Abstract
In a distributed storage system, due to increase of storage capacity of a node, efficient repair of failed nodes has become increasingly important in addition to ensuring a given level of reliability and low storage overhead. Locally repairable codes 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. Three classes of maximally recoverable codes (MRC) based on the topology of the local parities will be introduced (i) MRC with locality (iii) MRC with hierarchical locality and (iii) Maximally Recoverable Tensor codes. Bounds, constructions and open problems related to these classes of MRCs will be discussed.