Efficient Fiber-optic Data Transmission in the Nonlinear Regime**

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The vast majority of the world's Internet and long-distance telecommunications is carried over fiber-optic networks that criss-cross the continents and span between them via ultra-long undersea cables. Despite their obvious importance to just about every person and organization on the planet, it is a curious fact that the ultimate information-carrying capacity (in an information-theoretic sense) of optical fibers remains unknown. This means that we are not yet sure that we are squeezing as much capacity out of a fiber as we possibly can. This is a question of great practical importance as---due to the immense cost of laying fibers between cities and across oceans---it is much preferred to optimize the use of the existing fiber infrastructure.** The theoretical difficulty in establishing the capacity of optical fibers is that, at the very high optical intensities needed to send information over vast distances, the fiber-optic channel is a nonlinear medium. The so-called optical Kerr effect causes the index of refraction of the silica glass material of a fiber to change in response to the intensity of the light impinging upon it. Light-pulse propagation is governed by a notoriously intractable stochastic partial differential equation called the generalized nonlinear Schroedinger equation, that describes the physical effects and interactions among chromatic dispersion, nonlinearity, and amplifier noise. The resulting mathematical channel model goes far beyond the well-studied information theory textbook models.** The overall goal of this project is to study the fundamental limits and practical engineering potential of fiber-optic nonlinearity mitigation using techniques based on three approaches: the so-called nonlinear Fourier transform, spherical codes, and the Kolmogorov-Zhakarov weak wave turbulence model. If successful, this research may yield interesting new methods to coordinate information transmission over wide-band channels, particularly in the highly nonlinear transmission regime, with the potential to achieve greater data transmission rates than existing approaches.******