有限卷积模型中的近似均匀性

中文摘要 AI 辅助

均匀分布作为两个独立分布之和的问题已被充分研究。本文研究了在以下差异度量下，均匀分布对具有固定支撑的两个分布之和的近似问题：曼哈顿距离、欧几里得距离、前向库尔贝克-莱布勒散度以及基于线度量的瓦瑟斯坦-一距离。均匀分布在该模型中的隶属问题已被充分研究。在两个模型中获得了显式结果，其中一个模型中的两个分布之一是伯努利分布，另一个模型中两个分布具有相同的支撑，并包含一个猜想。最后，我们展示了我们的重建方法在关于加性噪声信道编码容量的一个近期猜想中的应用。

英文摘要

The problem of the uniform law being a sum of two independent distributions has been well studied. Here, we study the approximation of the uniform law to a sum of two distributions with fixed support, under the following discrepancies: the Manhattan distance, the Euclidean distance, the forward Kullback--Leibler divergence and the Wasserstein-one distance based on the line metric. The problem of membership of the uniform law in this model has been well studied. Explicit results are obtained in two models, one where one of the distributions is a Bernoulli and the other when both distributions have the same support, including one conjecture. Finally, we show an application of our reconstruction method to a recent conjecture about the coding capacity of an additive noise channel.

发表机构

• Rutgers University–New Brunswick（罗格斯大学新不伦瑞克分校）
• National University of Singapore（新加坡国立大学）

机构由 AI 辅助整理，请以论文原文为准。