  Nonlinear interference (NLI) generated during the propagation of an optical
waveform through the fiber depends on the fourth order standardized moment of
the channel input distribution, also known as kurtosis.
Probabilistically-shaped inputs optimized for the linear Gaussian channel have
a Gaussian-like distribution with high kurtosis. For optical channels, this
leads to an increase in NLI power and consequently, a decrease in effective
signal-to-noise ratio (SNR). In this work, we propose kurtosis-limited
enumerative sphere shaping (K-ESS) as an algorithm to generate low-kurtosis
shaped inputs. Numerical simulations at a shaping blocklength of 108 amplitudes
demonstrate that with K-ESS, it is possible to increase the effective SNRs by
0.4 dB in a single-span single-channel scenario at 400 Gbit/s. K-ESS offers
also a twofold decrease in frame error rate with respect to
Gaussian-channel-optimal sphere shaping.
