Codes with Locality for Two Erasures

Prakash, N and Lalitha, V and Kumar, Vijay P (2015) Codes with Locality for Two Erasures. In: IEEE International Symposium on Information Theory (ISIT), JUN 29-JUL 04, 2014, Honolulu, HI, pp. 1962-1966.

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Abstract

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated with small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan et al, in which recovery from a single erasure is considered. By studying the generalized Hamming weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turan graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from 2 erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.

Item Type:	Conference Proceedings
Series.:	IEEE International Symposium on Information Theory
Publisher:	IEEE
Additional Information:	Copy right for this article belongs to the IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, JUN 29-JUL 04, 2014
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	05 Mar 2015 12:53
Last Modified:	05 Mar 2015 12:53
URI:	http://eprints.iisc.ac.in/id/eprint/51011

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