A novel coding scheme for exact repair-regenerating codes is presented in this paper. The codes proposed in this work can trade between the repair bandwidth of nodes (number of downloaded symbols from each surviving node in a repair process) and the required storage overhead of the system. These codes work for general system parameters $(n,k,d)$ , which are the total number of nodes, the number of nodes suffice for data recovery, and the number of helper nodes in a repair process, respectively. The proposed construction offers a unified scheme to develop exact-repair regenerating codes for the entire trade-off, including the MBR and MSR points. We conjecture that the new storage-vs.-bandwidth trade-off achieved by the proposed codes is optimum. Some other key features of this code include: the construction is linear; the required field size is only $\Theta (n)$ ; and the code parameters and in particular sub-packetization level is at most $(d-k+1)^{k}$ ; which is independent of the number of the parity nodes. Moreover, the proposed repair mechanism is helper-independent, that is the data sent from each helper only depends on the identity of the helper and failed nodes, but independent of the identity of other helper nodes participating in the repair process.

中文翻译：

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分布式存储系统的级联代码

本文提出了一种用于精确修复-再生码的新编码方案。这项工作中提出的代码可以在节点的修复带宽（修复过程中从每个幸存节点下载的符号数）和系统所需的存储开销之间进行权衡。这些代码适用于一般系统参数 $(n,k,d)$ ，分别为节点总数、数据恢复所需节点数和修复过程中的辅助节点数。提议的结构提供了一个统一的方案来为整个权衡开发精确修复再生代码，包括 MBR 和 MSR 点。我们推测所提出的代码实现的新的存储与带宽权衡是最佳的。该代码的其他一些关键特性包括： 结构是线性的；所需的字段大小仅为 $\Theta (n)$ ; 并且代码参数，特别是子包化级别最多是 $(d-k+1)^{k}$ ; 这与奇偶校验节点的数量无关。此外，建议的修复机制是独立于帮手，即每个helper发送的数据只取决于helper和故障节点的身份，而与参与修复过程的其他helper节点的身份无关。