This thesis investigates lattice compression of polynomial matrices over finite fields. For an m x n matrix, the goal of lattice compression is to find an m x (m+k) matrix, for some relatively small k, such that the lattice span of two matrices are equivalent. For any m x n polynomial matrix with degree bound d, it can be compressed by multiplying by a random n x (m+k) matrix B with degree bound s. In this thesis, we prove that there is a positive probability that L(A)=L(AB) with k(s+1)=\Theta(\log(md)). This is shown to hold even when s=0 (i.e., where B is a matrix of constants). We also design a competitive probabilistic lattice compression algorithm of the Las Vegas type that has a positive probability of success on any input and requires O~(nm^{\theta-1}B(d)) field operations.

No description available.

A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implies that a covers a ∧ b. L is consistent if for every join-irreducible j and every element x in L, the element x ∨ j is a join-irreducible in the upper interval [x,l]. In this paper, finite dually semimodular consistent lattices are investigated. Examples of these lattices are the lattices of subnormal subgroups of a finite group. In 1954, R. P. Dilworth proved that in a finite modular lattice, the number of elements covering exactly k elements is equal to the number of elements covered by exactly k elements. Here, it is established that if a finite dually semimodular consistent lattice has the same number of join-irreducibles as meet-irreducibles, then it is modular. Hence, a converse of Dilworth's theorem, in the case when k equals 1, is obtained for finite dually semimodular consistent lattices. Several combinatorial results are shown for finite consistent lattices similar to those already established for finite geometric lattices. The reach of an element x in a lattice L is the difference between the rank of x*, the join of x and all the elements covering x, and the rank of x; the maximum reach of all elements in L is the reach of L. Sharp lower bounds for the total number of elements and the number of elements of a given reach in a semimodular consistent lattice given the rank, the reach, and the number of join-irreducibles are found. Extremal lattices attaining these bounds are described. Similar results are then obtained for finite dually semimodular consistent lattices.

In wireless communication, MIMO (multiple input multiple output) is one of the promising technologies which improves the range and performance of transmission without increasing the bandwidth, while providing high rates. High speed hardware MIMO decoders are one of the keys to apply this technology in applications. In order to support the high data rates, the underlying hardware must have significant processing capabilities. FPGA improves the speed of signal processing using parallelism and reconfigurability advantages. The objective of this thesis is to develop an efficient hardware architectural model for the universal lattice decoder and prototype it on FPGA. The original algorithm is modified to ensure the high data rate via taking the advantage of FPGA features. The simulation results of software, hardware are verified and the BER performance of both the algorithms is estimated. The system prototype of the decoder with 4-transmit and 4-receive antennas using a 4-PAM (Pulse amplitude modulation) supports 6.32 Mbit/s data rate for parallelpipeline implementation on FPGA platform, which is about two orders of magnitude faster than its DSP implementation.

No description available.

Bibliography: leaves 124-127.

Bibliography: leaves 124-127. / ix, 127 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2002

Bibliography: p. 222-229. / vii, 229 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Constructs an overlap operator to realise chiral symmetry on a quantum chromodynamic lattice that is faster to evaluate computationally than the Dirac operator, though the use of an alternative kernel, the Fat Link Irrelevant Clover (FLIC) action. Investigates the properties of FLIC Overlap fermions through the quark propagator in momentum space via topology. These calculations are performed in both the quenched and the dynamical kernel approximation, a type of partial quenching. In the quenched approximation, the effects of fermion vacuum fluctuations are neglected in the creation of gluon field configurations, In the partially quenched approximation, a different fermionic action is used in the sea and valence sectors. Develops a means of including the effects of FLIC sea fermions in the gluonic background field and presents an implementation of code optimised for cluster computing. / Thesis (Ph.D.)--University of Adelaide, School of Chemistry and Physics, Discipline of Physics, 2004

No description available.

Thesis--Bonn. Extra t.p. with thesis statement inserted. / Includes bibliographical references (p. 45).