Blind-Adaptive Quantizers

TL;DR

This paper introduces a blind, adaptive quantization method that minimizes distribution mismatch errors without prior knowledge, using nonlinear transformations and modulo-folding to achieve near-uniform output distributions across various input types.

Contribution

The proposed approach eliminates the need for prior distribution knowledge in quantization, employing nonlinear transformations and unfolding techniques for improved accuracy.

Findings

Effective reduction of quantization error across multiple distributions

Near-uniform output distribution achieved with sufficient amplification

Trade-off between oversampling and mismatch reduction demonstrated

Abstract

Sampling and quantization are crucial in digital signal processing, but quantization introduces errors, particularly due to distribution mismatch between input signals and quantizers. Existing methods to reduce this error require precise knowledge of the input's distribution, which is often unavailable. To address this, we propose a blind and adaptive method that minimizes distribution mismatch without prior knowledge of the input distribution. Our approach uses a nonlinear transformation with amplification and modulo-folding, followed by a uniform quantizer. Theoretical analysis shows that sufficient amplification makes the output distribution of modulo-folding nearly uniform, reducing mismatch across various distributions, including Gaussian, exponential, and uniform. To recover the true quantized samples, we suggest using existing unfolding techniques, which, despite requiring significant oversampling, effectively reduce mismatch and quantization error, offering a favorable trade-off similar to predictive coding strategies.