We derive a lower bound on the amount of information accessed to repair failed nodes within a single rack from any number of helper racks in the rack-aware storage model that allows collective information processing in the nodes that share the same rack. Furthermore, we construct a family of rack-aware minimum-storage regenerating (MSR) codes with the property that the number of symbols accessed for repairing a single failed node attains the bound with equality for all admissible parameters. Constructions of rack-aware optimal-access MSR codes were only known for limited parameters. We also present a family of Reed-Solomon (RS) codes that only require accessing a relatively small number of symbols to repair multiple failed nodes in a single rack. In particular, for certain code parameters, the RS construction attains the bound on the access complexity with equality and thus has optimal access.
翻译：Translated abstract:
我们推导出在同一机架内来自任意数量的辅助机架用于修复失败节点时被访问的信息量下界，其中机架感知存储模型允许在共享同一机架的节点之间进行集体信息处理。此外，我们构建了一族支持机架感知的最少存储再生（MSR）码，其具有这样一种特性，即用于修复单个失败节点的符号数量对于所有可接受的参数都等于该下界。此前，仅针对有限参数已知如何构造支持机架感知的最优访问 MSR 码。我们还提出了一族 Reed-Solomon（RS）码，它们在修复一个机架内多个失败节点时只需要访问相对较少的符号。特别地，对于某些码参数，RS 构造方法获得了访问复杂度下界，并且因此具有最优访问。
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