A Systematic Construction of MDS Codes with Small Sub-Packetization Level and Near-Optimal Repair Bandwidth

Jie Li*, Yi Liu, Xiaohu Tang

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small sub-packetization level, existing constructions and theoretical bounds imply that one may sacrifice the optimality of the repair bandwidth. Partly motivated by the work of Tamo et al. (IEEE Trans. Inform. Theory, 59(3), 1597-1616, 2013), in this paper, we present a transformation that can greatly reduce the sub-packetization level of MDS codes with the optimal repair bandwidth with respect to the same code length n. As applications of the transformation, four high-rate MDS codes having both small sub-packetization level and near-optimal repair bandwidth can be obtained, where three of them are explicit and the required field sizes are around or even smaller than the code length {n}. Additionally, we propose another explicit MDS code which has a similar structure as that of the first resultant code obtained by the generic transformation, but can be built on a smaller finite field.

Original languageEnglish
Article number9252158
Pages (from-to)2162-2180
Number of pages19
JournalIEEE Transactions on Information Theory
Volume67
Issue number4
DOIs
Publication statusPublished - Apr 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Distributed storage
  • high-rate
  • MDS codes
  • repair bandwidth
  • sub-packetization

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