In distributed storage, erasure codes provide fault-tolerance while reducing the storage overhead compared to replication. The network traffic cost during the repair of node failures, called repair bandwidth, is an important metric in code design. Regenerating codes are a class of erasure codes developed with the aim of reducing the repair bandwidth while maintaining a high level of fault-tolerance. They exhibit a tradeoff between the storage overhead per node and the repair bandwidth. However, a fundamental understanding of the storage-repair bandwidth tradeoff under exact repair is open in general. In this work, we consider the exact repair problem of multiple failures in a centralized way. Building upon techniques from the literature, we first provide an alternative proof of the functional repair bound. Then, we derive a new outer bound for linear centralized multi-node exact repair codes and illustrate its performance under various parameter settings. The derived outer bound shows that, in general, the centralized multi-node functional repair tradeoff is not achievable under linear exact repair.

中文翻译：

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线性多节点精确修复再生码的外界


在分布式存储中，纠删码提供容错能力，同时与复制相比减少了存储开销。修复节点故障期间的网络流量成本（称为修复带宽）是代码设计中的一个重要指标。再生码是一类纠删码，旨在减少修复带宽，同时保持高水平的容错能力。它们展示了每个节点的存储开销和修复带宽之间的权衡。然而，对于精确修复下的存储修复带宽权衡的基本理解总体上是开放的。在这项工作中，我们集中考虑多个故障的精确修复问题。基于文献中的技术，我们首先提供功能修复界限的替代证明。然后，我们推导了线性集中多节点精确修复代码的新外界，并说明了其在各种参数设置下的性能。推导的外界表明，一般来说，集中式多节点功能修复权衡在线性精确修复下是无法实现的。