论文标题
带有K + 1个助手节点的新合作维修方案（N，K）Hadamard MSR码，带有小子包装
A New Cooperative Repair Scheme with k + 1 Helper Nodes for (n, k) Hadamard MSR codes with Small Sub-packetization
论文作者
论文摘要
合作维修模型是一种可用的技术，可以处理分布式存储系统中的多个节点故障。最近，Ye（信息理论的IEEE交易，2020年）给出了合作MSR码的明确结构，其子包装级别$（D-K+H）（D-K+1）^n $。具体而言，当$ d = k+1 $时，子包装水平为$（H+1）2^n $。在本文中，我们提出了一种新的合作维修方案，并通过基础和实体内的配对从完美的代码继承而来，该代码将子包装降低到$ 2^n $时，$（h+1）| 2^n $ and $（2 \ ell+1）2^n $时$ d = k+1 $助手节点。也就是说，子包装是$ h + 1美元或$ 2^m的$ $ $倍。事实证明，这是迄今为止已知的最好的结果。
Cooperative repair model is an available technology to deal with multiple node failures in distributed storage systems. Recently, explicit constructions of cooperative MSR codes were given by Ye (IEEE Transactions on Information Theory, 2020) with sub-packetization level $(d-k+h)(d-k+1)^n$. Specifically, the sub-packetization level is $(h+1)2^n$ when $d=k+1$. In this paper, we propose a new cooperative repair scheme by means of the inter-instance and intra-instance pairing inherited from the perfect code which reduces the sub-packetization to $2^n$ when $(h+1)|2^n$ and $(2\ell+1)2^n$ when $h+1=(2\ell+1)2^m$ for $m\ge 0$, $\ell\ge 1$ with $d=k+1$ helper nodes. That is to say, the sub-packetization is $h + 1 $ times or $2^m$ times less than Ye's. It turned out to be the best result so far known.
