System-theoretic properties of convolutional codes over rings

Author

Fagnani, Fabio ; Zampieri, Sandro

Author_Institution

Dipartimento di Matematica, Politecnico di Torino, Italy

Volume

47

Issue

6

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

2256

Lastpage

2274

Abstract

Convolutional codes over rings are particularly suitable for representing codes over phase-modulation signals. In order to develop a complete structural analysis of this class of codes, it is necessary to study rational matrices over rings, which constitutes the generator matrices (encoders) for such convolutional codes. Noncatastrophic, minimal, systematic, and basic generator matrices are introduced and characterized by using a canonical form for polynomial matrices over rings. Finally, some classes of convolutional codes, defined according to the generator matrix they admit, are introduced and analyzed from a system-theoretic point of view

Keywords

convolutional codes; modulation coding; phase modulation; polynomial matrices; Noetherian rings; basic generator matrices; complete structural analysis; convolutional codes; minimal generator matrices; noncatastrophic generator matrices; phase-modulation signals; polynomial matrices; rational matrices; rings; system-theoretic properties; systematic generator matrices; Character generation; Convolutional codes; Modulation coding; Orbits; Phase shift keying; Polynomials; Power generation;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.945247

Filename

945247