Title :
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
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;
Conference_Titel :
Information Theory, 2000. Proceedings. IEEE International Symposium on
Conference_Location :
Sorrento
Print_ISBN :
0-7803-5857-0
DOI :
10.1109/ISIT.2000.866348
