多节点故障集中修复及其在通信高效秘密共享中的应用
Centralized Repair of Multiple Node Failures with Applications to Communication Efficient Secret Sharing
摘要：
本文考虑了一个分布式存储系统，其中多个存储节点可以在一个集中的位置同时重建。这种集中式多节点修复（CMR）模型是再生代码的推广，允许对单个故障节点进行带宽有效的修复。这项工作的重点是在此CMR模型中存储的数据量和修复带宽之间的权衡。特别是，修复带宽的界限推导出的最小存储多节点修复（MSMR）和最小带宽多节点修复（MBMR）的工作点。这些界限的紧密性通过代码结构进行分析。MSMR点的特征在于，通过代码实现这一点的功能修复的通用CMR参数集，以及与代码，使精确修复某些CMR参数。MBMR点，另一方面，其特征在于与精确的修复代码的所有CMR参数的系统，满足一定的熵累积属性。最后，将该模型应用于秘密共享问题，利用多节点修复问题的编码构造了具有带宽有效共享修复性质的通信有效秘密共享方案.
英文摘要：
This paper considers a distributed storage system, where multiple storage nodes can be reconstructed simultaneously at a centralized location. This centralized multi-node repair (CMR) model is a generalization of regenerating codes that allow for bandwidth-efficient repair of a single failed node. This work focuses on the trade-off between the amount of data stored and repair bandwidth in this CMR model. In particular, repair bandwidth bounds are derived for the minimum storage multi-node repair (MSMR) and the minimum bandwidth multi-node repair (MBMR) operating points. The tightness of these bounds are analyzed via code constructions. The MSMR point is characterized through codes achieving this point under functional repair for general set of CMR parameters, as well as with codes enabling exact repair for certain CMR parameters. The MBMR point, on the other hand, is characterized with exact repair codes for all CMR parameters for systems that satisfy a certain entropy accumulation property. Finally, the model proposed here is utilized for the secret sharing problem, where the codes for the multi-node repair problem is used to construct communication efficient secret sharing schemes with the property of bandwidth efficient share repair.
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