A generalized Euclidean algorithm for multisequence shift-register synthesis

Author

Feng, Gui-Liang ; Tzeng, Kenneth K.

Author_Institution

Dept. of Comput. Sci. & Electr. Eng., Lehigh Univ., Bethlehem, PA, USA

Volume

35

Issue

3

fYear

1989

fDate

5/1/1989 12:00:00 AM

Firstpage

584

Lastpage

594

Abstract

The problem of finding a linear-feedback shift register of shortest length capable of generating prescribed multiple sequences is considered. A generalized Euclidean algorithm, which is based on a generalized polynomial division algorithm, is presented. A necessary and sufficient condition for the uniqueness of the solution is given. When the solution is not unique, the set of all possible solutions is also derived. It is shown that the algorithm can be applied to the decoding of many cyclic codes for which multiple syndrome sequences are available. When it is applied to the case of a single sequence, the algorithm reduces to that introduced by Y. Sugiyama et al. (Inf. Control, vol.27, p.87-9, Feb. 1975) in the decoding of BCH codes

Keywords

binary sequences; decoding; shift registers; cyclic codes; decoding; generalized Euclidean algorithm; generalized polynomial division algorithm; linear-feedback shift register; multiple syndrome sequences; multisequence shift-register synthesis; Combinatorial mathematics; Computer science; Iterative algorithms; Iterative decoding; Linear feedback shift registers; Milling machines; Polynomials; Shift registers; Sufficient conditions;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.30981

Filename

30981