We extend the Shannon information theory to a nonlinear system and present a model for calculating the channel capacity of an optical-fiber transmission system using dispersion-free fiber. For this particular fiber,a closed-form solution for the nonlinear Schroedinger equation exists. This allows us to derive an analytical result for the channel capacity that is exact and valid for arbitrary input power. We will study the single-span case and examine the dependence of the capacity on operating input power, the number of channels (Nc), the noise power (PW), etc. The maximum capacity is shown to follow a simple scaling law with log2(1+CNc-2/3PW-2/3) dependence.
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