On MBR codes with replication

Krishnan, Nikhil M and Kumar, Vijay P (2016) On MBR codes with replication. In: IEEE International Symposium on Information Theory (ISIT), JUL 10-15, 2016, Barcelona, SPAIN, pp. 71-75.

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Abstract

An early paper by Rashmi et al. presented the construction of an (n, k, d = n - 1) MBR regenerating code featuring the inherent double replication of all code symbols and repair-by-transfer (RBT), both of which are important in practice. We first show that no MBR code can contain even a single code symbol that is replicated more than twice. We then go on to present two new families of MBR codes which feature double replication of all systematic message symbols. The codes also possess a set of d nodes whose contents include the message symbols and which can be repaired through help-by-transfer (HBT). As a corollary, we obtain systematic RBT codes for the case d = (n - 1) that possess inherent double replication of all code symbols and having a field size of O(n) in comparison with the general, O(n(2)) field size requirement of the earlier construction by Rashmi et al. For the cases (k = d = n - 2) or (k + 1 = d = n - 2), the field size can be reduced to q = 2, and hence the codes can be binary. We also give a necessary and sufficient condition for the existence of MBR codes having double replication of all code symbols and also suggest techniques which will enable an arbitrary MBR code to be converted to one with double replication of all code symbols.

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:	31 Jan 2017 08:33
Last Modified:	31 Jan 2017 08:33
URI:	http://eprints.iisc.ac.in/id/eprint/56189

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