Under which condition is quantization optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and power constraints. We compute analytically the capacity-achieving input distribution as a function of the noise level, the average power constraint and the exponent of the power constraint. We found that when the cost constraint is tight and the cost function is concave, the capacity-achieving input distribution is discrete, whereas when the cost function is convex, the support of the capacity-achieving input distribution spans the entire interval.

翻译：量化在何种条件下是最优的？我们在峰值幅度与功率约束下的加性均匀噪声信道背景下探讨这一问题。我们解析地计算了容量可达输入分布作为噪声水平、平均功率约束及功率约束指数的函数。研究发现，当成本约束严格且成本函数为凹函数时，容量可达输入分布是离散的；而当成本函数为凸函数时，容量可达输入分布的支撑集覆盖整个区间。