Distributed storage systems (DSS) are increasingly being employed by various technologies. While the size of data, number of storage components, and number of users connecting to these servers are dramatically growing, efficiency of the system, in the sense of a fundamental tradeoff between the overhead penalty paid to provide robustness and the cost of system maintenance, is becoming the key factor to determine their performance. Exact-repairability is a desired property for the underlying storage code in order to ease the system maintenance. Characterizing the optimal tradeoff between storage and repair-bandwidth is a challenging open problem for a general DSS with exact-repair property, which is not only of theoretical interest, but also has a significant influence on the design of practical and efficient storage systems.
Motivated by the prevalence and practical applicability of linear codes, we have considered the exact repair trade-off when the underlying code is restricted to be linear. We established new information-theoretical bounds on the trade-off of the system, for an important class of network parameters. The new approach utilizes the properties of linear codes and vector spaces over finite fields, together with the exact repair constraints. These constraints are formally captured through an optimization problem with a recursive structure, and its solution yields the new bounds for the linear DSS. Inspired by the solution of the optimization problem, we were able to design a class of codes, which beside having other practically desired properties, can perform at the derived upper bound. These matching performances yield to a complete characterization for linear DSS with the parameters of interest.
Soheil Mohajer is an Assistant Professor at the Electrical and Computer Engineering department, University of Minnesota, Twin Cities. He received the B.S. degree from Sharif University of Technology, Tehran, in 2004, and his M.Sc. and Ph.D. degrees from Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland, in 2005 and 2010, respectively. He was with Princeton University, New Jersey, as a post-doctoral research associate for one year, before joining UC Berkeley as post-doctoral fellow in October 2011. He was a recipient of the Swiss National Science Foundation Prospective Researcher Fellowship in 2010.
His research interests include information theory, distributed storage, statistical machine learning, and bioinformatics.