Slepian-type codes on a flat torus

Quotients of R/sup 2/ 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 R/sup 4/, we show such graph signal sets generate [M,4] Slepian-type cyclic codes for M=a/sup 2/+b/sup 2/; a,b/spl isin/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/sub 1/-PSK and M/sub 2/-PSK, M/sub 1/M/sub 2/=M.