论文标题
两个带有柔性子包装的背包代码，以实现较低的维修带宽
Two Piggybacking Codes with Flexible Sub-Packetization to Achieve Lower Repair Bandwidth
论文作者
论文摘要
作为一类特殊的数组代码，$（n，k，m）$背带代码是MDS代码（即，$ n $ nodes中的任何$ k $都可以检索所有数据符号），可以实现低副包装$ m $ M $的单节点故障的低维修带宽。在本文中，我们提出了两个新的背式背包代码，这些代码的维修带宽低于相同参数的现有背带代码。我们的第一个背包代码可以支持灵活的子包装$ m $，其中$ 2 \ leq m \ leq n-k $，其中$ n-k> 3 $。我们表明，当$ n -k = 8,9 $，$ m = 6 $和$ 30 \ leq k \ leq k \ leq leq 100 $时，我们的第一个背带代码的任何单节点故障的维修带宽都比现有的背负式代码较低。此外，我们提出了第二个背包代码，以使子包装是奇偶节点数量的倍数（即$（n-k）| m $），它是通过共同设计用于数据节点修复和转换功能的Parity节点节点修复的piggyback函数。我们表明，在所有现有的背式背包代码中，评估参数的所有单节点故障$ k/n = 0.75、0.8、0.9，0.9 $和$ n-k \ geq 4 $中，建议的第二个背包代码的维修带宽最低。
As a special class of array codes, $(n,k,m)$ piggybacking codes are MDS codes (i.e., any $k$ out of $n$ nodes can retrieve all data symbols) that can achieve low repair bandwidth for single-node failure with low sub-packetization $m$. In this paper, we propose two new piggybacking codes that have lower repair bandwidth than the existing piggybacking codes given the same parameters. Our first piggybacking codes can support flexible sub-packetization $m$ with $2\leq m\leq n-k$, where $n - k > 3$. We show that our first piggybacking codes have lower repair bandwidth for any single-node failure than the existing piggybacking codes when $n - k = 8,9$, $m = 6$ and $30\leq k \leq 100$. Moreover, we propose second piggybacking codes such that the sub-packetization is a multiple of the number of parity nodes (i.e., $(n-k)|m$), by jointly designing the piggyback function for data node repair and transformation function for parity node repair. We show that the proposed second piggybacking codes have lowest repair bandwidth for any single-node failure among all the existing piggybacking codes for the evaluated parameters $k/n = 0.75, 0.8, 0.9$ and $n-k\geq 4$.
