We construct a randomized vector quantizer which has a smaller maximum error compared to all known lattice quantizers with the same entropy for dimensions 5, 6, ..., 48, and also has a smaller mean squared error compared to known lattice quantizers with the same entropy for dimensions 35, ..., 48, in the high resolution limit. Moreover, our randomized quantizer has a desirable property that the quantization error is always uniform over the ball and independent of the input. Our construction is based on applying rejection sampling on universal quantization, which allows us to shape the error distribution to be any continuous distribution, not only uniform distributions over basic cells of a lattice as in conventional dithered quantization. We also characterize the high SNR limit of one-shot channel simulation for any additive noise channel under a mild assumption (e.g., the AWGN channel), up to an additive constant of 1.45 bits.

翻译：我们构建了一种随机向量量化器，在维度5至48的高分辨率极限下，其最大误差小于所有已知具有相同熵的格点量化器；且在维度35至48的高斯极限下，其均方误差也小于已知具有相同熵的格点量化器。此外，该随机量化器具有一个理想特性：量化误差始终在球面上均匀分布且与输入无关。我们的构建基于对通用量化应用拒绝采样，这使得误差分布可塑造成任意连续分布，而不仅限于传统抖动量化中格点基本胞腔上的均匀分布。我们还表征了在温和假设（如AWGN信道）下，任意加性噪声信道单次信道模拟的高信噪比极限，其附加常数不超过1.45比特。