On the quantization goodness of polar lattices

TL;DR

This paper proves that polar lattices are quantization-good for lossy compression, with their normalized second moments approaching the optimal value as dimension increases, confirming their effectiveness in achieving rate-distortion bounds.

Contribution

The paper establishes that polar lattices are quantization-good in lossy compression, providing a rigorous proof of their asymptotic optimality in this context.

Findings

Polar lattices' normalized second moments approach 1/(2πe) as dimension increases.

Polar lattices can achieve the rate-distortion bound for Gaussian sources.

Theoretical confirmation of polar lattices' quantization goodness in lossy compression.

Abstract

In this work, we prove that polar lattices, when tailored for lossy compression, are quantization-good in the sense that their normalized second moments approach $\frac{1}{2\pi e}$ as the dimension of lattices increases. It has been predicted by Zamir et al. \cite{ZamirQZ96} that the Entropy Coded Dithered Quantization (ECDQ) system using quantization-good lattices can achieve the rate-distortion bound of i.i.d. Gaussian sources. In our previous work \cite{LingQZ}, we established that polar lattices are indeed capable of attaining the same objective. It is reasonable to conjecture that polar lattices also demonstrate quantization goodness in the context of lossy compression. This study confirms this hypothesis.