Rotated $D_n$-lattices in dimensions power of 3

Agnaldo J. Ferrari; Grasiele C. Jorge; Antonio A. De Andrade

Rotated $D_n$-lattices in dimensions power of 3

Öz

In this work, we present constructions of families of rotated $D_n$-lattices which may be good for signal transmission over both Gaussian and Rayleigh fading channels. The lattices are obtained as sublattices of a family of rotated $\mathbb{Z} \oplus \mathcal{A}_{2}^{k}$ lattices, where $\mathcal{A}_{2}^{k}$ is a direct sum of $k=\frac{3^{r-1}-1}{2}$ copies of the $A_2$-lattice, using free $\mathbb{Z}$-modules in $\mathbb{Z}[\zeta_{3^{r}}+\zeta_{3^{r}}^{-1}]$.

Anahtar Kelimeler

Kaynakça

[1] A. A. Andrade, C. Alves, T. B. Carlos, Rotated lattices via th cyclotomic field Q(2r ), International Journal of Applied Mathematics 19(3) (2006) 321-331.
[2] E. Bayer-Fluckiger, Lattices and number fields, Contemporary Mathematics 241 (1999) 69-84.
[3] E. Bayer-Fluckiger, Upper bounds for Euclidean minima of algebraic number fields, Journal of Number Theory 121(2) (2006) 305-323.
[4] E. Bayer-Fluckiger, G. Nebe, On the Euclidean minimum of some real number fields, Journal de ThÃlorie des Nombres de Bordeaux 17(2) (2005) 437-454.
[5] E. Bayer-Fluckiger, F. Oggier, E. Viterbo, New algebraic constructions of rotated Zn-lattice constellations for the Rayleigh fading channel, IEEE Transactions on Information Theory 50(4) (2004) 702-714.
[6] E. Bayer-Fluckiger, I. Suarez, Ideal lattices over totally real number fields and Euclidean minima, Archiv der Mathematik 86(3) (2006) 217-225.
[7] J. Boutros, E. Viterbo, C. Rastello, J. C. Belfiori, Good lattice constellations for both Rayleigh fading and Gaussian channels, IEEE Trans. Inform. Theory 42(2) (1996) 502-517.
[8] J. H. Conway, N. J. A. Sloane, Sphere packings, lattices and groups, Springer-Verlag (1988).

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Araştırma Makalesi

Yazarlar

Agnaldo J. Ferrari ^* Bu kişi benim
0000-0002-1422-1416
Brazil

Grasiele C. Jorge Bu kişi benim
0000-0002-1474-6001
Brazil

Antonio A. De Andrade Bu kişi benim
Brazil

Yayımlanma Tarihi

15 Eylül 2021

Gönderilme Tarihi

15 Mayıs 2020

Kabul Tarihi

15 Mayıs 2021

Yayımlandığı Sayı

Yıl 2021 Cilt: 8 Sayı: 3

IZ

https://izlik.org/JA62UN88ZS

Kaynak Göster

RIS / Bibtex

APA

Ferrari, A. J., Jorge, G. C., & De Andrade, A. A. (2021). Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications, 8(3), 151-160. https://izlik.org/JA62UN88ZS

AMA

1.Ferrari AJ, Jorge GC, De Andrade AA. Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8(3):151-160. https://izlik.org/JA62UN88ZS

Chicago

Ferrari, Agnaldo J., Grasiele C. Jorge, ve Antonio A. De Andrade. 2021. “Rotated $D_n$-lattices in dimensions power of 3”. Journal of Algebra Combinatorics Discrete Structures and Applications 8 (3): 151-60. https://izlik.org/JA62UN88ZS.

EndNote

Ferrari AJ, Jorge GC, De Andrade AA (01 Eylül 2021) Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications 8 3 151–160.

IEEE

[1]A. J. Ferrari, G. C. Jorge, ve A. A. De Andrade, “Rotated $D_n$-lattices in dimensions power of 3”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 8, sy 3, ss. 151–160, Eyl. 2021, [çevrimiçi]. Erişim adresi: https://izlik.org/JA62UN88ZS

ISNAD

Ferrari, Agnaldo J. - Jorge, Grasiele C. - De Andrade, Antonio A. “Rotated $D_n$-lattices in dimensions power of 3”. Journal of Algebra Combinatorics Discrete Structures and Applications 8/3 (01 Eylül 2021): 151-160. https://izlik.org/JA62UN88ZS.

JAMA

1.Ferrari AJ, Jorge GC, De Andrade AA. Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8:151–160.

MLA

Ferrari, Agnaldo J., vd. “Rotated $D_n$-lattices in dimensions power of 3”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 8, sy 3, Eylül 2021, ss. 151-60, https://izlik.org/JA62UN88ZS.

Vancouver

1.Agnaldo J. Ferrari, Grasiele C. Jorge, Antonio A. De Andrade. Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications [Internet]. 01 Eylül 2021;8(3):151-60. Erişim adresi: https://izlik.org/JA62UN88ZS