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：本文在机架感知存储模型中，推导了从任意数量的辅助机架修复单个机架内故障节点时所需访问信息量的下界，该模型允许共享同一机架的节点进行集体信息处理。进一步地，我们构造了一族机架感知极小存储再生（MSR）码，其修复单个故障节点时所访问的符号数对所有容许参数均能达到该下界。此前，机架感知最优访问MSR码的构造仅对有限参数成立。此外，我们还提出一族里德-所罗门（RS）码，该码在修复单个机架内多个故障节点时仅需访问相对较少的符号数。特别地，对于特定码参数，该RS构造在访问复杂度上达到下界，因此具有最优访问性能。