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.

中文翻译：

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加速标量量化器设计的信号源分布近似


使用 Lloyd-Max 算法（或 k 均值）的经典量化器设计方法已服务于信号处理应用三十多年。随着边缘设备分布式信号处理和机器学习的出现，人们需要新的量化器设计替代方案来解决能源、通信和硬件限制。为了解决这些资源挑战，我们提出了一种模型驱动的方法，称为近似 Lloyd-Max (ALM) 设计，基于信号源概率密度的分段线性近似。根据 ALM 设计的原理，我们使用统计学习方法开发了数据驱动的量化器，或学习 ALM (LALM)。通过数学分析，我们证明了 ALM 量化器的收敛性接近 Lloyd-Max 量化器的极限。 ALM 和 LALM 量化器都满足渐近最优性和指数收敛速度。对平滑信号源分布进行的仿真验证了我们的数学分析。 LALM 量化器的实验是在基于 Android 的边缘设备上实现的，所提出的量化器在算法加速、能源使用和内存利用率方面表现出优于 k 均值的性能。