Slepian-type Codes On A Flat Torus

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-dimensional surface in a 3-dimensional 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 M1-PSK and M2-PSK, M1M2 = M.58Agustini, E., et, alli., Codes in regular graphs on a flat torus Proceedings of ISIT-2000Costa, S.I.R., et, alli., The symmetry group of Zq n in the lee space and the Zqn-linearity (1997) Lecture Notes in Computer Science, (1255), pp. 66-77. , Springer Verlag. New YorkForney, D., Geometrically uniform codes (1991) IEEE Transactions on Information Theory, 37 (5), pp. 1241-126