The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We ...

In this thesis, we study problems under the theme of discovering joint sparsity structure in a set of high-dimensional data samples from linear measurements. Our primary focus is on the regime where the number of samples ...

The setting of the transmission of information over noisy, binary-input, memoryless channels is today well-understood, owing to the work of several information theorists, beginning with Claude Shannon. It is known that it ...

The goal of group testing, also called pool testing, is to successfully identify a set of k defectives from a population of n items using only m (< n) group tests. In each group test, a subset of the n items is tested ...

Information-theoretic arguments focus on modeling the reliability of information transmission, assuming availability of infinite data at sources, thus ignoring randomness in message generation times at the respective ...

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 ...

The classical binary error correcting codes, and subspace codes for error correction in random network coding are two different forms of error control coding. We identify common features between these two forms and study ...

In multiuser wireless communications, interference not only limits the performance of the system, but also allows users to eavesdrop on other users’ messages. Hence, interference management in multiuser wireless communication ...

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 ...