On Optimal Quantization in Sequential Detection

TL;DR

This paper investigates the design of optimal quantization rules for sequential detection, characterizing the optimal detector and quantizer, and proposing performance bounds to address computational challenges.

Contribution

It introduces a framework for optimal quantization in sequential detection, characterizes the optimal solutions, and proposes new bounds to simplify analysis.

Findings

Optimal quantization rules require solving nonconvex optimization problems.

Proposed bounds are easier to evaluate and potentially tighter than existing ones.

Numerical examples demonstrate the bounds and properties of optimal quantizers.

Abstract

The problem of designing optimal quantization rules for sequential detectors is investigated. First, it is shown that this task can be solved within the general framework of active sequential detection. Using this approach, the optimal sequential detector and the corresponding quantizer are characterized and their properties are briefly discussed. In particular, it is shown that designing optimal quantization rules requires solving a nonconvex optimization problem, which can lead to issues in terms of computational complexity and numerical stability. Motivated by these difficulties, two performance bounds are proposed that are easier to evaluate than the true performance measures and are potentially tighter than the bounds currently available in the literature. The usefulness of the bounds and the properties of the optimal quantization rules are illustrated with two numerical examples.