This paper presents flexible storage codes, a class of error-correcting codes that can recover information from a flexible number of storage nodes. As a result, one can make a better use of the available storage nodes in the presence of unpredictable node failures and reduce the data access latency. Let us assume a storage system encodes $k\ell$ information symbols over a finite field $\mathbb{F}$ into $n$ nodes, each of size $\ell$ symbols. The code is parameterized by a set of tuples $\{(R_j,k_j,\ell_j): 1 \le j \le a\}$, satisfying $k_1\ell_1=k_2\ell_2=...=k_a\ell_a$ and $k_1>k_2>...>k_a = k, \ell_a=\ell$, such that the information symbols can be reconstructed from any $R_j$ nodes, each node accessing $\ell_j$ symbols. In other words, the code allows a flexible number of nodes for decoding to accommodate the variance in the data access time of the nodes. Code constructions are presented for different storage scenarios, including LRC (locally recoverable) codes, PMDS (partial MDS) codes, and MSR (minimum storage regenerating) codes. We analyze the latency of accessing information and perform simulations on Amazon clusters to show the efficiency of presented codes.

翻译：本文展示了灵活的存储代码, 是一个可以从灵活的存储节点数中回收信息的信息的错误校正代码类别。 因此, 在存在不可预测的节点失败的情况下, 可以更好地利用可用的存储节点, 并减少数据访问长期性 。 让我们假设一个存储系统, 将限定字段$k\ ell$ 的信息符号编码为$k\ ellb{F} 美元, 每个大小为$@ 美元符号。 该代码由一组 $( R_ j, k_ j,\ell_ j) 代码进行参数化。 该代码由一组 $@ ( R_ j, k_ j,\ ell_ j): 1\ j\ le a$, 满足 $k_\ ell_ 2\ k\\\ ell_ 2=... k_ a$, 和 $k_ 1>... k>... k_ a = k, = k, = k, elex_ aell$ des, 这样信息符号可以从任何 ladr_ rad comm codeal codeal codement 中校验校验校正 mSR 数据, 。