Interconnection networks play important roles in designing high performance computers. Recently two new classes of interconnection networks based on the concept of Gaussian and Eisenstein-Jacobi integers were introduced. In this research, efficient routing and broadcasting algorithms for these networks are developed. Furthermore, constructing edge disjoint Hamiltonian cycles in Gaussian networks...
Parallel processors are classified into two classes: shared-memory multiprocessors and distributed- memory multiprocessors. In the shared-memory system, processors communicate through a common memory unit. However, in the distributed multiprocessor system, each processor has its own memory unit and the communications among the processors are performed through an interconnection network. Thus,...
Many algorithms in parallel systems can be easily solved if we can generate a Hamiltonian cycle on the underly network. Finding Hamiltonian cycle is a well known NP-complete problem. For specific instances of regular graphs, such as Torus and Gaussian network, one can easily find Hamiltonian cycles. In this thesis,...
A relatively new model of error control is the limited magnitude error over high radix channels. In this error model, the error magnitude does not exceed a certain limit known beforehand. In this dissertation, we study systematic error control codes for common channels under the assumption that the maximum error...
An n-bit Gray code is an ordered set of all 2n binary strings of length n. The
special property of this listing is that Hamming distance between consecutive vectors
is exactly 1. If the last and first codeword also have a Hamming distance 1 then the
code is said to...
In diversity combining automatic repeat request (ARQ), erroneous packets are combined together forming a single, more reliable, packet. In this thesis, we give a diversity combining scheme for the m-ary unidirectional channel. A system using the given scheme with a t-unidirectional error detecting code is able to correct up to...
This work gives some theory and efficient design of binary block codes capable of controlling the deletions of the symbol “0” (referred to as 0-deletions) and/or the insertions of the symbol “0” (referred to as 0-insertions). This problem of controlling 0-deletions and/or 0-insertions (referred to as symmetric 0-errors) is shown...