Curves on torus layers and coding for continuous alphabet sources

In this paper we consider the problem of transmitting a continuous alphabet discrete-time source over an AWGN channel. The design of good curves for this purpose relies on geometrical properties of spherical codes and projections of $N$-dimensional lattices. We propose a constructive scheme based on a set of curves on the surface of a 2N-dimensional sphere and present comparisons with some previous works.Comment: 5 pages, 4 figures. Accepted for presentation at 2012 IEEE International Symposium on Information Theory (ISIT). 2th version: typos corrected. 3rd version: some typos corrected, a footnote added in Section III B, a comment added in the beggining of Section V and Theorem I adde