  Since Shannon proved that Gaussian distribution is the optimum for a linear
channel with additive white Gaussian noise and he calculated the corresponding
channel capacity, it remains the most applied distribution in optical
communications while the capacity result is celebrated as the seminal linear
Shannon limit. Yet, when it is applied in nonlinear channels (e.g.
fiber-optics) it has been shown to be non-optimum, yielding the same result as
for uncoded transmission in the high nonlinear regime. This has led to the
notion of nonlinear Shannon limit, which predicts vanishing capacity at high
nonlinearity. However, recent findings indicate that non-Gaussian distribution
may lead to improved capacity estimations, urging for an exciting search for
novel methods in nonlinear optical communications. Here for the first time, we
show that it is possible to transmit information above the existing limits by
using a novel probabilistic shaping of the input signal, which we call ripple
distribution
