拒绝采样通用量化以减小量化误差
Rejection-Sampled Universal Quantization for Smaller Quantization Errors
AI总结：
本文提出基于拒绝采样的通用量化器，在高分辨率下对多个维度减小最大误差和均方误差，并实现误差均匀分布，同时刻画了加性噪声信道单次模拟的高信噪比极限。
摘要：
我们构造了一种随机向量量化器，在高分辨率极限下，对于维度5, 6, ..., 48，其最大误差小于所有已知的具有相同熵的格点量化器；对于维度35, ..., 47，其均方误差也小于已知的具有相同熵的格点量化器。此外，我们的随机量化器具有一个理想特性：量化误差始终在球上均匀分布且与输入无关。我们的构造基于对通用量化应用拒绝采样，这使得我们能够将误差分布塑造成任何连续分布，而不仅仅是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（例如AWGN信道）下，任何加性噪声信道的单次信道模拟的高信噪比极限，精确到1.45比特的加性常数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
