eisenstein, "Fokker-Planck and Langevin analyses of noise accompanying the amplification of optical pulses in semiconductor optical amplifiers," J. Opt. Soc. Am. B 22, 1632-1639 (2005).
[CrossRef]

T. Lu and D. O. Yevick, "Efficient multicanonical algorithms," IEEE Photon. Technol. Lett. 17, 861-863 (2005).
[CrossRef]

A. O. Lima, J. Ivan, T. Lima, and C. R. Menyuk, "Error estimation in multicanonical Monte Carlo simulations with applications to polarization-mode-dispersion emulators," J. Lightwave Technol. 23, 3781-3789 (2005).
[CrossRef]

R. Holzlöhner, A. Mahadevan, C. R. Menyuk, J. M. Morris, and J. Zweck, "Evaluation of the very low BER of FEC codes using dual adaptive importance sampling," IEEE Commun. Lett. 9, 163-165 (2005).
[CrossRef]

I. Neokosmidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, "Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method," Opt. Lett. 30, 11-13 (2005).
[CrossRef] [PubMed]

2004 (2)

T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, "An experimental approach to multicanonical sampling," IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
[CrossRef]

T. Kamalakis, D. Varoutas, and T. Sphicopoulos, "Statistical study of in-band crosstalk noise using the multicanonical Monte Carlo method," IEEE Photon. Technol. Lett. 16, 2242-2244 (2004).
[CrossRef]

2003 (3)

D. Yevick, "The accuracy of multicanonical system models," IEEE Photon. Technol. Lett. 15, 224-226 (2003).
[CrossRef]

D. Yevick, "Multicanonical evaluation of joint probability density functions in communication system modeling," IEEE Photon. Technol. Lett. 15, 1540-1542 (2003).
[CrossRef]

R. Holzlöhner and C. R. Menyuk, "Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems," Opt. Lett. 28, 1894-1896 (2003).
[CrossRef] [PubMed]

2002 (1)

J. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath, and C. R. Menyuk, "Analysis of PMD compensators with fixed DGD using importance sampling," IEEE Photon. Technol. Lett. 14, 627-629 (2002).
[CrossRef]

2001 (1)

2000 (1)

B. A. Berg, "Introduction to multicanonical Monte Carlo simulations," Fields Inst. Commun. 26, 1-24 (2000).

Berg, B. A.

B. A. Berg, "Introduction to multicanonical Monte Carlo simulations," Fields Inst. Commun. 26, 1-24 (2000).

Bilenca, A.

A. Bilenca and G. Eisenstein, "Fokker-Planck and Langevin analyses of noise accompanying the amplification of optical pulses in semiconductor optical amplifiers," J. Opt. Soc. Am. B 22, 1632-1639 (2005).
[CrossRef]

A. Bilenca and G. Eisenstein, "Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier," IEEE J. Quantum Electron. 41, 36-44 (2005).
[CrossRef]

Biondini, G.

J. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath, and C. R. Menyuk, "Analysis of PMD compensators with fixed DGD using importance sampling," IEEE Photon. Technol. Lett. 14, 627-629 (2002).
[CrossRef]

Chipouras, A.

Dumas, D.

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, and M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
[CrossRef]

Eisenstein, G.

A. Bilenca and G. Eisenstein, "Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier," IEEE J. Quantum Electron. 41, 36-44 (2005).
[CrossRef]

A. Bilenca and G. Eisenstein, "Fokker-Planck and Langevin analyses of noise accompanying the amplification of optical pulses in semiconductor optical amplifiers," J. Opt. Soc. Am. B 22, 1632-1639 (2005).
[CrossRef]

Grigoryan, V. S.

O. V. Sinkin, R. Holzlohner, V. S. Grigoryan, J. Zweck, and C. R. Menyuk, "Probabilistic description of the nonlinear penalties in WDM RZ systems using multicanonical Monte Carlo simulations," in The Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS (IEEE, 2003), Vol. 2, p. ThI5.

Hamilton, B.

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, and M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
[CrossRef]

Holzlohner, R.

O. V. Sinkin, R. Holzlohner, V. S. Grigoryan, J. Zweck, and C. R. Menyuk, "Probabilistic description of the nonlinear penalties in WDM RZ systems using multicanonical Monte Carlo simulations," in The Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS (IEEE, 2003), Vol. 2, p. ThI5.

Holzlöhner, R.

R. Holzlöhner, A. Mahadevan, C. R. Menyuk, J. M. Morris, and J. Zweck, "Evaluation of the very low BER of FEC codes using dual adaptive importance sampling," IEEE Commun. Lett. 9, 163-165 (2005).
[CrossRef]

R. Holzlöhner and C. R. Menyuk, "Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems," Opt. Lett. 28, 1894-1896 (2003).
[CrossRef] [PubMed]

Huang, W.

Ivan, J.

Janke, W.

W. Janke, "Statistical analysis of simulations: data correlations and error estimation," in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, Lecture Notes, J.Grotendorst, D.Marx, and A.Muramatsu, eds., Vol. 10 of the John von Neumann Institute for Computing Series (John von Neumann Institute for Computing, 2002), pp. 423-445.

Kamalakis, T.

I. Neokosmidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, "Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method," Opt. Lett. 30, 11-13 (2005).
[CrossRef] [PubMed]

T. Kamalakis, D. Varoutas, and T. Sphicopoulos, "Statistical study of in-band crosstalk noise using the multicanonical Monte Carlo method," IEEE Photon. Technol. Lett. 16, 2242-2244 (2004).
[CrossRef]

Karlsson, M.

Kath, W. L.

J. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath, and C. R. Menyuk, "Analysis of PMD compensators with fixed DGD using importance sampling," IEEE Photon. Technol. Lett. 14, 627-629 (2002).
[CrossRef]

Lima, A. O.

Lima, J. I. T.

J. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath, and C. R. Menyuk, "Analysis of PMD compensators with fixed DGD using importance sampling," IEEE Photon. Technol. Lett. 14, 627-629 (2002).
[CrossRef]

Lima, T.

Lu, T.

T. Lu and D. O. Yevick, "Efficient multicanonical algorithms," IEEE Photon. Technol. Lett. 17, 861-863 (2005).
[CrossRef]

T. Lu,W. Huang, D. Yevick, M. O'Sullivan, and M. Reimer, "Multicanonical comparison of polarization-mode dispersion compensator performance," J. Opt. Soc. Am. A 22, 2804-2809 (2005).
[CrossRef]

T. Lu and D. Yevick, "Biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 1420-1422 (2005).
[CrossRef]

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, and M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
[CrossRef]

T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, "An experimental approach to multicanonical sampling," IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
[CrossRef]

T. Lu, D. Yevick, L. Yan, and A. E. Willner, "Experimental realization of multi-canonical sampling," in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics (Optical Society of America, 2004), Vol. 1, pp. 1012-1014.

L. Yan, T. Lu, B. Zhang, C. Yu, D. Yevick, and A. Willner, "Fiber transmission system application and limitation of multicanonical sampling in PMD emulation," in Optical Fiber Communications Conference (OFC), Postconference Digest, 2005), paper OThT4.

Mahadevan, A.

R. Holzlöhner, A. Mahadevan, C. R. Menyuk, J. M. Morris, and J. Zweck, "Evaluation of the very low BER of FEC codes using dual adaptive importance sampling," IEEE Commun. Lett. 9, 163-165 (2005).
[CrossRef]

Marks, B. S.

J. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath, and C. R. Menyuk, "Analysis of PMD compensators with fixed DGD using importance sampling," IEEE Photon. Technol. Lett. 14, 627-629 (2002).
[CrossRef]

Menyuk, C. R.

R. Holzlöhner, A. Mahadevan, C. R. Menyuk, J. M. Morris, and J. Zweck, "Evaluation of the very low BER of FEC codes using dual adaptive importance sampling," IEEE Commun. Lett. 9, 163-165 (2005).
[CrossRef]

A. O. Lima, J. Ivan, T. Lima, and C. R. Menyuk, "Error estimation in multicanonical Monte Carlo simulations with applications to polarization-mode-dispersion emulators," J. Lightwave Technol. 23, 3781-3789 (2005).
[CrossRef]

R. Holzlöhner and C. R. Menyuk, "Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems," Opt. Lett. 28, 1894-1896 (2003).
[CrossRef] [PubMed]

J. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath, and C. R. Menyuk, "Analysis of PMD compensators with fixed DGD using importance sampling," IEEE Photon. Technol. Lett. 14, 627-629 (2002).
[CrossRef]

O. V. Sinkin, R. Holzlohner, V. S. Grigoryan, J. Zweck, and C. R. Menyuk, "Probabilistic description of the nonlinear penalties in WDM RZ systems using multicanonical Monte Carlo simulations," in The Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS (IEEE, 2003), Vol. 2, p. ThI5.

Morris, J. M.

R. Holzlöhner, A. Mahadevan, C. R. Menyuk, J. M. Morris, and J. Zweck, "Evaluation of the very low BER of FEC codes using dual adaptive importance sampling," IEEE Commun. Lett. 9, 163-165 (2005).
[CrossRef]

Neokosmidis, I.

Orenstein, M.

Y. Yadin, M. Shtaif, and M. Orenstein, "Bit-error rate of optical DPSK in fiber systems by multicanonical Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1355-1357 (2005).
[CrossRef]

O'Sullivan, M.

Reimer, M.

T. Lu,W. Huang, D. Yevick, M. O'Sullivan, and M. Reimer, "Multicanonical comparison of polarization-mode dispersion compensator performance," J. Opt. Soc. Am. A 22, 2804-2809 (2005).
[CrossRef]

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, and M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
[CrossRef]

Shtaif, M.

Y. Yadin, M. Shtaif, and M. Orenstein, "Bit-error rate of optical DPSK in fiber systems by multicanonical Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1355-1357 (2005).
[CrossRef]

Sinkin, O. V.

O. V. Sinkin, R. Holzlohner, V. S. Grigoryan, J. Zweck, and C. R. Menyuk, "Probabilistic description of the nonlinear penalties in WDM RZ systems using multicanonical Monte Carlo simulations," in The Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS (IEEE, 2003), Vol. 2, p. ThI5.

Sphicopoulos, T.

I. Neokosmidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, "Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method," Opt. Lett. 30, 11-13 (2005).
[CrossRef] [PubMed]

T. Kamalakis, D. Varoutas, and T. Sphicopoulos, "Statistical study of in-band crosstalk noise using the multicanonical Monte Carlo method," IEEE Photon. Technol. Lett. 16, 2242-2244 (2004).
[CrossRef]

Varoutas, D.

T. Kamalakis, D. Varoutas, and T. Sphicopoulos, "Statistical study of in-band crosstalk noise using the multicanonical Monte Carlo method," IEEE Photon. Technol. Lett. 16, 2242-2244 (2004).
[CrossRef]

Willner, A.

L. Yan, T. Lu, B. Zhang, C. Yu, D. Yevick, and A. Willner, "Fiber transmission system application and limitation of multicanonical sampling in PMD emulation," in Optical Fiber Communications Conference (OFC), Postconference Digest, 2005), paper OThT4.

Willner, A. E.

T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, "An experimental approach to multicanonical sampling," IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
[CrossRef]

T. Lu, D. Yevick, L. Yan, and A. E. Willner, "Experimental realization of multi-canonical sampling," in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics (Optical Society of America, 2004), Vol. 1, pp. 1012-1014.

Yadin, Y.

Y. Yadin, M. Shtaif, and M. Orenstein, "Bit-error rate of optical DPSK in fiber systems by multicanonical Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1355-1357 (2005).
[CrossRef]

Yan, L.

T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, "An experimental approach to multicanonical sampling," IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
[CrossRef]

T. Lu, D. Yevick, L. Yan, and A. E. Willner, "Experimental realization of multi-canonical sampling," in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics (Optical Society of America, 2004), Vol. 1, pp. 1012-1014.

L. Yan, T. Lu, B. Zhang, C. Yu, D. Yevick, and A. Willner, "Fiber transmission system application and limitation of multicanonical sampling in PMD emulation," in Optical Fiber Communications Conference (OFC), Postconference Digest, 2005), paper OThT4.

Yevick, D.

T. Lu,W. Huang, D. Yevick, M. O'Sullivan, and M. Reimer, "Multicanonical comparison of polarization-mode dispersion compensator performance," J. Opt. Soc. Am. A 22, 2804-2809 (2005).
[CrossRef]

T. Lu and D. Yevick, "Biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 1420-1422 (2005).
[CrossRef]

D. Yevick, "The accuracy of multicanonical system models," IEEE Photon. Technol. Lett. 15, 224-226 (2003).
[CrossRef]

D. Yevick, "Multicanonical evaluation of joint probability density functions in communication system modeling," IEEE Photon. Technol. Lett. 15, 1540-1542 (2003).
[CrossRef]

D. Yevick, A First Course in Computational Physics and Object-Oriented Programming with C++ (Cambrige U. Press, 2005).

D. Yevick, A First Course in Computational Physics and Object-Oriented Programming with C++ (Cambrige U. Press, 2005), Chap. 22.

L. Yan, T. Lu, B. Zhang, C. Yu, D. Yevick, and A. Willner, "Fiber transmission system application and limitation of multicanonical sampling in PMD emulation," in Optical Fiber Communications Conference (OFC), Postconference Digest, 2005), paper OThT4.

T. Lu, D. Yevick, L. Yan, and A. E. Willner, "Experimental realization of multi-canonical sampling," in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics (Optical Society of America, 2004), Vol. 1, pp. 1012-1014.

Yevick, D. O.

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, and M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
[CrossRef]

T. Lu and D. O. Yevick, "Efficient multicanonical algorithms," IEEE Photon. Technol. Lett. 17, 861-863 (2005).
[CrossRef]

T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, "An experimental approach to multicanonical sampling," IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
[CrossRef]

Yu, C.

L. Yan, T. Lu, B. Zhang, C. Yu, D. Yevick, and A. Willner, "Fiber transmission system application and limitation of multicanonical sampling in PMD emulation," in Optical Fiber Communications Conference (OFC), Postconference Digest, 2005), paper OThT4.

Zhang, B.

T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, "An experimental approach to multicanonical sampling," IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
[CrossRef]

L. Yan, T. Lu, B. Zhang, C. Yu, D. Yevick, and A. Willner, "Fiber transmission system application and limitation of multicanonical sampling in PMD emulation," in Optical Fiber Communications Conference (OFC), Postconference Digest, 2005), paper OThT4.

Zweck, J.

R. Holzlöhner, A. Mahadevan, C. R. Menyuk, J. M. Morris, and J. Zweck, "Evaluation of the very low BER of FEC codes using dual adaptive importance sampling," IEEE Commun. Lett. 9, 163-165 (2005).
[CrossRef]

O. V. Sinkin, R. Holzlohner, V. S. Grigoryan, J. Zweck, and C. R. Menyuk, "Probabilistic description of the nonlinear penalties in WDM RZ systems using multicanonical Monte Carlo simulations," in The Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS (IEEE, 2003), Vol. 2, p. ThI5.

Fields Inst. Commun. (1)

B. A. Berg, "Introduction to multicanonical Monte Carlo simulations," Fields Inst. Commun. 26, 1-24 (2000).

IEEE Commun. Lett. (1)

R. Holzlöhner, A. Mahadevan, C. R. Menyuk, J. M. Morris, and J. Zweck, "Evaluation of the very low BER of FEC codes using dual adaptive importance sampling," IEEE Commun. Lett. 9, 163-165 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Bilenca and G. Eisenstein, "Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier," IEEE J. Quantum Electron. 41, 36-44 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (9)

T. Kamalakis, D. Varoutas, and T. Sphicopoulos, "Statistical study of in-band crosstalk noise using the multicanonical Monte Carlo method," IEEE Photon. Technol. Lett. 16, 2242-2244 (2004).
[CrossRef]

T. Lu and D. Yevick, "Biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 1420-1422 (2005).
[CrossRef]

Y. Yadin, M. Shtaif, and M. Orenstein, "Bit-error rate of optical DPSK in fiber systems by multicanonical Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1355-1357 (2005).
[CrossRef]

D. Yevick, "The accuracy of multicanonical system models," IEEE Photon. Technol. Lett. 15, 224-226 (2003).
[CrossRef]

D. Yevick, "Multicanonical evaluation of joint probability density functions in communication system modeling," IEEE Photon. Technol. Lett. 15, 1540-1542 (2003).
[CrossRef]

T. Lu, D. O. Yevick, L. Yan, B. Zhang, and A. E. Willner, "An experimental approach to multicanonical sampling," IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
[CrossRef]

T. Lu, D. O. Yevick, B. Hamilton, D. Dumas, and M. Reimer, "An experimental realization of biased multicanonical sampling," IEEE Photon. Technol. Lett. 17, 2583-2585 (2005).
[CrossRef]

J. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath, and C. R. Menyuk, "Analysis of PMD compensators with fixed DGD using importance sampling," IEEE Photon. Technol. Lett. 14, 627-629 (2002).
[CrossRef]

T. Lu and D. O. Yevick, "Efficient multicanonical algorithms," IEEE Photon. Technol. Lett. 17, 861-863 (2005).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Other (6)

O. V. Sinkin, R. Holzlohner, V. S. Grigoryan, J. Zweck, and C. R. Menyuk, "Probabilistic description of the nonlinear penalties in WDM RZ systems using multicanonical Monte Carlo simulations," in The Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS (IEEE, 2003), Vol. 2, p. ThI5.

L. Yan, T. Lu, B. Zhang, C. Yu, D. Yevick, and A. Willner, "Fiber transmission system application and limitation of multicanonical sampling in PMD emulation," in Optical Fiber Communications Conference (OFC), Postconference Digest, 2005), paper OThT4.

T. Lu, D. Yevick, L. Yan, and A. E. Willner, "Experimental realization of multi-canonical sampling," in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics (Optical Society of America, 2004), Vol. 1, pp. 1012-1014.

D. Yevick, A First Course in Computational Physics and Object-Oriented Programming with C++ (Cambrige U. Press, 2005).

D. Yevick, A First Course in Computational Physics and Object-Oriented Programming with C++ (Cambrige U. Press, 2005), Chap. 22.

W. Janke, "Statistical analysis of simulations: data correlations and error estimation," in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, Lecture Notes, J.Grotendorst, D.Marx, and A.Muramatsu, eds., Vol. 10 of the John von Neumann Institute for Computing Series (John von Neumann Institute for Computing, 2002), pp. 423-445.

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Figures (6)

Fig. 1
Fig. 1

Quantity p ( E ) E 2 of a 15-section PMD emulator calculated with the Monte Carlo method (solid curve) together with three iterations of 500,000 samples obtained from the multicanonical method in which p ( E ) = 1 E 2 is added each time a bin is sampled in place of unity.

Fig. 2
Fig. 2

pdf of the DGD of a 15-section PMD emulator calculated with four iterations of 10,000 samples obtained from the analytic expression (solid curve), the standard multicanonical method (dashed curve), the modified procedure of Ref. [6]. (curve with short bars), the barrier method (dotted curve), and a combination of all the other techniques of this paper (dashed–dotted curve).

Fig. 3
Fig. 3

Average of log 10 2 ( p p exact ) over 100 separate calculations corresponding to Fig. 2.

Fig. 4
Fig. 4

Same as Fig. 2, except for four 100,000 sample iterations.

Fig. 5
Fig. 5

Average of log 10 2 ( p p exact ) (denoted by σ 2 ) over 100 separate calculations corresponding to Fig. 4.

Fig. 6
Fig. 6

Average of log 10 2 ( p p exact ) over 100 separate calculations (denoted by σ 2 ) for four iterations of 10,000 samples for the power method of Subsection 2A after combining intermediate results according to Eq. (1) (dotted curve), histogram interpolation of Subsection 2E (dashed curve), intermediate result combination of Subsection 2C (crosses), the Gaussian displacement technique of Subsection 2D (circles) and all techniques except for the barrier method (dashed–dotted curve).

Equations (2)

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p ( E i ) = k = 0 m 1 p ̃ k ( E i ) H k ( E i ) k = 0 m 1 H k ( E i ) ,
F k ( τ ) = { exp ( τ 1 τ α τ ave ) ( τ < τ 1 ) exp ( τ τ 2 α τ ave ) ( τ > τ 2 ) 1 ( τ 1 τ τ 2 ) } ,

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