In this paper, we address the node repair problem of Reed-Solomon (RS) coded distributed storage systems. Specifically, to overcome the challenges of multiple-node failures of RS codes under the rack-aware storage model, we employ good polynomials to guide the placement of the conventional RS codes into racks and then propose a novel repair framework for the resultant rack-aware RS codes, which can transform its repair to that under the homogeneous storage model. As applications of our repair framework, firstly we present the repair scheme of multiple-node failures for some existing constructions, which can only repair a single-node failure before. Secondly, we deduce several new constructions of rack-aware RS codes supporting the repair of multiple-node failures.

翻译：本文研究Reed-Solomon（RS）编码分布式存储系统中的节点修复问题。具体而言，为克服机架感知存储模型下RS码的多节点故障挑战，我们采用优良多项式引导传统RS码在机架中的放置，并提出一种适用于所得机架感知RS码的新型修复框架，该框架可将其修复过程转换为同构存储模型下的修复。作为该修复框架的应用，首先针对现有的一些仅能修复单节点故障的构造方案，给出了多节点故障的修复方法；其次，推导出若干支持多节点故障修复的新型机架感知RS码构造方案。