## Abstract

Construction C^{∗} was recently introduced as a generalization of the multilevel Construction C (or Forney's code-formula), such that the coded levels may be dependent. Both constructions do not produce a lattice in general, hence the central idea of this paper is to present a 3-level lattice Construction C^{∗} scheme that admits an efficient nearest-neighborhood decoding. In order to achieve this objective, we choose coupled codes for levels 1 and 3, and set the second level code C 2 as an independent linear binary self-dual code, which is known to have a rich mathematical structure among families of linear codes. Our main result states a necessary and sufficient condition for this construction to generate a lattice. We then present examples of efficient lattices and also non-lattice constellations with good packing properties.

Original language | English |
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Title of host publication | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 537-541 |

Number of pages | 5 |

ISBN (Electronic) | 9781728164328 |

DOIs | |

State | Published - Jun 2020 |

Event | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2020-June |

ISSN (Print) | 2157-8095 |

### Conference

Conference | 2020 IEEE International Symposium on Information Theory, ISIT 2020 |
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Country/Territory | United States |

City | Los Angeles |

Period | 21/07/20 → 26/07/20 |

## Keywords

- Construction C
- Construction C
- Multilevel construction
- self-dual codes
- sphere packing

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