Minimality and canonicity tests for rational generator matrices for convolutional codes

Author

Donoghue, Conor O. ; Burkley, Cyril J.

Author_Institution

Dept. of Electron. Eng., Limerick Univ., Ireland

fYear

1998

fDate

22-26 Jun 1998

Firstpage

112

Lastpage

113

Abstract

We derive computationally efficient minimality and canonicity tests for rational generator matrices for convolutional codes. The first set of tests are given in terms of easily obtained equivalent polynomial generator matrices and are suitable for small k and n. New tests are derived based on the scalar generator matrix G which are computationally more efficient for large k and n and small v. The application of these tests to generator matrices for (P)UM codes is studied. Finally, the results of O´Donoghue and Burkley (see Lecture Notes in Computer Science, vol.1365, p.258-65, 1997) are extended to the enumeration of minimal and canonical rational generator matrices

Keywords

convolutional codes; polynomial matrices; canonicity test; computationally efficient tests; convolutional codes; equivalent polynomial generator matrices; minimality test; rational generator matrices; scalar generator matrix; Character generation; Computational Intelligence Society; Constraint theory; Convolutional codes; Electronic equipment testing; Galois fields; Polynomials; State-space methods; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory Workshop, 1998

Conference_Location

Killarney

Print_ISBN

0-7803-4408-1

Type

conf

DOI

10.1109/ITW.1998.706459

Filename

706459