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Beyond the MDS Bound in Distributed Cloud Storage
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2020-07-01 , DOI: 10.1109/tit.2020.2993038
Jian Li , Tongtong Li , Jian Ren

Regenerating code is a class of distributed storage codes that can optimally trade the bandwidth with the amount of data stored per node to repair a failed node. There are two extreme points in the optimal regenerating trade-off curve, which correspond to minimum-storage regenerating (MSR) and minimum-bandwidth regenerating (MBR). Recently, Reed-Solomon (RS) code based regenerating codes (RS-RC) were constructed under the product-matrix framework. It can also achieve the maximum distance separable (MDS) property in code regeneration and reconstruction. However, in case that the network is hostile and the storage nodes could be compromised or packets be modified, the storage capacity and the bandwidth required to regenerate or reconstruct the original file can be significantly affected. In this paper, we propose Hermitian code based regenerating codes (H-RC) by developing constructions under the product-matrix framework for minimum storage regenerating (H-MSR) and the minimum bandwidth regenerating (H-MBR). We also propose data regeneration and reconstruction algorithms for both H-MSR and H-MBR codes under both error-free and hostile networks. We demonstrate that the proposed algorithms can also successfully determine the erroneous decodings in hostile networks. Theoretical evaluation shows that our proposed H-RC can detect and correct more errors in hostile networks well beyond the RS-RC with the same code rate. Our analysis shows that the proposed H-RC have lower computational complexity than the RS-RC for both code regeneration and code reconstruction.

中文翻译:

超越分布式云存储中的 MDS 界限

再生代码是一类分布式存储代码,可以优化带宽与每个节点存储的数据量来修复故障节点。最优再生权衡曲线有两个极值点,分别对应最小存储再生(MSR)和最小带宽再生(MBR)。最近,在乘积矩阵框架下构建了基于 Reed-Solomon (RS) 码的再生码 (RS-RC)。它还可以在代码重新生成和重构中实现最大距离可分离 (MDS) 属性。但是,如果网络存在恶意,并且存储节点可能受到损害或数据包被修改,则重新生成或重建原始文件所需的存储容量和带宽可能会受到显着影响。在本文中,我们通过在最小存储再生(H-MSR)和最小带宽再生(H-MBR)的乘积矩阵框架下开发结构,提出了基于 Hermitian 码的再生码(H-RC)。我们还为无差错和恶意网络下的 H-MSR 和 H-MBR 代码提出了数据再生和重建算法。我们证明了所提出的算法也可以成功地确定敌对网络中的错误解码。理论评估表明,我们提出的 H-RC 可以在敌对网络中检测和纠正更多错误,远远超过具有相同码率的 RS-RC。我们的分析表明,在代码重新生成和代码重构方面,所提出的 H-RC 具有比 RS-RC 更低的计算复杂度。
更新日期:2020-07-01
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