Signal Source Distribution Approximation to Speedup Scalar Quantizer Design

Classical quantizer design approaches using the Lloyd-Max algorithm (or
$k$
-means) have served signal processing applications for more than three decades. With the advent of distributed signal processing and machine learning at edge devices, novel alternatives for quantizers design will be desired to address the energy, communication and hardware constraints. To address these resource challenges, we propose a model-driven approach, termed Approximate Lloyd-Max (ALM) design, based on piecewise linear approximation of the signal-source probability density. From the principles of the ALM design, we develop a data-driven quantizer, or Learning ALM (LALM), using statistical learning methods. By mathematical analysis, we show convergence of the ALM quantizer near the limit of the Lloyd-Max quantizer. Both ALM and LALM quantizers satisfy asymptotic optimality and exponential convergence rate. Simulation performed over smooth signal source distributions validate our mathematical analysis. Experiments for LALM quantizer are implemented on an Android-based edge device, and the proposed quantizer demonstrate improved performance over
$k$
-means, in terms of algorithm speedup, energy usage and memory utilization.