Kurtosis-limited Sphere Shaping for Nonlinear Interference Noise Reduction in Optical Channels

TL;DR

This paper introduces kurtosis-limited sphere shaping (K-ESS), an algorithm that reduces nonlinear interference in optical channels by generating low-kurtosis input distributions, leading to improved SNR and lower error rates.

Contribution

The paper presents K-ESS, a novel algorithm for shaping optical signals with limited kurtosis, enhancing performance over traditional Gaussian-like distributions.

Findings

K-ESS increases effective SNR by 0.4 dB in single-span scenarios.

K-ESS reduces frame error rate by twofold compared to Gaussian-optimal shaping.

Numerical simulations validate the effectiveness of K-ESS at 400 Gbit/s.

Abstract

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.