Abstract

We compare the accuracy of the multicanonical procedure with that of transition-matrix models of static and dynamic communication system properties incorporating different acceptance rules. We find that for appropriate ranges of the underlying numerical parameters, algorithmically simple yet highly accurate procedures can be employed in place of the standard multicanonical sampling algorithm.

© 2008 Optical Society of America

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References

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  1. B. Berg and T. Neuhaus, “Multicanonical algorithms for first-order phase transitions,” Phys. Lett. B 267, 249-253 (1991).
    [CrossRef]
  2. D. Yevick, “Multicanonical communication system modeling--Application to PMD statistics,” IEEE Photon. Technol. Lett. 14, 1512-1514 (2002).
    [CrossRef]
  3. D. Yevick, “The accuracy of multicanonical system models,” IEEE Photon. Technol. Lett. 15, 224-226 (2003).
    [CrossRef]
  4. T. Lu, D. Yevick, L. Yan, B. Zhang, and A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978-1980 (2004).
    [CrossRef]
  5. J-S. Wang and R. Swendsen, “Transition matrix Monte Carlo method,” J. Stat. Phys. 106, 245-285 (2002).
    [CrossRef]
  6. M. Fitzgerald, R. Picard, and R. Silver, “Monte Carlo transition dynamics and variance reduction,” J. Stat. Phys. 98, 321-345 (2000).
    [CrossRef]
  7. D. Yevick and M. Reimer, “Transition matrix analysis of system outages,” IEEE Photon. Technol. Lett. 19, 1529-1531 (2007).
    [CrossRef]
  8. D. Yevick and T. Lu, “Improved multicanonical algorithms,” J. Opt. Soc. Am. A 23, 2912-2918 (2006).
    [CrossRef]
  9. M. S. Shell, P. Debenedetti, and A. Panagiotopoulos, “An improved Monte Carlo method for direct calculation of the density of states,” J. Chem. Phys. 119, 9406-9411 (2003).
    [CrossRef]
  10. R. Ghulghazaryan, S. Hayryan, and C. Hu, “Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations,” J. Comput. Chem. 28, 715-726 (2006).
    [CrossRef] [PubMed]
  11. D. Yevick and M. Reimer, “Modified transition matrix simulations of communication systems,” IEEE Commun. Lett. 12, 755-757 (2008).
    [CrossRef]
  12. M. Karlsson, “Probability density functions of the differential group delay in optical fiber communication systems,” J. Lightwave Technol. 19, 324-331 (2001).
    [CrossRef]
  13. T. Lu, D. Yevick, B. Hamilton, D. Dumas, and M. Reimer, “An experimental realization of biased multicanonical sampling,” IEEE Photon. Technol. Lett. 17, 1583-2585 (2005).

2008 (1)

D. Yevick and M. Reimer, “Modified transition matrix simulations of communication systems,” IEEE Commun. Lett. 12, 755-757 (2008).
[CrossRef]

2007 (1)

D. Yevick and M. Reimer, “Transition matrix analysis of system outages,” IEEE Photon. Technol. Lett. 19, 1529-1531 (2007).
[CrossRef]

2006 (2)

D. Yevick and T. Lu, “Improved multicanonical algorithms,” J. Opt. Soc. Am. A 23, 2912-2918 (2006).
[CrossRef]

R. Ghulghazaryan, S. Hayryan, and C. Hu, “Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations,” J. Comput. Chem. 28, 715-726 (2006).
[CrossRef] [PubMed]

2005 (1)

T. Lu, D. Yevick, B. Hamilton, D. Dumas, and M. Reimer, “An experimental realization of biased multicanonical sampling,” IEEE Photon. Technol. Lett. 17, 1583-2585 (2005).

2004 (1)

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

2003 (2)

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

M. S. Shell, P. Debenedetti, and A. Panagiotopoulos, “An improved Monte Carlo method for direct calculation of the density of states,” J. Chem. Phys. 119, 9406-9411 (2003).
[CrossRef]

2002 (2)

J-S. Wang and R. Swendsen, “Transition matrix Monte Carlo method,” J. Stat. Phys. 106, 245-285 (2002).
[CrossRef]

D. Yevick, “Multicanonical communication system modeling--Application to PMD statistics,” IEEE Photon. Technol. Lett. 14, 1512-1514 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. Fitzgerald, R. Picard, and R. Silver, “Monte Carlo transition dynamics and variance reduction,” J. Stat. Phys. 98, 321-345 (2000).
[CrossRef]

1991 (1)

B. Berg and T. Neuhaus, “Multicanonical algorithms for first-order phase transitions,” Phys. Lett. B 267, 249-253 (1991).
[CrossRef]

Berg, B.

B. Berg and T. Neuhaus, “Multicanonical algorithms for first-order phase transitions,” Phys. Lett. B 267, 249-253 (1991).
[CrossRef]

Debenedetti, P.

M. S. Shell, P. Debenedetti, and A. Panagiotopoulos, “An improved Monte Carlo method for direct calculation of the density of states,” J. Chem. Phys. 119, 9406-9411 (2003).
[CrossRef]

Dumas, D.

T. Lu, D. Yevick, B. Hamilton, D. Dumas, and M. Reimer, “An experimental realization of biased multicanonical sampling,” IEEE Photon. Technol. Lett. 17, 1583-2585 (2005).

Fitzgerald, M.

M. Fitzgerald, R. Picard, and R. Silver, “Monte Carlo transition dynamics and variance reduction,” J. Stat. Phys. 98, 321-345 (2000).
[CrossRef]

Ghulghazaryan, R.

R. Ghulghazaryan, S. Hayryan, and C. Hu, “Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations,” J. Comput. Chem. 28, 715-726 (2006).
[CrossRef] [PubMed]

Hamilton, B.

T. Lu, D. Yevick, B. Hamilton, D. Dumas, and M. Reimer, “An experimental realization of biased multicanonical sampling,” IEEE Photon. Technol. Lett. 17, 1583-2585 (2005).

Hayryan, S.

R. Ghulghazaryan, S. Hayryan, and C. Hu, “Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations,” J. Comput. Chem. 28, 715-726 (2006).
[CrossRef] [PubMed]

Hu, C.

R. Ghulghazaryan, S. Hayryan, and C. Hu, “Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations,” J. Comput. Chem. 28, 715-726 (2006).
[CrossRef] [PubMed]

Karlsson, M.

Lu, T.

D. Yevick and T. Lu, “Improved multicanonical algorithms,” J. Opt. Soc. Am. A 23, 2912-2918 (2006).
[CrossRef]

T. Lu, D. Yevick, B. Hamilton, D. Dumas, and M. Reimer, “An experimental realization of biased multicanonical sampling,” IEEE Photon. Technol. Lett. 17, 1583-2585 (2005).

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

Neuhaus, T.

B. Berg and T. Neuhaus, “Multicanonical algorithms for first-order phase transitions,” Phys. Lett. B 267, 249-253 (1991).
[CrossRef]

Panagiotopoulos, A.

M. S. Shell, P. Debenedetti, and A. Panagiotopoulos, “An improved Monte Carlo method for direct calculation of the density of states,” J. Chem. Phys. 119, 9406-9411 (2003).
[CrossRef]

Picard, R.

M. Fitzgerald, R. Picard, and R. Silver, “Monte Carlo transition dynamics and variance reduction,” J. Stat. Phys. 98, 321-345 (2000).
[CrossRef]

Reimer, M.

D. Yevick and M. Reimer, “Modified transition matrix simulations of communication systems,” IEEE Commun. Lett. 12, 755-757 (2008).
[CrossRef]

D. Yevick and M. Reimer, “Transition matrix analysis of system outages,” IEEE Photon. Technol. Lett. 19, 1529-1531 (2007).
[CrossRef]

T. Lu, D. Yevick, B. Hamilton, D. Dumas, and M. Reimer, “An experimental realization of biased multicanonical sampling,” IEEE Photon. Technol. Lett. 17, 1583-2585 (2005).

Shell, M. S.

M. S. Shell, P. Debenedetti, and A. Panagiotopoulos, “An improved Monte Carlo method for direct calculation of the density of states,” J. Chem. Phys. 119, 9406-9411 (2003).
[CrossRef]

Silver, R.

M. Fitzgerald, R. Picard, and R. Silver, “Monte Carlo transition dynamics and variance reduction,” J. Stat. Phys. 98, 321-345 (2000).
[CrossRef]

Swendsen, R.

J-S. Wang and R. Swendsen, “Transition matrix Monte Carlo method,” J. Stat. Phys. 106, 245-285 (2002).
[CrossRef]

Wang, J-S.

J-S. Wang and R. Swendsen, “Transition matrix Monte Carlo method,” J. Stat. Phys. 106, 245-285 (2002).
[CrossRef]

Willner, A. E.

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

Yan, L.

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

Yevick, D.

D. Yevick and M. Reimer, “Modified transition matrix simulations of communication systems,” IEEE Commun. Lett. 12, 755-757 (2008).
[CrossRef]

D. Yevick and M. Reimer, “Transition matrix analysis of system outages,” IEEE Photon. Technol. Lett. 19, 1529-1531 (2007).
[CrossRef]

D. Yevick and T. Lu, “Improved multicanonical algorithms,” J. Opt. Soc. Am. A 23, 2912-2918 (2006).
[CrossRef]

T. Lu, D. Yevick, B. Hamilton, D. Dumas, and M. Reimer, “An experimental realization of biased multicanonical sampling,” IEEE Photon. Technol. Lett. 17, 1583-2585 (2005).

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

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

D. Yevick, “Multicanonical communication system modeling--Application to PMD statistics,” IEEE Photon. Technol. Lett. 14, 1512-1514 (2002).
[CrossRef]

Zhang, B.

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

IEEE Commun. Lett. (1)

D. Yevick and M. Reimer, “Modified transition matrix simulations of communication systems,” IEEE Commun. Lett. 12, 755-757 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

T. Lu, D. Yevick, B. Hamilton, D. Dumas, and M. Reimer, “An experimental realization of biased multicanonical sampling,” IEEE Photon. Technol. Lett. 17, 1583-2585 (2005).

D. Yevick, “Multicanonical communication system modeling--Application to PMD statistics,” IEEE Photon. Technol. Lett. 14, 1512-1514 (2002).
[CrossRef]

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

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

D. Yevick and M. Reimer, “Transition matrix analysis of system outages,” IEEE Photon. Technol. Lett. 19, 1529-1531 (2007).
[CrossRef]

J. Chem. Phys. (1)

M. S. Shell, P. Debenedetti, and A. Panagiotopoulos, “An improved Monte Carlo method for direct calculation of the density of states,” J. Chem. Phys. 119, 9406-9411 (2003).
[CrossRef]

J. Comput. Chem. (1)

R. Ghulghazaryan, S. Hayryan, and C. Hu, “Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations,” J. Comput. Chem. 28, 715-726 (2006).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

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

J. Stat. Phys. (2)

J-S. Wang and R. Swendsen, “Transition matrix Monte Carlo method,” J. Stat. Phys. 106, 245-285 (2002).
[CrossRef]

M. Fitzgerald, R. Picard, and R. Silver, “Monte Carlo transition dynamics and variance reduction,” J. Stat. Phys. 98, 321-345 (2000).
[CrossRef]

Phys. Lett. B (1)

B. Berg and T. Neuhaus, “Multicanonical algorithms for first-order phase transitions,” Phys. Lett. B 267, 249-253 (1991).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Ratio between the numerical and analytic pdfs for the standard multicanonical procedure (△), our modified transition matrix procedure with a multicanonical acceptance rule (method 1, ○), an acceptance rule that rejects transitions to more visited histogram bins (method 2, dashed–dotted curve), and a procedure that restricts transitions out of a recently visited bin (method 3, crosses) as functions of the normalized DGD for a N sec = 10 segment fiber emulator (solid curve).

Fig. 2
Fig. 2

Total number of times each histogram bin is visited for the standard multicanonical procedure (△), method 1 (○), and method 2 (dashed–dotted curve).

Fig. 3
Fig. 3

Variation of the error, Eq. (2), weighted by the histogram bin probability as a function of the average DGD change over one Markov step for the standard multicanonical method (△), method 1 (○), method 2 (dashed–dotted curve), and method 3 (crosses).

Equations (2)

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p m + 1 = p m T m + 1 , m T m , m + 1 .
m = 1 N B p m analytic log 10 ( p m numerical p m analytic ) ,

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