The Asymptotic Capacity of the Optical Fiber

It is shown that signal energy is the only available degree-of-freedom (DOF) for fiber-optic transmission as the input power tends to infinity. With n signal DOFs at the input, n ́ 1 DOFs are asymptotically lost to signal-noise interactions. The main observation is that, nonlinearity introduces a multiplicative noise in the channel, similar to fading in wireless channels. The channel is viewed in the spherical coordinate system, where signal vector ̄ X P C is represented in terms of its norm | ̄ X| and direction ˆ ̄ X . The multiplicative noise causes signal direction ˆ ̄ X to vary randomly on the surface of the unit p2n ́ 1q-sphere in C, in such a way that the effective area of the support of ˆ ̄ X does not vanish as | ̄ X| Ñ 8. On the other hand, the surface area of the sphere is finite, so that ˆ ̄ X carries finite information. This observation is used to show several results. Firstly, let CpPq be the capacity of a discrete-time periodic model of the optical fiber with distributed noise and frequency-dependent loss, as a function of the average input power P . It is shown that asymptotically as P Ñ 8, C “ 1 n log `