Perfect graph codes over two dimensional lattices

Author

Martínez, C. ; Camarero, C. ; Beivide, R.

Author_Institution

Dept. of Electron. & Comput., Univ. of Cantabria, Cantabria, Spain

fYear

2010

fDate

13-18 June 2010

Firstpage

1047

Lastpage

1051

Abstract

In this paper we consider perfect codes over two dimensional QAM-type constellations of any cardinal. Such constellations are going to be modeled by L-graphs, which are the two-dimensional family of multidimensional circulants, defined. We show that Gaussian graphs, Lee graphs and the Kronecker product of two cycles are included in this family. Therefore, our method to obtain perfect codes over these lattice subsets is a generalization of the techniques for searching perfect two-dimensional Lee codes and perfect codes over the Kronecker products of two cycles. In addition, we introduce some previously unreported perfect codes.

Keywords

Gaussian processes; error correction codes; graph theory; quadrature amplitude modulation; Gaussian graphs; Kronecker product; L-graphs; Lee graphs; QAM-type constellations; error correcting codes; multidimensional circulants; perfect codes; perfect two dimensional Lee codes; Constellation diagram; Error correction codes; Extraterrestrial measurements; Lattices; Multidimensional systems; Signal design;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on

Conference_Location

Austin, TX

Print_ISBN

978-1-4244-7890-3

Electronic_ISBN

978-1-4244-7891-0

Type

conf

DOI

10.1109/ISIT.2010.5513724

Filename

5513724