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Error-Correcting Regenerating and Locally Repairable Codes via Rank-Metric Codes

机译：通过等级度量代码进行纠错的重新生成代码和本地可修复代码

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摘要

This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable codes. The concatenated coding scheme brings together a maximum rank distance code as an outer code and either a globally regenerating or a locally repairable code as an inner code. In addition, error resilience for combination of locally repairable codes with regenerating codes is considered. This concatenated coding system is designed to handle two different types of adversarial errors: the first type includes an adversary that can replace the content of an affected node only once; while the second type studies an adversary that is capable of polluting data an unbounded number of times. The paper establishes an upper bound on the resilience capacity for a locally repairable code. This paper also proves that the proposed concatenated coding approach attains the upper bound on the resilience capacity in the presence of the first type of adversary for both minimum storage regenerating codes and locally repairable codes. Further, this paper presents mechanisms that combine the presented concatenated coding scheme with subspace signatures to achieve error resilience for the second type of errors.
机译：本文提出并分析了一种新颖的级联编码方案，该方案可在两种分布式存储设置中实现错误恢复能力：一种是使用现有再生代码进行存储，第二种是使用本地可修复代码进行存储。级联编码方案将最大秩距离代码作为外部代码，将全局重新生成的代码或本地可修复的代码作为内部代码。此外，还考虑了将本地可修复代码与重新生成代码结合使用的错误恢复能力。此级联编码系统旨在处理两种不同类型的对抗性错误：第一种类型包括一个只能替换一次受影响节点内容的对手。而第二种类型研究的对手可以无限制地污染数据。本文确定了本地可修复代码的复原能力的上限。本文还证明，对于最小存储再生代码和本地可修复代码，在存在第一类对手的情况下，所提出的级联编码方法均达到了弹性能力的上限。此外，本文提出了将所提出的级联编码方案与子空间签名相结合的机制，以实现针对第二种错误的错误恢复能力。

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