The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. One often overlooked way to achieve this decomposition is using a so-called measure of union information - which quantifies the information that is present in at least one of the sources - from which a synergy measure stems. In this paper, we introduce a new measure of union information based on adopting a communication channel perspective, compare it with existing measures, and study some of its properties. We also include a comprehensive critical review of characterizations of union information and synergy measures that have been proposed in the literature.

翻译：部分信息分解（PID）框架旨在将一组（两个或更多）随机变量（源变量）关于另一变量（目标变量）的信息分解为三种类型：独特信息、冗余信息和协同信息。经典信息论本身并未提供以这种方式分解信息的唯一方法，因此需要引入额外假设。一种常被忽视的实现该分解的途径是使用所谓的联合信息度量——该度量量化了至少在一个源变量中存在的信息——并由此衍生出协同性度量。本文基于通信信道视角引入了一种新的联合信息度量，将其与现有度量进行比较，并研究了其若干性质。文中还对文献中已提出的联合信息与协同性度量的特征化描述进行了全面的批判性综述。