Zigzag-decodable codes have been proposed for distributed storage systems to achieve fast decoding of uncoded data packets through the iterative decoding of data bits from coded packets. To maintain high data availability, it is critical to minimize the repair bandwidth by downloading the least amount of bits for repairing any lost packet. In this work, we propose zigzag-decodable reconstruction (ZDR) codes which achieve asymptotically minimum repair bandwidth for repairing a single node, while preserving the high computational efficiency due to zigzag decoding. We present two explicit constructions of ZDR codes such that any node of ZDR codes can be repaired with asymptotically minimum repair bandwidth. The first construction is based on the well-designed encoding matrix and a generic transformation, while the second construction is designed by recursively employing the proposed generic transformation for any existing zigzag-decodable code. Moreover, we show that the proposed two classes of ZDR codes can be decoded by the zigzag decoding algorithm and have less computational complexity than the existing codes with asymptotically or exactly minimum repair bandwidth.

中文翻译：

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对所有节点具有渐近最优修复的锯齿形可解码重构代码

已经为分布式存储系统提出了锯齿形可解码代码，以通过对编码包中的数据位进行迭代解码来实现对未编码数据包的快速解码。为了保持高数据可用性，通过下载最少量的比特来修复任何丢失的数据包来最小化修复带宽是至关重要的。在这项工作中，我们提出了锯齿形可解码重建 (ZDR) 代码，该代码可实现用于修复单个节点的渐近最小修复带宽，同时由于锯齿形解码而保持高计算效率。我们提出了 ZDR 码的两种显式构造，使得 ZDR 码的任何节点都可以用渐近最小修复带宽进行修复。第一个构造基于精心设计的编码矩阵和通用变换，而第二种结构是通过对任何现有的锯齿形可解码代码递归地采用所提议的通用转换来设计的。此外，我们表明所提出的两类 ZDR 代码可以通过 zigzag 解码算法进行解码，并且比具有渐近或精确最小修复带宽的现有代码具有更少的计算复杂度。