published_or_final_version / Electrical Engineering / Doctoral / Doctor of Philosophy

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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.

The concept of systems accounts for the organization and patterns of order that characterize the natural world. Throughout the history of science, scientific activity has been based on this concept, either implicitly under a mechanistic approach or explicitly under an holistic systems approach. Contemporary science is now based on an holistic systems viewpoint that encompasses both the natural and social worlds as objects for study. Based on this context for the systems viewpoint, the thesis addresses archival constructs, arising spontaneously as a byproduct of societal activity, as instances of systems. This is an aspect of their nature that was recognized by traditional theorists, who devised the methodology that still fundamentally guides archival practice. However, the archival field has not yet recognized the applicability and utility of formal systems notions to the work of the archivist, specifically to the tasks of arrangement, description, and appraisal. The thesis argues that appropriate handling of archival constructs requires that they be treated as systems, that the concept of systems provides a necessary framework for archival theory, and that by adopting a systems viewpoint, the archival field may regain the status of a recognized profession and join with other fields of applied science that contribute to systems research.

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