Aaditya M Nair received his MS-Dual Degree in Computer Science and Engineering. His research work was supervised by Dr. Lalitha Vadlamani. Here’s a summary of Aaditya M Nair’s M.S thesis, Maximally Recoverable Codes with Hierarchical Locality as explained by him:
With the exponential increase in the amount of data being stored in the cloud, a lot of distributed storage systems have started moving to erasure coding based storage schemes due to their advantage of providing the same reliability as replication with a smaller storage overhead. Locally recoverable codes have started being the defacto code of choice for their ability to correct a small number of erasures by only accessing a small number of other coordinates. Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with locality. The notion of locality has been extended to hierarchical locality, which allows for locality to gradually increase in levels with the increase in the number of erasures. We consider the locality constraints imposed by codes with two-level hierarchical locality and define maximally recoverable codes with data-local and local hierarchical locality. We derive certain properties related to their punctured codes and minimum distance. We give a procedure to construct hierarchical data-local MRCs from hierarchical local MRCs. We then provide a construction of hierarchical local MRCs for all parameters. We then provide an alternate construction using tensor product codes that construct the code in a smaller field. This construction works for a restricted set of parameters. Research shows that the most commonly deployed LRCs have low number of global parities. Hence, we then consider three cases, with a small (and sometimes fixed) number of global and mid-level parities and provide a separate construction for them. These constructions use smaller fields still.