IIIT Hyderabad Publications |
|||||||||
|
Codes with Locality for Two ErasuresAuthors: N Prakash,Lalitha Vadlamani,P Vijay Kumar, S.B. S.B. Balaji Journal: 2014 IEEE International Symposium on Information Theory (link) Pages: 7771-7789 Date: 2019-08-09 Report no: IIIT/TR/2019/120 AbstractIn this paper, we study codes with locality that canrecover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, wemean recovery via a single parity-check equation associated withsmall Hamming weight. Earlier approaches considered recoveryin parallel; the sequential approach allows us to potentiallyconstruct codes with improved minimum distance. These codes,which we refer to as locally 2-reconstructible codes, are anatural generalization along one direction, of codes with all-symbol locality introduced by Gopalanet al, in which recoveryfrom a single erasure is considered. By studying the generalizedHamming weights of the dual code, we derive upper boundson the minimum distance of locally 2-reconstructible codes andprovide constructions for a family of codes based on Tur ́angraphs, that are optimal with respect to this bound. The minimumdistance bound derived here is universal in the sense that no codewhich permits all-symbol local recovery from2erasures can havelarger minimum distance regardless of approach adopted. Ourapproach also leads to a new bound on the minimum distanceof codes with all-symbol locality for the single-erasure case. Full article: pdf Centre for Communications |
||||||||
Copyright © 2009 - IIIT Hyderabad. All Rights Reserved. |