For uniform scalar quantization, the error distribution is approximately a uniform distribution over an interval (which is also a 1-dimensional ball). Nevertheless, for lattice vector quantization, the error distribution is uniform not over a ball, but over the basic cell of the quantization lattice. In this paper, we construct vector quantizers where the error is uniform over the n-ball, or any other prescribed set. We then prove bounds on the entropy of the quantized signals.

翻译：对于均匀标量量化，误差分布近似于某个区间（也是一维球）上的均匀分布。然而，对于格点向量量化，误差分布并非均匀于球上，而是均匀于量化格点的基本胞元上。本文构建了误差在n维球或任意指定集合上均匀分布的向量量化器，并进一步证明了量化信号熵的界限。