Thesis (M. Phil.)--University of Hong Kong, 2007. / Also available online.

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Includes bibliographical references (p. 84-87).

A new approach to the analysis of the structural properties of multivariable convolutional codes over finite fields is presented. It is based on the properties of the state transition graph which can be considered as a generalization to the multivariable case of the classical Good-De-Bruijn graph associated with linear shift register sequences. The concept of a minimal graph is introduced and shown to be isomorphic to the class of all minimal encoders previously defined by Forney. Straightforward algorithms based on simple algebraic and graph manipulations are introduced to allow for the reduction of any state transition graph to a minimal form. Furthermore each stage in the reduction procedure is shown to be related to some fundamental system theoretic concept including the conditions for causal invertibility, pseudo invertibility and polynomial invertibility of a linear feedforward system. By using the concept of dual codes and introducing a straightforward algorithm for the construction of a dual encoder in minimal form which is valid on any field; a simple procedure is further devised providing for the reduction of any rational basis to a minimal polynomial form and the applications of this result to multivariable realization theory are discussed. Finally several non exhaustive applications of the above mentioned concepts to linear system theory are developed. A special emphasis is placed on the solution of the problem associated with the construction of the class of all minimal order, minimal delay pseudo inverses of any realizable linear system. Furthermore, we present a solution to the minimal partial realization problem for vectored sequences based on the use of a Berlekamp-Massey type algorithm.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 73-75). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 73-75). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 76-79). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 76-79). Also available on the Internet.