In this paper, we define a new measure of the redundancy of information from a fault tolerance perspective. The partial information decomposition (PID) emerged last decade as a framework for decomposing the multi-source mutual information $I(T;X_1, ..., X_n)$ into atoms of redundant, synergistic, and unique information. It built upon the notion of redundancy/synergy from McGill's interaction information (McGill 1954). Separately, the redundancy of system components has served as a principle of fault tolerant engineering, for sensing, routing, and control applications. Here, redundancy is understood as the level of duplication necessary for the fault tolerant performance of a system. With these two perspectives in mind, we propose a new PID-based measure of redundancy $I_{\text{ft}}$, based upon the presupposition that redundant information is robust to individual source failures. We demonstrate that this new measure satisfies the common PID axioms from (Williams 2010). In order to do so, we establish an order-reversing correspondence between collections of source-fallible instantiations of a system, on the one hand, and the PID lattice from (Williams 2010), on the other.

翻译：在本文中，我们从容错视角定义了一种新的信息冗余度量方法。过去十年间提出的部分信息分解（PID）框架，将多源互信息 $I(T;X_1, ..., X_n)$ 分解为冗余信息、协同信息和独特信息的基本原子，该框架建立在McGill交互信息（McGill 1954）中的冗余/协同概念之上。与此同时，系统组件的冗余性已成为容错工程的基本原理，广泛应用于传感、路由和控制等领域。在此语境下，冗余被理解为系统实现容错性能所必需的重复程度。结合这两种视角，我们基于"冗余信息对单个源故障具有鲁棒性"这一预设，提出了一种基于PID的新冗余度量指标 $I_{\text{ft}}$。我们证明该新度量满足（Williams 2010）中提出的常见PID公理。为此，我们建立了系统可源故障实例化集合与（Williams 2010）中PID格之间的逆序对应关系。