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首页> 外文期刊>Information Theory, IEEE Transactions on >Codes With Local Regeneration and Erasure Correction
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Codes With Local Regeneration and Erasure Correction

机译：具有局部再生和纠删码

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摘要

Regenerating codes and codes with locality are two coding schemes that have recently been proposed, which in addition to ensuring data collection and reliability, also enable efficient node repair. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. This paper presents results in two directions. In one, this paper extends the notion of codes with locality so as to permit local recovery of an erased code symbol even in the presence of multiple erasures, by employing local codes having minimum distance >2. An upper bound on the minimum distance of such codes is presented and codes that are optimal with respect to this bound are constructed. The second direction seeks to build codes that combine the advantages of both codes with locality as well as regenerating codes. These codes, termed here as codes with local regeneration, are codes with locality over a vector alphabet, in which the local codes themselves are regenerating codes. We derive an upper bound on the minimum distance of vector-alphabet codes with locality for the case when their constituent local codes have a certain uniform rank accumulation property. This property is possessed by both minimum storage regeneration (MSR) and minimum bandwidth regeneration (MBR) codes. We provide several constructions of codes with local regeneration which achieve this bound, where the local codes are either MSR or MBR codes. Also included in this paper, is an upper bound on the minimum distance of a general vector code with locality as well as the performance comparison of various code constructions of fixed block length and minimum distance.
机译：再生代码和具有局部性的代码是最近提出的两种编码方案，它们除了确保数据收集和可靠性之外，还能够进行有效的节点修复。在尝试修复故障节点的情况下，重新生成代码试图将为节点修复下载的数据量最小化，而具有局部性的代码则试图使访问的辅助节点数量最小化。本文介绍了两个方向的结果。在一中，本文通过使用最小距离> 2的局部代码扩展了局部代码的概念，从而即使在多次擦除的情况下也允许局部恢复已擦除的代码符号。给出了这种代码的最小距离的上限，并构造了相对于该边界最佳的代码。第二个方向旨在构建将两种代码的优点与局部性以及重新生成的代码相结合的代码。这些代码在这里称为具有局部再生的代码，是局部于矢量字母上的代码，其中局部代码本身就是再生代码。当它们的组成局部代码具有一定的均匀秩累积特性时，我们推导了局部向量字母代码最小距离的上限。最小存储再生（MSR）和最小带宽再生（MBR）代码都具有此属性。我们提供了具有本地再生功能的几种代码结构，可以实现此限制，其中本地代码是MSR或MBR代码。本文还包括通用矢量代码在局部位置的最小距离的上限，以及固定块长和最小距离的各种代码结构的性能比较。

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