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

Yunus Can Gültekin (Corresponding author), Alex Alvarado, Olga Vassilieva, Inwoong Kim, Paparao Palacharla, Chigo M. Okonkwo, Frans M.J. Willems

Research output: Contribution to journalArticleAcademicpeer-review

17 Citations (Scopus)
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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.

Original languageEnglish
Article number9580735
Pages (from-to)101-112
Number of pages12
JournalJournal of Lightwave Technology
Issue number1
Early online date19 Oct 2021
Publication statusPublished - 1 Jan 2022


  • AWGN channels
  • Adaptive optics
  • Forward error correction
  • Interference
  • Nonlinear optics
  • Optical fiber communication
  • Probabilistic shaping
  • Wavelength division multiplexing
  • amplitude shaping
  • kurtosis
  • nonlinear interference


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