# Comparison-limited Vector Quantization

## TL;DR

This paper introduces a new vector quantization architecture constrained by the number of comparators, not output cardinality, and proposes an algorithm to optimize its configuration for minimal distortion.

## Contribution

It presents the first algorithm for optimal configuration of comparator-based vector quantizers and evaluates its performance for specific source distributions.

## Key findings

- Algorithm effectively minimizes distortion for given comparator constraints.
- Performance evaluated for uniform and Gaussian sources.
- New architecture suitable for low-cost, energy-efficient A2D conversion.

## Abstract

A variation of the classic vector quantization problem is considered, in which the analog-to-digital (A2D) conversion is not constrained by the cardinality of the output but rather by the number of comparators available for quantization. More specifically, we consider the scenario in which a vector quantizer of dimension d is comprised of k comparators, each receiving a linear combination of the inputs and producing zero/one when this signal is above/below a threshold. Given a distribution of the inputs and a distortion criterion, the value of the linear combinations and thresholds are to be configured so as to minimize the distortion between the quantizer input and its reconstruction. This vector quantizer architecture naturally arises in many A2D conversion scenarios in which the quantizer's cost and energy consumption are severely restricted. For this novel vector quantizer architecture, we propose an algorithm to determine the optimal configuration and provide the first performance evaluation for the case of uniform and Gaussian sources.