Error estimation in multicanonical Monte Carlo Simulations with applications to polarization-mode-dispersion emulators

• Published in: Journal of lightwave technology Vol. 23; no. 11; pp. 3781 - 3789
• Main Authors: Lima, A.O., Lima, I.T., Menyuk, C.R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Computational modeling; Computer science; Computer simulation; Delay estimation; Emulators; Error analysis; Estimates; Exact sciences and technology; Group delay; Iterative methods; Metal matrix composites; Monte Carlo methods; Multicanonical Monte Carlo (MMC) simulations; Nonlinear optics; optical communications; Optical fiber communication; Optical fiber communications; Optical telecommunications; Permissible error; Polarization; polarization-mode dispersion (PMD); Probability density functions; Probability distribution; statistical error; Telecommunications; Telecommunications and information theory; Error analysis; Error probability; Error estimation; Optical telecommunication; Iterative method; Emulator; Polarization mode dispersion; Transition matrix; Probability density function; Bootstrap; Optical fiber communication; Growth of error; Estimation error; Monte Carlo method; Outage; optical communications; Statistical method; Matrix method; Numerical simulation; polarization-mode dispersion (PMD); statistical error; Comparative study; Multicanonical Monte Carlo (MMC) simulations; Transmission error; Group delay
• ISSN: 0733-8724; 1558-2213
• DOI: 10.1109/JLT.2005.857728

This paper shows how to estimate errors in multicanonical Monte Carlo (MMC) simulations using a transition-matrix method. MMC is a biasing Monte Carlo technique that allows one to compute the probability of rare events, such as the outage probability in optical-fiber communication systems. Since MMC is a Monte Carlo technique, it is subject to statistical errors, and it is essential to determine their magnitude. Since MMC is a highly nonlinear iterative method, linearized error-propagation techniques and standard error analyses do not work, and a more sophisticated method is needed. The proposed method is based on bootstrap techniques. This method was applied to efficiently estimate the error in the probability density function (pdf) of the differential group delay (DGD) of polarization-mode-dispersion (PMD) emulators that has been calculated using MMC. The method was validated by comparison to the results obtained using a large ensemble of MMC simulations.