A Signal-Space Distance Measure for Nondispersive Optical Fiber

• Published in: IEEE transactions on information theory Vol. 67; no. 9; pp. 5903 - 5921
• Main Authors: Borujeny, Reza Rafie, Kschischang, Frank R.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Channel models; Computer networks; constellation design; Constellations; Control theory; Fiber-optic communications; Mathematical analysis; Mathematical model; minimum distance; Noise; nonlinear control; Nonlinear differential equations; Optical fibers; Optical noise; Optical sensors; Optical variables measurement; Optimal control; Perturbation methods; Quadrature amplitude modulation; Smoothness; Trajectory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2021.3100931

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. This minimum noise energy is then taken as a measure of distance between the points in the input alphabet. 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. It is shown how to find the distance between two input points by solving this system of differential equations. 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 constellation is designed and compared with conventional quadrature amplitude modulation. A computationally efficient approximation for the proposed distance measure is provided. It is shown how to use this approximation to design large constellations with large minimum distances. Based on the control-theoretic viewpoint of this paper, a new decoding scheme for such nonlinear channels is proposed.