An independent set in a graph G is a set of pairwise nonadjacent vertices, and the maximum size, alpha(G), of an independent set in G is called the independence number. Given a graph G and weight matrix A of G with entries ...

Joint source-channel coding (JSCC) has emerged to be a major field of research recently. Channel optimized vector quantization (COVQ) is a simple feasible JSCC scheme introduced for communication over practical channels. In ...

Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this thesis, we introduce the notion of a ...

Linear programming (LP) decoding of low-density parity-check codes was introduced by Feldman et al. in [1]. In his formulation it is assumed that communication takes place over a memoryless channel and that the source is ...

In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper ...

Traditionally, source coding (data compression) and channel coding (error protection) are performed separately and sequentially, resulting in what we call a tandem (separate) coding system. In practical implementations, ...

Reduction theory for systems with symmetry deals with the problem of understanding dynamics on a manifold with an action of a Lie group. In geometric mechanics, this problem can be formulated in the Lagrangian, Hamiltonian ...