Rare Event Simulation for Lightwave Systems Using the Cross-Entropy Method

Graham Mauch Donovan

doi:https://doi.org/10.21985/N2C43F

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Rare Event Simulation for Lightwave Systems Using the Cross-Entropy Method

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Rare events are studied in an increasing number of areas, ranging from lightwave and optical communication systems, to industrial routing problems, to rogue ocean waves, to financial asset pricing, to the rare failure of something as common as Gaussian elimination, as well as numerous others. In optical communication systems, a per-bit error rate of one part in 10^10 quickly becomes relevant because of high data rates, currently 40 Gb/s or greater. Minimizing error rates at a reasonable cost and understanding sources of errors are important aspects of these practical engineering problems. In this thesis a new method is described which allows the use of multiple importance sampled Monte Carlo simulations for these systems. The key step is to provide a numerical algorithm for the determination of the biasing distributions, modified probability distributions under which rare events in the system are no longer rare. This new method makes use of a stochastic optimization scheme known as the cross-entropy (CE) method to solve an optimization problem for these distributions, and the singular value decomposition (SVD), linear operator decomposition, to efficiently compute the important directions in the system, the system modes. The details of the SVD-CE-IS method are presented in a more general context (it is not constrained to optical systems), and then it is applied to specific optical communication systems. A further application of this new SVD-CE-IS method is also demonstrated: it can be used as a performance probe, targeting the behavior of the simulated system in regions of specific interest. In these regions, system characteristics can be examined in greater detail to help explain the reasons for the type of performance being considered. For example, simulation trials which generate particular types of errors can be examined to determine the underlying root causes. This capability is another desirable feature of the new method.

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