The goal of the work outlined in this proposal is to develop Monte Carlo-based statistical techniques to calculate the likelihood of rare events such as dropped bits in optical communications systems. These techniques will be applicable to problems that are so complex (through nonlinear and nonautonomous terms, for example) as to be analytically intractable, for calculating the probability of events that are so rare as to be impossible to quantify using standard computational methods. The techniques will rely on using perturbation methods and variational principles, in conjunction with optimization methods, to reduce the dimension of the underlying partial differential equations in order to determine appropriate sampling heuristics.
The immediate application of this work will be to determine the impact of modulation formats on the robustness of a fiber-optic communications line when exposed to random impairments such as amplifier noise. More broadly, the strict tolerances in optical communications (a single dropped bit for each gigabit or terabit transmitted) provide for a large host of problems in the industry to which these techniques will be well suited. Finally, there are many situations that arise in industry and nature where one would like to determine the probability of a rare event in the context of a stochastic nonlinear wave setting; this work will provide techniques to accomplish this. This GOALI project was jointly funded by the Division of Mathematical Sciences (DMS) and the MPS Office of Multidisciplinary Activities (OMA).
