Huffman-Coded Sphere Shaping for Extended Reach Single-Span Links

Pavel Skvortcov, Ian David Phillips, Wladek Forysiak, Toshiaki Koike-akino, Keisuke Kojima, Kieran Parsons, David Millar

Research output: Contribution to journalArticlepeer-review


Huffman-coded sphere shaping (HCSS) is an algorithm for finite-length probabilistic constellation shaping, which provides nearly optimal energy efficiency at low implementation complexity. In this paper, we experimentally study the nonlinear performance of HCSS employing dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) in an extended-reach single-span link comprising 200 km of standard single-mode fiber (SSMF). We investigate the effects of shaping sequence length, dimensionality of symbol mapping, and shaping rate. We determine that the naïve approach of Maxwell-Boltzmann distribution matching-which is optimal in the additive white Gaussian noise channel-provides a maximum achievable information rate (AIR) gain of 0.18 bits/4D-symbol with respect to uniform signaling at optimum launch power in the infinite length regime. Conversely, HCSS can achieve a gain of 0.37 bits/4D-symbol over uniform signaling using amplitude sequence length of 32, which may be implemented without multiplications, using integer comparison and addition operations only. Coded system performance, with a net data rate of approximately 425 Gb/s for both shaped and uniform inputs, is also analyzed.

Original languageEnglish
Article number9340268
JournalIEEE Journal of Selected Topics in Quantum Electronics
Issue number3
Early online date29 Jan 2021
Publication statusPublished - 1 May 2021

Bibliographical note

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Funding: The experimental work carried out at Aston University was
supported by UK EPSRC grant EP/M009092/1. We thank
Lumentum UK for loan of the CFP2-ACO and studentship
support of Pavel Skvortcov, and Socionext for loan of the
DAC/ADC DKs used in this work.


  • Adaptive optics
  • Lattices
  • Nonlinear optics
  • Optical fiber communication
  • Optical polarization
  • Optical pulse shaping
  • Optical transmitters
  • Probabilistic logic
  • nonlinear fiber channel
  • probabilistic shaping
  • single-span links
  • sphere shaping


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