In this work, we study network coding technique, its relation to random matrices, and their applications to communication systems. The dissertation consists of three main contributions. First, we propose efficient algorithms for data synchronization via a broadcast channel using random network coding. Second, we study the resiliency of network coding...
Nonnegative matrices have a myriad of applications in the biological, social, and physical genres. Of particular importance are the primitive matrices. A nonnegative matrix, M, is primitive exactly when there is a positive integer, k, such that M[superscript k] has only positive entries; that is, all the entries in M[superscript...
Computing eigenpairs of a matrix corresponding to a specific geometry in the complex plane is an important topic in real time signal processing, pattern recognition, spectral analysis, systems theory, radar, sonar, and geophysics. We have studied the matrix sign and matrix sector function iterations to extract the eigenpairs belonging to...
Fully efficient systolic arrays for the solution of Toeplitz
matrices using Schur algorithm [1] have been obtained. By applying
clustering mapping method [2], the complexity of the algorithm is
0(n) and it requires n/2 processing elements as opposed to n
processing elements developed elsewhere [1].
The motivation of this thesis...
Advances in VLSI array processing have led to many new
parallel structures for real-time Digital Signal Processing (DSP)
applications. Among all the architectures, systolic arrays have played
an important role because systolic arrays have regular, local
interconnections with modular structure. In ordinary systolic arrays,
however, all processing operations and data...
This paper studies necessary and sufficient conditions for
a matrix to be conjunctive with its adjoint. The problem is solved
completely in the usual complex case, in which it is shown that a
matrix is conjunctive to its adjoint iff it is conjunctive to a real
matrix. The problem is...
In this thesis we define two nxn matrices T and S to be isoconjunctive if there exists an nxn nonsingular hermitian matrix H such that T = HSH. We then proceed to establish necessary and sufficient conditions that two nxn matrices T and S be isoconjunctive in the case where...