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Explicit MDS Codes for Optimal Repair Bandwidth

Wang, Zhiying and Tamo, Itzhak and Bruck, Jehoshua (2014) Explicit MDS Codes for Optimal Repair Bandwidth. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20160120-152728882

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Abstract

MDS codes are erasure-correcting codes that can correct the maximum number of erasures for a given number of redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting all the remaining data in the code, the original information can be recovered. However, it was shown that in order to recover a single symbol erasure, only a fraction of 1/r of the information needs to be transmitted. This fraction is called the repair bandwidth (fraction). Explicit code constructions were given in previous works. If we view each symbol in the code as a vector or a column over some field, then the code forms a 2D array and such codes are especially widely used in storage systems. In this paper, we address the following question: given the length of the column l, number of parities r, can we construct high-rate MDS array codes with optimal repair bandwidth of 1/r, whose code length is as long as possible? In this paper, we give code constructions such that the code length is (r +1) log_r l.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1411.6328arXivDiscussion Paper
Additional Information:Submitted on 24 Nov 2014.
Record Number:CaltechAUTHORS:20160120-152728882
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160120-152728882
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:63812
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Jan 2016 16:52
Last Modified:05 Jan 2018 17:48

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