Sample Abundance for Signal Processing: A Brief Introduction

TL;DR

This paper introduces the concept of sample abundance in low-precision signal processing, demonstrating how large volumes of one-bit and few-bit measurements simplify complex constraints into linear feasibility problems, with theoretical and algorithmic insights.

Contribution

It presents the novel concept of sample abundance, showing its impact on simplifying signal processing constraints and introducing the sample abundance singularity phenomenon.

Findings

Constraints become redundant with large low-precision samples

Algorithms and theoretical guarantees are provided

Computational complexity drops sharply at singularity

Abstract

This paper reports, by way of introduction, on the advances made by our group and the broader signal processing community on the concept of sample abundance; a phenomenon that naturally arises in one-bit and few-bit signal processing frameworks. By leveraging large volumes of low-precision measurements, we show how traditionally costly constraints, such as matrix semi-definiteness and rank conditions, become redundant, yielding simple overdetermined linear feasibility problems. We illustrate key algorithms, theoretical guarantees via the Finite Volume Property, and the sample abundance singularity phenomenon, where computational complexity sharply drops.