Lattice index coding from Construction πA lattices

Autores/as

  • Juliana G. F. Souza IMECC - UNICAMP
  • Sueli I. R. Costa IMECC - UNICAMP

DOI:

https://doi.org/10.5540/03.2025.011.01.0420

Palabras clave:

Lattices, Lattice codes, Chinese remainder theorem, Index coding

Resumen

This paper investigates Construction πA lattices over Z applied to index coding which is used for efficiency in transmissions when the receiver may have side information. Key parameters as code size and side information gain are analyzed.

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Biografía del autor/a

Juliana G. F. Souza, IMECC - UNICAMP

Pesquisadora em codificação de índices de rede e construção de redes.

Sueli I. R. Costa, IMECC - UNICAMP

Especialista em redes e comunicações seguras.

Citas

N. J. Conway J. H.; Sloane. Sphere packings, lattices and groups. Vol. 290. Springer Science & Business Media, 2013. doi: 10.1007/978-1-4757-6568-7.

S. I. R. Costa, F. Oggier, A. Campello, J. C. Belfiore, and E. Viterbo. Lattices applied to coding for reliable and secure communications. Springer, 2017. doi: 10.1007/978-3-319-67882-5.

Y. C. Huang. “Lattice index codes from algebraic number fields”. In: IEEE Transactions on Information Theory 63.4 (2017), pp. 2098–2112. doi: 10.1109/ISIT.2015.7282903.

Y. C. Huang, Y. Hong, E. Viterbo, and L. Natarajan. “Layered Space-Time Index Coding”. In: IEEE Transactions on Information Theory 65.1 (2019), pp. 142–158. doi: 10.1109/TIT.2018.2842144.

Y. C. Huang and K. R. Narayanan. “Construction πA and πD Lattices: Construction, Goodness, and Decoding Algorithms”. In: IEEE Transactions on Information Theory 63.9 (2017), pp. 5718–5733. doi: 10.1109/TIT.2017.2721421.

L. Natarajan, Y. Hong, and E. Viterbo. “Lattice Index Coding”. In: IEEE Transactions on Information Theory 61.12 (2015), pp. 6505–6525. doi: 10.1109/TIT.2015.2491924.

K. H. Rosen. Elementary number theory and its applications. Addison-Weley Publishing Company, 2005. isbn: 0-321-26314-6.

J. G. F. Souza, S. I. R. Costa, and C. Ling. “Multilevel lattice codes from Hurwitz quaternion integers”. In: arXiv e-prints, arXiv:2401.10773 (Jan. 2024), arXiv:2401.10773. doi: 10.48550/arXiv.2401.10773. arXiv: 2401.10773 [cs.IT].

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Publicado

2025-01-20

Número

Sección

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