On shaping gain in the nonlinear fiber-optic channel

Fiber´s nonlinearity fundamentally bounds the achievable information rates in fiber-optic communication systems. In a wavelength-division multiplexed system it induces a nonlinear interference between adjacent channels, an interference that was recently shown to have a strong dependance on the input distribution. In this work we show that a ball shaped input constellation may significantly reduce the nonlinear effects. We study the shaping gains in the fiber-optic channel and show that in certain scenarios the maximum gains may be higher than the 1.53dB ultimate shaping gain in linear additive white Gaussian noise channels. Furthermore, the maximum gain is achieved with a finite-dimensional ball shaping region.