Caitriona Lucey graduated in 2007.
PhD. Thesis Title: FIR Paraunitary Multirate Filter Banks over GF(2r) and their Factorisations
Abstract: From an applications perspective, M-channel PU filter banks have recently been used to design error correction codes and new cryptographic schemes. In this thesis we examine a new type of hard-decision decoder for quasi-cyclic block codes, called a polyphase decoder. This decoder arises from a multirate filter bank view on block codes. We discover on further investigation, however, that the polyphase decoder is isomorphic to a previously known decoder, which was introduced by Karlin. Nevertheless, other positive results exist on designing error correction codes using a multirate filter bank approach. It is envisaged that the M-channel PU factorisation results of this thesis will enable further investigations of these codes.