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，误差分布近似为区间（即一维球体）上的均匀分布。然而，对于格矢量量化，误差分布并非均匀分布于球体，而是量化格的基本胞元上。本文构造了一种误差分布在n维球体或任意指定集合上呈均匀分布的矢量量化器，并进一步证明了量化信号熵的边界。