分数重复码的对偶性和文件大小层次
On the Duality and File Size Hierarchy of Fractional Repetition Codes
摘要：
部署纠删码的分布式存储系统可以提供更好的特性，例如更低的存储开销和更高的数据可靠性。分数重复（FR）码是一类具有非编码精确修复和最小修复带宽特性的存储码。我们研究了FR码的对偶性，并研究了FR码的支持文件大小与其对偶码之间的关系。基于建立的关系，我们得到了一个改进的对偶界的支持文件大小的FR码。我们进一步表明，FR码构造从$t$ -设计是最佳的存储文件的大小是足够大的。此外，我们提出了张量积技术相结合的FR代码，并阐述了文件大小的层次结构的结果代码。
英文摘要：
Distributed storage systems that deploy erasure codes can provide better features such as lower storage overhead and higher data reliability. In this paper, we focus on fractional repetition (FR) codes, which are a class of storage codes characterized by the features of uncoded exact repair and minimum repair bandwidth. We study the duality of FR codes, and investigate the relationship between the supported file size of an FR code and its dual code. Based on the established relationship, we derive an improved dual bound on the supported file size of FR codes. We further show that FR codes constructed from $t$-designs are optimal when the size of the stored file is sufficiently large. Moreover, we present the tensor product technique for combining FR codes, and elaborate on the file size hierarchy of resulting codes.
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