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A New Design of Binary MDS Array Codes With Asymptotically Weak-Optimal Repair

机译：具有渐近弱最优修复的二进制MDS阵列代码的新设计

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摘要

Binary maximum distance separable (MDS) array codes are a special class of erasure codes for distributed storage that not only provides fault tolerance with minimum storage redundancy but also achieves low computational complexity. They are constructed by encoding k information columns into r parity columns, in which each element in a column is a bit, such that any k out of the k + r columns suffice to recover all information bits. In addition to providing fault tolerance, it is critical to improve repair performance in practical applications. Specifically, if a single column fails, then our goal is to minimize the repair bandwidth by downloading the least amount of bits from d healthy columns, where k <= d <= k + r-1. If one column of an MDS code is failed, it is known that we need to download at least 1/(d-k + 1) fraction of the data stored in each of the d healthy columns. If this lower bound is achieved for the repair of the failure column from accessing arbitrary d healthy columns, we say that the MDS code has optimal repair. However, if such lower bound is only achieved by d specific healthy columns, then we say the MDS code has weak-optimal repair. In this paper, we propose two explicit constructions of binary MDS array codes with more parity columns (i.e., r >= 3) that achieve asymptotically weak-optimal repair, where k + 1 <= d <= k + [(r-1)/2], and "asymptotic" means that the repair bandwidth achieves the minimum value asymptotically in d. Codes in the first construction have odd number of parity columns and asymptotically weak-optimal repair for anyone information failure, while codes in the second construction have even number of parity columns and asymptotically weak-optimal repair for any one column failure.
机译：二进制最大距离可分离（MDS）阵列代码是一类特殊的分布式存储擦除代码，不仅可提供容错性和最小的存储冗余性，而且计算复杂度低。它们是通过将k个信息列编码为r个奇偶校验列而构造的，其中列中的每个元素都是一位，因此k + r列中的任何k个都足以恢复所有信息位。除了提供容错能力外，在实际应用中提高维修性能也至关重要。具体来说，如果单个列发生故障，那么我们的目标是通过从d个健康列中下载最少的位（其中k <= d <= k + r-1）来最大程度地减少修复带宽。如果MDS代码的一列失败，则已知我们需要下载存储在d个健康列中每列中的数据的至少1 /（d-k + 1）分数。如果通过访问任意d个健康列来修复故障列达到了这个下限，那么我们说MDS代码具有最佳的修复能力。但是，如果仅通过d个特定的健康列才能达到这样的下限，那么我们可以说MDS代码的修复效果较差。在本文中，我们提出了两个具有更多奇偶校验列（即r> = 3）的二进制MDS阵列代码的显式构造，它们实现了渐近弱最优修复，其中k + 1 <= d <= k + [（r-1 ）/ 2]，并且“渐近”表示修复带宽在d中渐近达到最小值。第一种结构中的代码具有奇数个奇偶校验列，并且对于任何信息故障，其渐近弱最优修复，而第二种结构中的代码具有偶数个奇偶校验列，并且针对任何一个列故障，其渐近弱最优修复。

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  • 来源
    《IEEE Transactions on Information Theory》 |2019年第11期|7095-7113|共19页
  • 作者

    Hou Hanxu; Han Yunghsiang S.; Lee Patrick P. C.; Hu Yuchong; Li Hui;

  • 作者单位

    Dongguan Univ Technol Sch Elect Engn & Intelligentizat Dongguan 523808 Peoples R China;

    Chinese Univ Hong Kong Dept Comp Sci & Engn Hong Kong Peoples R China;

    Huazhong Univ Sci & Technol Shenzhen Huazhong Univ Sci & Technol Res Inst Sch Comp Sci & Technol Wuhan 430074 Peoples R China;

    Peking Univ Shenzhen Grad Sch Shenzhen Key Lab Informat Theory & Future Interne Peng Cheng Lab Future Network PKU Lab Natl Major Shenzhen 518055 Peoples R China;

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  • 正文语种 eng
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  • 关键词

    MDS code; binary MDS array code; optimal repair bandwidth;

    机译：MDS代码;二进制MDS阵列代码;最佳维修带宽;

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