Applications of Lindeberg Principle in Communications and Statistical Learning

TL;DR

This paper applies a generalized Lindeberg principle to establish universality in communication, statistical learning, and random matrix theory, showing that complex systems can be approximated by simpler sparse models.

Contribution

It introduces a generalized Lindeberg approach to prove universality and links dense systems to sparse systems for easier analysis in various information theory problems.

Findings

Universality properties are proven for multiple systems using the generalized Lindeberg principle.

Dense systems can be approximated by sparse systems, simplifying analysis.

The approach has potential applications across many problems in information theory.

Abstract

We use a generalization of the Lindeberg principle developed by Sourav Chatterjee to prove universality properties for various problems in communications, statistical learning and random matrix theory. We also show that these systems can be viewed as the limiting case of a properly defined sparse system. The latter result is useful when the sparse systems are easier to analyze than their dense counterparts. The list of problems we consider is by no means exhaustive. We believe that the ideas can be used in many other problems relevant for information theory.