论文标题
通过二阶统计的熵率边界
Entropy Rate Bounds via Second-Order Statistics
论文作者
论文摘要
这项工作包含两个单字母的上限，这是离散值固定随机过程的熵速率上的，仅取决于二阶统计，主要适用于由相对较大的字母组成的模型。第一结合源于高斯的最大值考虑因素，并取决于该过程的功率光谱密度（PSD）功能。虽然不能总是以封闭形式计算PSD函数，但我们还提出了第二个界限，该界限仅依赖于该过程的自动协方差值的某些有限收集。两个边界都由一个维积分组成，而第二个界限也由在边界区域上的最小化问题组成，因此可以有效地通过数值计算它们。还提供了示例，以表明新边界的表现优于标准条件熵结合。
This work contains two single-letter upper bounds on the entropy rate of a discrete-valued stationary stochastic process, which only depend on second-order statistics, and are primarily suitable for models which consist of relatively large alphabets. The first bound stems from Gaussian maximum-entropy considerations and depends on the power spectral density (PSD) function of the process. While the PSD function cannot always be calculated in a closed-form, we also propose a second bound, which merely relies on some finite collection of auto-covariance values of the process. Both of the bounds consist of a one-dimensional integral, while the second bound also consists of a minimization problem over a bounded region, hence they can be efficiently calculated numerically. Examples are also provided to show that the new bounds outperform the standard conditional entropy bound.
