A Generic Transformation for Optimal Node Repair in MDS Array Codes over F2

Jie Li*, Xiaohu Tang, Camilla Hollanti

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

For high-rate linear systematic maximum distance separable (MDS) codes, most early constructions could initially optimally repair all the systematic nodes but not all the parity nodes. Fortunately, this issue was first solved by Li et al. in (IEEE Trans. Inform. Theory, 64(9), 6257-6267, 2018), where a transformation that can convert any nonbinary MDS array code into another one with desired properties was proposed. However, the transformation does not work for binary MDS array codes. In this paper, we address this issue by proposing another generic transformation that can convert any [n,k] binary MDS array code into a new one, which endows any r=n−k≥2chosen nodes with optimal repair bandwidth and optimal rebuilding access properties, and at the same time, preserves the normalized repair bandwidth/rebuilding access for the remaining k nodes under some conditions. As two immediate applications, we show that 1) by applying the transformation multiple times, any binary MDS array code can be converted into one with optimal rebuilding access for all nodes, 2) any binary MDS array code with optimal repair bandwidth or optimal rebuilding access for the systematic nodes can be converted into one with the corresponding optimality property for all nodes.

Original languageEnglish
Pages (from-to)727-738
Number of pages12
JournalIEEE Transactions on Communications
Volume70
Issue number2
DOIs
Publication statusPublished - 1 Feb 2022
MoE publication typeA1 Journal article-refereed

Keywords

  • Binary MDS array codes
  • distributed storage
  • high-rate
  • optimal rebuilding access
  • optimal repair bandwidth

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