Collaborative Research: Mathematical and Computational Methods in High Data-Rate Optical Fiber Communications

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NSF Award Abstract - DMS-0101387 Mathematical Sciences: FRG: Mathematical and Computational Methods for High-Data-Rate Optical Fiber Communications AbstractDMS-0101387 Menyuk The goal of this research project is to develop new methods that can be used to determine the behavior of optical transmission systems under realistic circumstances. This will be accomplished by a combination of various techniques. One approach will exploit the mathematical structure of fiber transmission models in order to eliminate unessential degrees of freedom. The reduced models that will result will be more tractable mathematically and also much more computationally efficient. Another approach that will be used is the application of linearization and importance sampling techniques to enable the simulation of systems at realistic data error rates. These methods will be combined to study the main sources of impairment in optical fibers in order to achieve an accurate evaluation of system performance. All the techniques to be developed will be carefully validated by comparison to more computationally time-consuming models and to experiments. The development of high-data-rate optical fiber communications is one of the great technological achievements of the late 20th century; in the last decade alone, data rates have increased by four orders of magnitude. This enormous increase has made possible the growth of the global Internet that promises to continue to revolutionize day-to-day communications. Because demand for further growth continues unabated, however, system capacity is becoming limited by fiber transmission effects. It has therefore become crucial to accurately model and calculate the impairments due to non-ideal fiber properties when designing systems. Due to the tremendous data capacity that will be required of future transmission systems (terabits per second of aggregate capacity) and the need for extremely small transmission error rates (less than one error per trillion bits), realistic attempts to model and predict the effects of these impairments as they appear in practical systems present a number of difficult mathematical and computational challenges. The techniques that will be developed in this collaborative research project are expected to yield large reductions in the computational time required to model optical communication systems, and at the same time produce new insights into system behavior. Because these methods will be capable of providing detailed information about system performance at realistic data error rates, we believe they will lead to significant changes in the way in which optical transmission systems are modeled, and, ultimately, in the way that they are built.