### Abstract

Gaussian channel inputs are required to achieve the capacity of additive white Gaussian noise (AWGN) channels. Equivalently, the n-dimensional constellation boundary must be an n-sphere. In this work, constellation shaping is discussed for short block lengths. Two different approaches are considered: Sphere shaping and constant composition distribution matching (CCDM). It is shown that both achieve the maximum rate and generate Maxwell-Boltzmann (MB) distributed inputs. However sphere shaping achieves this maximum faster than CCDM and performs more efficiently in the short block length regime. This is shown by computing the finite-length rate losses. Then the analysis is justified by numerical simulations employing low-density parity-check (LDPC) codes of the IEEE 802.11 standard.

Original language | English |
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Title of host publication | Proceedings of the 2018 Symposium on Information Theory and Signal Processing in the Benelux |

Editors | Luuk Spreeuwers, Jasper Goseling |

Place of Publication | Enschede |

Publisher | Twente University |

Pages | 86-96 |

ISBN (Electronic) | 978-90-365-4570-9 |

Publication status | Published - Jun 2018 |

Event | 2018 Symposium on Information Theory and Signal Processing in the Benelux (SITB 2018) - University of Twente, Enschede, Netherlands Duration: 31 May 2018 → 1 Jun 2018 https://www.utwente.nl/en/eemcs/sitb2018/ |

### Conference

Conference | 2018 Symposium on Information Theory and Signal Processing in the Benelux (SITB 2018) |
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Abbreviated title | SITB 2018 |

Country | Netherlands |

City | Enschede |

Period | 31/05/18 → 1/06/18 |

Internet address |

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## Prizes

## The Best Young PhD Researcher Paper Award

Gültekin, Yunus Can (Recipient), 2018

Prize: Other › Career, activity or publication related prizes (lifetime, best paper, poster etc.) › Scientific

## Cite this

Gultekin, Y. C., van Houtum, W. J., & Willems, F. M. J. (2018). On constellation shaping for short block lengths. In L. Spreeuwers, & J. Goseling (Eds.),

*Proceedings of the 2018 Symposium on Information Theory and Signal Processing in the Benelux*(pp. 86-96). Twente University.