Curves on torus layers and coding for continuous alphabet sources

TL;DR

This paper introduces a geometric scheme for transmitting continuous alphabet sources over AWGN channels using curves on high-dimensional spheres, leveraging lattice projections and spherical codes.

Contribution

It presents a novel constructive method for designing curves on 2N-dimensional spheres for improved source transmission over AWGN channels.

Findings

Enhanced transmission schemes based on spherical curves

Comparative analysis showing improvements over previous methods

Geometric properties of lattice projections applied to coding

Abstract

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.