论文标题
评论“有限区块长度制度中的频道编码率”：有关信息率功能的二次衰减属性
Comments on "Channel Coding Rate in the Finite Blocklength Regime": On the Quadratic Decaying Property of the Information Rate Function
论文作者
论文摘要
信息速率函数的二次衰减属性指出，给定固定条件分布$ p _ {\ MathSf {y} | \ Mathsf {x}} $，（有限的）随机变量$ \ m athsf {x}} $和$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ { $ p_ \ mathsf {x} $从容量调整输入分布中移开。它是信息速率函数的属性，在研究高阶渐进性和有限的扩展信息理论的研究中特别有用，在该理论中，strassen [1] [1]和更明确地，由polyandkiy-poor-verdú[2]隐式地使用了它。但是，这两部作品中概述的证据都包含差距，这些空白是不平凡的。此评论提供了此属性的替代，完整的证明。
The quadratic decaying property of the information rate function states that given a fixed conditional distribution $p_{\mathsf{Y}|\mathsf{X}}$, the mutual information between the (finite) discrete random variables $\mathsf{X}$ and $\mathsf{Y}$ decreases at least quadratically in the Euclidean distance as $p_\mathsf{X}$ moves away from the capacity-achieving input distributions. It is a property of the information rate function that is particularly useful in the study of higher order asymptotics and finite blocklength information theory, where it was already implicitly used by Strassen [1] and later, more explicitly, by Polyanskiy-Poor-Verdú [2]. However, the proofs outlined in both works contain gaps that are nontrivial to close. This comment provides an alternative, complete proof of this property.
