MDS与重构性

MDS与重构性不太一样，但是我又搞不懂是哪里不同，先记录下来，通过不断的学习强化自己的理解。

 

MDS性质：通过访问和下载与原始文件大小相同的数据量，重建源文件；然后通过源文件去修复失效节点。（For example, to accomplish this task, the repair process of the classical MDS codes is to first reconstruct the original file by accessing and downloading an amount of data equal to the size of the original file, and then repair the failed node, which is called naive repair.）IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 70, NO. 2, FEBRUARY 2022，A Generic Transformation for Optimal Node Repair in MDS Array Codes Over F2，李杰，唐小虎等。

 

具体：An [n, k] MDS array code possesses the MDS property that the original file can be reconstructed by contacting any k out of the n nodes, and is preferable to have optimal repair bandwidth, i.e., a failed node can be regenerated by downloading α/r symbols from each surviving node [6]. Generally, the data downloaded from node j to repair node i can be represented by Si,j fj , where Si,j is an α × α matrix with its rank indicating the amount of data that should be downloaded, and Si,j is usually referred to as repair matrix. Besides the repair bandwidth, the rebuilding access (also known as repair access in [35]) should also be optimized. Formally, rebuilding access is the amount of data that needs to be accessed (or read) to repair a failed node, which is of course no less than the repair bandwidth. It would be preferable for an MDS array code to have optimal rebuilding access, which can be achieved if only α/r symbols are accessed at each surviving node [25], i.e., there are exactly α/r nonzero columns in Si,j , where i, j ∈ [0, n) with i = j. This appealing property reinforces the repair bandwidth requirement, and can reduce the disk I/O overhead during the repair process.

 

2025年1月6日 记：

MDS属性和重构性在分布式存储系统中，侧重点不同。

MDS属性主要是针对纠删码本身的Coding性质出发，如果该编码满足Singleton Bound：d=n-k+1，即说明该Code具有MDS性质；在形式上表示为：任意的k位都可以恢复data位。

重构性主要体现在分布式存储系统的数据收集(Data Collector)和数据修复(再生码之前的方法)中：当用户需要数据时，通过重构性满足DC功能，当数据出错需要修复时，通过重构性重构出Data数据，再替换失败数据，其重构性运用的就是Coding当中的MDS性质。