This thesis deals with the problem of code design in the setting of distributed storage systems consisting of multiple storage nodes, storing many different data les. A primary goal in such systems is the efficient repair ...

In this thesis, three problems have been considered and new coding schemes have been devised for each of them. The first is related to distributed function computation, the second to coding for distributed storage and the ...

We study minimization problems with respect to a one-parameter family of generalized relative entropies. These relative entropies, which we call relative -entropies (denoted I (P; Q)), arise as redundancies under mismatched ...

We study combinatorial optimization problems on graphs in the mean-field model, which assigns independent and identically distributed random weights to the edges of the graph. Specifically, we focus on two generalizations ...