Research Statement:
The current research focus of our group is on

1) Developing new approaches for studying problems in bioinformatics and bioengineering using coding and information theory. In particular, we investigate fundamental questions pertaining to design methodologies for DNA microarrays with error- and quality-control features and DNA microarrays that utilize compressed sensing principles.

2) Providing a bridge between the theory of compressed sensing and superimposed coding; non-linear compressive sensing with quantization and fault-tolerant sensing algorithms.

3) Using coding and information theory to study problems such as RNA folding, reverse engineering of gene-regulatory networks, and cost-constrained genome reversal distances.

4) Constructing and analyzing codes on graphs and developing new methods for studying the combinatorial properties of random ensembles of low-density parity-check codes. Our studies mainly focus on the computational complexity of problems quantifying the error-floor phenomena.

5) Analyzing the connections between network coding, matroid theory, and algebraic coding theory.

6) Analyzing the average case complexity of algorithms in coding theory and computer algebra.