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A class of binary MDS array codes with asymptotically weak-optimal repair

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Abstract

Binary maximum distance separable (MDS) array codes contain k information columns and r parity columns in which each entry is a bit that can tolerate r arbitrary erasures. When a column in an MDS code fails, it has been proven that we must download at least half of the content from each helper column if k+1 columns are selected as the helper columns. If the lower bound is achieved such that the k+1 helper columns can be selected from any k + r − 1 surviving columns, then the repair is an optimal repair. Otherwise, if the lower bound is achieved with k + 1 specific helper columns, the repair is a weak-optimal repair. This paper proposes a class of binary MDS array codes with k ⩾ 3 and r ⩾ 2 that asymptotically achieve weak-optimal repair of an information column with k + 1 helper columns. We show that there exist many encoding matrices such that the corresponding binary MDS array codes can asymptotically achieve weak-optimal repair for repairing any information column.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61701115, 61671007).

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  1. School of Electrical Engineering & Intelligentization, Dongguan University of Technology, Dongguan, 523808, China

    Hanxu Hou & Yunghsiang S. Han

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  1. Hanxu Hou
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  2. Yunghsiang S. Han
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Correspondence to Hanxu Hou.

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Hou, H., Han, Y.S. A class of binary MDS array codes with asymptotically weak-optimal repair. Sci. China Inf. Sci. 61, 100302 (2018). https://doi.org/10.1007/s11432-018-9485-7

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  • DOI: https://doi.org/10.1007/s11432-018-9485-7

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