Title :
Dynamical systems and convolutional codes over finite Abelian groups
Author :
Fagnani, Fabio ; Zampieri, Sandro
Author_Institution :
Dipartimento di Elettronica e Inf., Padova Univ., Italy
fDate :
11/1/1996 12:00:00 AM
Abstract :
Polynomial algebraic techniques have always played a central role in linear systems theory and also in the theory of convolutional codes. We show how such techniques can be generalized to study systems and codes defined over Abelian groups. The systems are considered from the “behavioral” point of view as developed by Willems in the 1980s, and some of our results can be seen as extensions of Willems´ results to group systems. We also address a certain number of coding-oriented questions, and we propose concrete methods based on these algebraic techniques for the synthesis of encoders, inverters, and syndrome formers for codes over finite Abelian groups
Keywords :
convolutional codes; group theory; invertors; linear systems; polynomials; system theory; algebraic techniques; coding; convolutional codes; encoders; finite Abelian groups; group theory; inverters; linear systems theory; polynomial algebraic techniques; syndrome formers; systems behavior; Concrete; Control theory; Controllability; Convolutional codes; Difference equations; Helium; Inverters; Linear systems; Observability; Signal processing;
Journal_Title :
Information Theory, IEEE Transactions on