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, ..., 47, 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化向量量化器，在5、6、……、48维情况下，相比具有相同熵的所有已知格点量化器具有更小的最大误差；在35、……、47维情况下，在高分辨率极限下相比具有相同熵的已知格点量化器具有更小的均方误差。此外，我们的随机量化器具备一个理想特性：量化误差在球面上始终保持均匀分布，且与输入无关。我们的构造基于在通用量化中应用拒绝采样，这使得我们能够将误差分布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单元上的均匀分布。我们还刻画了在温和假设条件下（例如AWGN信道）任意加性噪声信道单次信道模拟的高信噪比极限，精度达到1.45比特的加性常数。