Maximally Recoverable Codesfor Distributed Storage Systems
In a distributed storage system, due to increase ofstorage capacity of a node, efficient repair of failed nodes is becomingincreasingly important in addition to ensuring a given level of reliability andlow storage overhead. Codes with locality are a class of codes designed forstorage systems which have the characteristic that they trade off repairlocality (number of nodes accessed to repair a failed node) for storageoverhead. Maximally recoverable codes are a class of codes which correct maximumpossible number of erasure patterns, given the locality constraints of the codeand hence of interest. Two classes of maximally recoverable codes (MRC) basedon the topology of the local parities will be introduced (i) MRC withhierarchical locality (ii) MRCs with product topologies. For the case of MRC with hierarchical locality, we willpresent explicit constructions for all parameters and field size bounds. Forthe case of MRCs with product topologies, we describe a certain regularitycondition necessary for the erasure patterns to be recoverable. Also, weestablish a connection between the regularity condition and a complete matchingin a suitably constructed bipartite graph. This is joint work with D.Shivakrishna, Aaditya M. Nair, V. Arvind Rameshwar and Birenjith Sasidharan.
LalithaVadlamani received her B.E. degree in Electronics and CommunicationEngineering from the Osmania University, Hyderabad, in 2003 and her M.E. andPh.D. degrees from the Indian Institute of Science (IISc), Bangalore, in 2005and 2015 respectively. From May 2015, she is working as Assistant professor inIIIT Hyderabad, where she is affiliated to Signal Processing and CommunicationsResearch Center. Prior to joining IIIT Hyderabad, she worked as a researchintern at Microsoft Research, Bangalore. Her research interests include codingfor distributed storage and computing, index coding, polar codes, Reed Mullercodes and coded blockchains