A Signal-Space Distance Measure for Nondispersive Optical Fiber
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The nondispersive per-sample channel model for the optical fiber channel is considered. Under certain smoothness assumptions, the problem of finding the minimum amount of noise energy that can render two different input points indistinguishable is formulated. Using the machinery of optimal control theory, necessary conditions that describe the minimum-energy noise trajectories are stated as a system of nonlinear differential equations. This minimum energy is taken as a distance measure. The problem of designing signal constellations with the largest minimum distance subject to a peak power constraint is formulated as a clique finding problem. As an example, a 16-point constellations is designed and compared with the conventional quadrature amplitude modulation. Based on the control-theoretic viewpoint of this paper, a new decoding scheme for such nonlinear channels is proposed.
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