Slepian-type codes on a flat torus

Author

Costa, Sueli I R ; Agustini, Edson ; Muniz, Marcelo ; Palazzo, Reginaldo, Jr.

Author_Institution

Inst. of Math., UNICAMP, Campinas, Brazil

fYear

2000

fDate

2000

Firstpage

58

Abstract

Quotients of R² by translation groups are metric spaces known as flat tori. We start from codes which are vertices of closed graphs on a flat torus and, through an identification of these with a 2-D surface in a 3-D sphere in R⁴, we show such graph signal sets generate [M,4] Slepian-type cyclic codes for M=a²+b²; a,b∈Z, gcd (a,b)=1. The cyclic labeling of these codes corresponds to walking step-by-step on a (a,b)-type knot on a flat torus and its performance is better when compared with either the standard M-PSK or any cartesian product of M ₁-PSK and M₂-PSK, M₁M₂=M

Keywords

cyclic codes; graph theory; group codes; identification; (a,b)-type knot; 2-D surface; 3-D sphere; R² quotients; Slepian-type codes; Slepian-type cyclic codes; closed graphs; cyclic labeling; flat torus; graph signal sets; identification; metric spaces; performance; translation groups; Code standards; Extraterrestrial measurements; Labeling; Lattices; Legged locomotion; Mathematics; Signal generators; Signal processing; Standards development; Visualization;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory, 2000. Proceedings. IEEE International Symposium on

Conference_Location

Sorrento

Print_ISBN

0-7803-5857-0

Type

conf

DOI

10.1109/ISIT.2000.866348

Filename

866348