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.

翻译：本文证明，当极化格点专为有损压缩设计时，其具有量化优良性，即随着格点维度增加，归一化二阶矩趋近于$\frac{1}{2\pi e}$。Zamir等人\cite{ZamirQZ96}曾预测，采用量化优良格点的熵编码抖动量化（ECDQ）系统能够达到独立同分布高斯信源的率失真界限。在前期工作\cite{LingQZ}中，我们已证明极化格点确实能够实现该目标。合理推测极化格点在有损压缩场景下同样展现量化优良性，本研究证实了这一假设。