Optimal Linear Codes with a Local-Error-Correction Property

Prakash, N and Kamath, Govinda M and Lalitha, V and Kumar, Vijay P (2012) Optimal Linear Codes with a Local-Error-Correction Property. In: IEEE International Symposium on Information Theory , JUL 01-06, 2012, Cambridge, MA.

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Abstract

Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.

Item Type:	Conference Paper
Series.:	IEEE International Symposium on Information Theory
Publisher:	IEEE
Additional Information:	Copy right for this article belongs to IEEE, NEW YORK, USA
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering > Electrical Communication Engineering - Technical Reports
Date Deposited:	07 Feb 2013 09:20
Last Modified:	07 Feb 2013 09:20
URI:	http://eprints.iisc.ac.in/id/eprint/45755

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