Asymptotically Scale-invariant Multi-resolution Quantization

TL;DR

This paper introduces an asymptotically scale-invariant multi-resolution quantizer that maintains consistent performance across various quantization steps and approaches optimal rate-error tradeoffs, especially in large input ranges.

Contribution

It proposes a novel scale-invariant multi-resolution quantizer that performs uniformly regardless of quantization step size and achieves near-optimal rate-error tradeoffs.

Findings

Performs uniformly across any average quantization step size

Achieves a rate-error tradeoff close to the theoretical optimum

Effective in worst-case or adversarial input scenarios

Abstract

A multi-resolution quantizer is a sequence of quantizers where the output of a coarser quantizer can be deduced from the output of a finer quantizer. In this paper, we propose an asymptotically scale-invariant multi-resolution quantizer, which performs uniformly across any choice of average quantization step, when the length of the range of input numbers is large. Scale invariance is especially useful in worst case or adversarial settings, ensuring that the performance of the quantizer would not be affected greatly by small changes of storage or error requirements. We also show that the proposed quantizer achieves a tradeoff between rate and error that is arbitrarily close to the optimum.