Ripple Distribution for Nonlinear Fibre-Optic Channels
  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 
Mariia Sorokina, Stylianos Sygletos, and Sergei Turitsyn
cs.IT math-ph math.IT math.MP