论文标题
rényi在信息组合上界定
Rényi Bounds on Information Combining
论文作者
论文摘要
信息组合的范围是熵不平等，这些不平等明确了一组随机变量的信息或熵在以某些规定的方式组合时会改变它们。这样的界限在信息理论中起着重要的作用，尤其是在编码和香农理论中。可以说，大多数基本的信息组合是添加两个二进制随机变量，即一个cnot门，在研究信仰传播和极性编码时，所得数量是基本的。在这项工作中，我们将把这个概念推广到Rényi熵。我们基于一定的凸度或凹陷属性，在结合后的条件性rényi熵上给出了最佳界限，并讨论了该属性何时确实存在。由于没有普遍同意的有条件的Rényi熵的定义，因此我们考虑了文献中的四个不同版本。最后，我们讨论了这些边界在极地代码下的Rényi熵极化中的应用。
Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in information theory, particularly in coding and Shannon theory. The arguably most elementary kind of information combining is the addition of two binary random variables, i.e. a CNOT gate, and the resulting quantities are fundamental when investigating belief propagation and polar coding. In this work we will generalize the concept to Rényi entropies. We give optimal bounds on the conditional Rényi entropy after combination, based on a certain convexity or concavity property and discuss when this property indeed holds. Since there is no generally agreed upon definition of the conditional Rényi entropy, we consider four different versions from the literature. Finally, we discuss the application of these bounds to the polarization of Rényi entropies under polar codes.
