A Simple Extension of the $\modulo$-$\Lambda$ Transformation

TL;DR

This paper introduces a simple transformation that converts complex scalar and multi-access channels into modulo-additive noise channels, enabling the application of linear coding techniques to more general network models.

Contribution

It presents a new, straightforward lemma that extends the utility of modulo-additive models to a broader class of channels, despite some information loss.

Findings

Transformation enables use of linear coding in non-Gaussian channels

Allows capacity analysis of complex channels via simpler models

Facilitates extension of Gaussian network results to general channels

Abstract

A simple lemma is derived that allows to transform a general scalar (non-Gaussian, non-additive) continuous-alphabet channel as well as a general multiple-access channel into a modulo-additive noise channel. While in general the transformation is information lossy, it allows to leverage linear coding techniques and capacity results derived for networks comprised of additive Gaussian nodes to more general networks.