In a distributed storage system, due to increase of storage capacity of a node, efficient repair of failed nodes is becoming increasingly important in addition to ensuring a given level of reliability and low storage overhead. Codes with locality are a class of codes designed for storage systems which have the characteristic that they trade off repair locality (number of nodes accessed to repair a failed node) for storage overhead.
Maximally recoverable codes are a class of codes which correct maximum possible number of erasure patterns, given the locality constraints of the code and hence of interest. Two classes of maximally recoverable codes (MRC) based on the topology of the local parities will be introduced (i) MRC with hierarchical locality (ii) MRCs with product topologies. For the case of MRC with hierarchical locality, we will present explicit constructions for all parameters and field size bounds. For the case of MRCs with product topologies, we describe a certain regularity condition necessary for the erasure patterns to be recoverable. Also, we establish a connection between the regularity condition and a complete matching in a suitably constructed bipartite graph. This is joint work with D. Shivakrishna, Aaditya M. Nair, V. Arvind Rameshwar and Birenjith Sasidharan.
Bio: Lalitha Vadlamani received the B.E. degree in electronics and communication engineering from Osmania University, Hyderabad, in 2003, and the M.E. and Ph.D. degrees from the Indian Institute of Science (IISc), Bengaluru, in 2005 and 2015, respectively. Since May 2015, she has been working as an Assistant Professor with IIIT Hyderabad, where she is currently with the Signal Processing and Communications Research Center. Her research interests include coding for distributed storage and computing, index coding, polar codes, learning-based codes and coded blockchains. She was a recipient of Prof. I. S. N. Murthy medal from IISc in 2005, and the TCS Research Scholarship for the year 2011. Her article won the runner up best paper award at NCC 2019.