论文标题
连接图上的节点修复，第二部分
Node repair on connected graphs, Part II
论文作者
论文摘要
我们继续研究分布式存储系统中的再生代码，其中节点之间的连接受图形约束。在此问题中，失败的节点下载了存储在图形顶点子集中的信息，目的是恢复丢失的数据。该信息在整个网络上移动，节点维修的成本取决于从辅助节点到失败节点的图形距离。这个问题是在我们最近的工作（IEEE IT交易，2022年5月）中提出的，我们表明，在中间节点上的信息处理可以节省维修带宽，而不是直接转发数据。 虽然先前的论文仅限于MSR案例，但在这里我们将研究扩展到了一般再生代码的情况。我们在维修带宽上得出了一个下限，并针对几个重生代码的家族进行了中间处理制定修复程序，并着重于多线性代数的最新结构。我们还考虑了图表上代码的数据检索的任务，从而在通信带宽上得出了一个下限，并表明它可以在存储式宽度折衷曲线的MBR点上实现。
We continue our study of regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the graph for the purpose of recovering the lost data. This information is moved across the network, and the cost of node repair is determined by the graphical distance from the helper nodes to the failed node. This problem was formulated in our recent work (IEEE IT Transactions, May 2022) where we showed that processing of the information at the intermediate nodes can yield savings in repair bandwidth over the direct forwarding of the data. While the previous paper was limited to the MSR case, here we extend our study to the case of general regenerating codes. We derive a lower bound on the repair bandwidth and formulate repair procedures with intermediate processing for several families of regenerating codes, with an emphasis on the recent constructions from multilinear algebra. We also consider the task of data retrieval for codes on graphs, deriving a lower bound on the communication bandwidth and showing that it can be attained at the MBR point of the storage-bandwidth tradeoff curve.
