Algebraic aspects of two-dimensional convolutional codes

Author

Fornasini, Ettore ; Valcher, Maria Elena

Author_Institution

Dept. of Electron. & Comput. Sci., Padova Univ., Italy

Volume

40

Issue

4

fYear

1994

fDate

7/1/1994 12:00:00 AM

Firstpage

1068

Lastpage

1082

Abstract

Two-dimensional (2D) codes are introduced as linear shift-invariant spaces of admissible signals on the discrete plane. Convolutional and, in particular, basic codes are characterized both in terms of their internal properties and by means of their input-output representations. The algebraic structure of the class of all encoders that correspond to a given convolutional code is investigated and the possibility of obtaining 2D decoders, free from catastrophic errors, as,veil as efficient syndrome decoders is considered. Some aspects of the state space implementation of 2D encoders and decoders via (finite memory) 2D system are discussed

Keywords

algebra; convolutional codes; decoding; state-space methods; admissible signals; algebraic structure; basic codes; decoders; discrete plane; encoders; finite memory 2D system; input-output representations; internal properties; linear shift-invariant space; state space implementation; syndrome decoder; two-dimensional convolutional codes; Convolution; Convolutional codes; Decoding; Ear; Helium; Inverse problems; Linear systems; Multidimensional systems; Polynomials; State-space methods;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.335967

Filename

335967