Abstract



Simulating Rare Events in Optical Transmission Systems

William L. Kath
Department of Engineering Sciences and Applied Mathematics
McCormick School of Engineering
Northwestern University
2145 Sheridan Road
Evanston, IL 60208-3125

Next-generation optical communication systems are now being designed to carry information at astounding transmission speeds, up to several terabits per second. Because transmission errors are handled at slower electronic speeds, it is desirable for these systems to have extremely small error rates, typically one error per 10^12 or more bits. Errors are thus extremely rare, and as a result realistic attempts to model and predict the effects of various transmission impairments as they appear in practical systems present a number of difficult mathematical and computational challenges. In this talk, recent work aimed at overcoming these challenges will be described.
First, polarization mode dispersion (PMD) will be discussed. PMD is a stochastic perturbation caused by variations in a fiber's refractive index profile leading to random changes in a pulse's polarization properties and pulse broadening. Large distortions due to PMD are very rare, but such events are precisely the ones which are most likely to cause transmission errors. We will demonstrate the application of importance sampling, which is one member of the general category of variance reduction techniques, to the numerical simulation of PMD in optical transmission systems. We will show that importance sampling can be used to speed up such Monte-Carlo simulations by several orders of magnitude, making it straightforward to observe events that would be impossible to obtain by brute-force simulation.
Second, a preliminary application of importance sampling to the amplitude and timing jitter of soliton-based transmission systems will be discussed. We will show that large deviations in a soliton's amplitude and position can be obtained with the method.
This work was done in collaboration with Gino Biondini, Curtis R. Menyuk, and Richard O. Moore

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