On Partial Maximally-Recoverable and Maximally-Recoverable Codes

Balaji, SB and Kumar, Vijay P (2015) On Partial Maximally-Recoverable and Maximally-Recoverable Codes. In: IEEE International Symposium on Information Theory (ISIT), JUN 14-19, 2015, Hong Kong, PEOPLES R CHINA, pp. 1881-1885.

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Abstract

An n, k] linear code C that is subject to locality constraints imposed by a parity check matrix H-0 is said to be a maximally recoverable (MR) code if it can recover from any erasure pattern that some k-dimensional subcode of the null space of H-0 can recover from. The focus in this paper is on MR codes constrained to have all-symbol locality r. Given that it is challenging to construct MR codes having small field size, we present results in two directions. In the first, we relax the MR constraint and require only that apart from the requirement of being an optimum all-symbol locality code, the code must yield an MDS code when punctured in a single, specific pattern which ensures that each local code is punctured in precisely one coordinate and that no two local codes share the same punctured coordinate. We term these codes as partially maximally recoverable (PMR) codes. We provide a simple construction for high-rate PMR codes and then provide a general, promising approach that needs further investigation. In the second direction, we present three constructions of MR codes with improved parameters, primarily the size of the finite field employed in the construction.

Item Type:	Conference Proceedings
Series.:	IEEE International Symposium on Information Theory
Additional Information:	Copy right for this article belongs to the IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	07 Dec 2016 05:45
Last Modified:	07 Dec 2016 05:45
URI:	http://eprints.iisc.ac.in/id/eprint/55512

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