Hardware-Limited Task-Based Quantization

Quantization plays a critical role in digital signal processing systems. Quantizers are typically designed to obtain an accurate digital representation of the input signal, operating independently of the system task, and are commonly implemented using scalar analog-to-digital converters (ADCs). In this work, we study hardware-limited task-based quantization, where a system utilizing a serial scalar ADC is designed to provide a suitable representation in order recover a parameter vector underlying the input signal. We propose hardware-limited task-based quantization systems for a fixed and finite quantization resolution, and characterize their achievable distortion. Our results illustrate that properly designed hardware-limited systems can approach the optimal performance achievable with vector quantizers, and that by taking the underlying task into account, the quantization error can be made negligible with a relatively small number of bits.

I. Introduction

Quantization refers to the representation of a continuous-amplitude signal using a finite dictionary, or equivalently, a finite number of bits [1]. Quantizers are implemented in digital signal processing systems using analog-to-digital convertors (ADCs), which typically operate in a serial scalar manner due to hardware-limitations. In such systems, each incoming continuous-amplitude sample is represented in digital form using the same mechanism [2]. The quantized representation is commonly selected to accurately match the original signal, such that the signal can be recovered with minimal error from the quantized measurements [3, Ch. 10], [4].