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01.01.2014 | Ausgabe 1-2/2014

Designs, Codes and Cryptography 1-2/2014

Realization of 2D convolutional codes of rate \(\frac{1}{n}\) by separable Roesser models

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 1-2/2014
Autoren:
Telma Pinho, Raquel Pinto, Paula Rocha
Wichtige Hinweise
This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding Theory and Applications”.

Abstract

In this paper, two-dimensional convolutional codes constituted by sequences in \((\mathbb F ^n)^{\mathbb{Z }^{2}}\) where \(\mathbb F \) is a finite field, are considered. In particular, we restrict to codes with rate \(\frac{1}{n}\) and we investigate the problem of minimal dimension for realizations of such codes by separable Roesser models. The encoders which allow to obtain such minimal realizations, called R-minimal encoders, are characterized.

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