Novel Near-Optimal Scalar Quantizers with Exponential Decay Rate and Global Convergence

TL;DR

This paper introduces a nearly-optimal approximate Lloyd-Max quantizer that converges exponentially fast and adapts to envelope constraints, improving efficiency in distributed sensor systems.

Contribution

The paper proposes a novel approximate Lloyd-Max quantizer with exponential convergence and adapts it for envelope constraints, enhancing quantization efficiency.

Findings

Converges to classical Lloyd-Max quantizer with increasing bitrate

Exponential convergence rate with the number of iterations

Effective for various finite support source distributions

Abstract

Many modern distributed real-time signal sensing/monitoring systems require quantization for efficient signal representation. These distributed sensors often have inherent computational and energy limitations. Motivated by this concern, we propose a novel quantization scheme called approximate Lloyd-Max that is nearly-optimal. Assuming a continuous and finite support probability distribution of the source, we show that our quantizer converges to the classical Lloyd-Max quantizer with increasing bitrate. We also show that our approximate Lloyd-Max quantizer converges exponentially fast with the number of iterations. The proposed quantizer is modified to account for a relatively new quantization model which has envelope constraints, termed as the envelope quantizer. With suitable modifications we show optimality and convergence properties for the equivalent approximate envelope quantizer. We illustrate our results using extensive simulations for different finite support source distributions.