Design and Analysis of Hardware-limited Non-uniform Task-based Quantizers

TL;DR

This paper introduces a new framework for designing hardware-limited task-based quantizers using generalized Bussgang decomposition, enabling effective handling of non-uniform quantizers and unbounded inputs for linear and quadratic tasks.

Contribution

It develops a generalized analysis and design framework for task-based quantizers that overcomes limitations of previous models, applicable to non-uniform quantizers and unbounded inputs.

Findings

Derived MSE-optimized linear mappings for linear tasks

Extended framework to quadratic tasks with accurate MSE predictions

Validated analytical expressions match empirical performance

Abstract

Hardware-limited task-based quantization is a new design paradigm for data acquisition systems equipped with serial scalar analog-to-digital converters using a small number of bits. By taking into account the underlying system task, task-based quantizers can efficiently recover the desired parameters from the low-bit quantized observation. Current design and analysis frameworks for hardware-limited task-based quantization are only applicable to inputs with bounded support and uniform quantizers with non-subtractive dithering. Here, we propose a new framework based on generalized Bussgang decomposition that enables the design and analysis of hardware-limited task-based quantizers that are equipped with non-uniform scalar quantizers or that have inputs with unbounded support. We first consider the scenario in which the task is linear. Under this scenario, we derive new pre-quantization and post-quantization linear mappings for task-based quantizers with mean squared error (MSE) that closely matches the theoretical MSE. Next, we extend the proposed analysis framework to quadratic tasks. We demonstrate that our derived analytical expression for the MSE accurately predicts the performance of task-based quantizers with quadratic tasks.