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.