Curves on Flat Tori and Analog Source-Channel Codes

TL;DR

This paper introduces a geometric coding scheme for transmitting continuous sources over AWGN channels using curves on flat tori, linking code design to spherical and lattice geometries, with theoretical and simulation results.

Contribution

It presents a novel constructive coding scheme based on curves on spheres, connecting geometric properties of spherical codes and lattice projections to source-channel coding.

Findings

The proposed scheme achieves competitive mean square error performance.

Theoretical analysis compares favorably with previous methods.

Simulation results validate the effectiveness of the geometric approach.

Abstract

In this paper we consider the problem of transmitting a continuous alphabet discrete-time source over an AWGN channel. We propose a constructive scheme based on a set of curves on the surface of a N-dimensional sphere. Our approach shows that the design of good codes for this communication problem is related to geometrical properties of spherical codes and projections of N-dimensional rectangular lattices. Theoretical comparisons with some previous works in terms of the mean square error as a function of the channel SNR as well as simulations are provided.