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On the locality of codeword symbols (2012)
| Venue: | IEEE Trans. Inform. Theory |
| Citations: | 49 - 2 self |
BibTeX
@ARTICLE{Gopalan12onthe,
author = {Parikshit Gopalan and Cheng Huang and Huseyin Simitci and Sergey Yekhanin},
title = {On the locality of codeword symbols},
journal = {IEEE Trans. Inform. Theory},
year = {2012},
pages = {6925--6934}
}
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Abstract
Consider a linear [n, k, d]q code C. We say that that i-th coordinate of C has locality r, if the value at this coordinate can be recovered from accessing some other r coordinates of C. Data storage applications require codes with small redundancy, low locality for information coordinates, large distance, and low locality for parity coordinates. In this paper we carry out an in-depth study of the relations between these parameters. We establish a tight bound for the redundancy n−k in terms of the message length, the distance, and the locality of information coordinates. We refer to codes attaining the bound as optimal. We prove some structure theorems about optimal codes, which are particularly strong for small distances. This gives a fairly complete picture of the tradeoffs between codewords length, worst-case distance and locality of information symbols. We then consider the locality of parity check symbols and erasure correction beyond worst case distance for optimal codes. Using our structure theorem, we obtain a tight bound for the locality of parity symbols possible in such codes for a broad class of parameter settings. We prove that there is a tradeoff between having good locality for parity checks and the ability to correct erasures beyond the minimum distance. 1
Keyphrases
codeword symbol information coordinate low locality optimal code tight bound worst case distance broad class message length parity coordinate large distance good locality data storage application parameter setting worst-case distance parity check symbol minimum distance structure theorem codewords length erasure correction small redundancy parity symbol complete picture information symbol parity check small distance i-th coordinate in-depth study
