ϵ-Minimum Storage Regenerating (E-MSR) codes form a special class of Maximum Distance Separable (MDS) codes, providing mechanisms for exact regeneration of a single code block in their codewords by downloading slightly suboptimal amount of information from the remaining code blocks. The key advantage of these codes is a significantly lower subpacketization that grows only logarithmically with the code length, while providing optimality in storage and error-correcting capacity. However, existing constructions of ϵ-MSR codes require each remaining code block to be available for the repair of any failed code block. In this paper, we construct ϵ-MSR codes that can repair any failed code block by contacting fewer number of available code blocks. When a code block fails, our repair procedure needs to contact a few compulsory code blocks and is free to choose any subset of available code blocks for the remaining choices. Our construction requires a field size linear in code length and ensures load balancing (in terms of information downloaded) among the contacted code blocks for repairing a failed code block.

中文翻译：

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系-MSR代码：联系更少的代码块进行精确修复


ε-最小存储再生 (E-MSR) 代码形成了一类特殊的最大距离可分离 (MDS) 代码，通过从剩余代码块下载稍微次优的信息量，提供了在其代码字中精确再生单个代码块的机制。这些代码的主要优点是子分组化程度显着降低，仅随代码长度呈对数增长，同时提供存储和纠错能力的优化。然而，现有的 ϵ-MSR 代码结构要求每个剩余的代码块可用于修复任何失败的代码块。在本文中，我们构建了 ϵ-MSR 代码，可以通过接触较少数量的可用代码块来修复任何失败的代码块。当代码块失败时，我们的修复过程需要联系一些强制代码块，并且可以自由地选择可用代码块的任何子集作为剩余的选择。我们的构造需要字段大小与代码长度成线性关系，并确保所联系的代码块之间的负载平衡（就下载的信息而言），以修复失败的代码块。