Bidirectional Piggybacking Design for Systematic Nodes with Sub-Packetization $l=2$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913686128427008 |
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| author | Wang, Ke |
| author_facet | Wang, Ke |
| contents | In 2013, Rashmi et al. proposed the piggybacking design framework to reduce the repair bandwidth of $(n,k;l)$ MDS array codes with small sub-packetization $l$ and it has been studied extensively in recent years. In this work, we propose an explicit bidirectional piggybacking design (BPD) with sub-packetization $l=2$ and the field size $q=O(n^{\lfloor r/2 \rfloor \!+\!1})$ for systematic nodes, where $r=n-k$ equals the redundancy of an $(n,k)$ linear code. And BPD has lower average repair bandwidth than previous piggybacking designs for $l=2$ when $r\geq 3$. Surprisingly, we can prove that the field size $q\leq 256$ is sufficient when $n\leq 15$ and $n-k\leq 4$. For example, we provide the BPD for the $(14,10)$ Reed-Solomon (RS) code over $\mathbb{F}_{2^8}$ and obtain approximately $41\%$ savings in the average repair bandwidth for systematic nodes compared with the trivial repair approach. This is the lowest repair bandwidth achieved so far for $(14,10)_{256}$ RS codes with sub-packetization $l=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bidirectional Piggybacking Design for Systematic Nodes with Sub-Packetization $l=2$ Wang, Ke Information Theory In 2013, Rashmi et al. proposed the piggybacking design framework to reduce the repair bandwidth of $(n,k;l)$ MDS array codes with small sub-packetization $l$ and it has been studied extensively in recent years. In this work, we propose an explicit bidirectional piggybacking design (BPD) with sub-packetization $l=2$ and the field size $q=O(n^{\lfloor r/2 \rfloor \!+\!1})$ for systematic nodes, where $r=n-k$ equals the redundancy of an $(n,k)$ linear code. And BPD has lower average repair bandwidth than previous piggybacking designs for $l=2$ when $r\geq 3$. Surprisingly, we can prove that the field size $q\leq 256$ is sufficient when $n\leq 15$ and $n-k\leq 4$. For example, we provide the BPD for the $(14,10)$ Reed-Solomon (RS) code over $\mathbb{F}_{2^8}$ and obtain approximately $41\%$ savings in the average repair bandwidth for systematic nodes compared with the trivial repair approach. This is the lowest repair bandwidth achieved so far for $(14,10)_{256}$ RS codes with sub-packetization $l=2$. |
| title | Bidirectional Piggybacking Design for Systematic Nodes with Sub-Packetization $l=2$ |
| topic | Information Theory |
| url | https://arxiv.org/abs/2502.07368 |