TY - GEN
T1 - Constructions a of lattices from number fields and division algebras
AU - Vehkalahti, Roope
AU - Kositwattanarerk, Wittawat
AU - Oggier, Frédérique
PY - 2014
Y1 - 2014
N2 - There is a rich theory of relations between lattices and linear codes over finite fields. However, this theory has been developed mostly with lattice codes for the Gaussian channel in mind. In particular, different versions of what is called Construction A have connected the Hamming distance of the linear code to the Euclidean structure of the lattice. This paper concentrates on developing a similar theory, but for fading channel coding instead. First, two versions of Construction A from number fields are given. These are then extended to division algebra lattices. Instead of the Euclidean distance, the Hamming distance of the finite codes is connected to the product distance of the resulting lattices, that is the minimum product distance and the minimum determinant respectively.
AB - There is a rich theory of relations between lattices and linear codes over finite fields. However, this theory has been developed mostly with lattice codes for the Gaussian channel in mind. In particular, different versions of what is called Construction A have connected the Hamming distance of the linear code to the Euclidean structure of the lattice. This paper concentrates on developing a similar theory, but for fading channel coding instead. First, two versions of Construction A from number fields are given. These are then extended to division algebra lattices. Instead of the Euclidean distance, the Hamming distance of the finite codes is connected to the product distance of the resulting lattices, that is the minimum product distance and the minimum determinant respectively.
UR - https://www.scopus.com/pages/publications/84906536017
U2 - 10.1109/ISIT.2014.6875249
DO - 10.1109/ISIT.2014.6875249
M3 - Conference contribution
AN - SCOPUS:84906536017
SN - 9781479951864
SN - 9781479951864
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2326
EP - 2330
BT - 2014 IEEE International Symposium on Information Theory, ISIT 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 IEEE International Symposium on Information Theory, ISIT 2014
Y2 - 29 June 2014 through 4 July 2014
ER -