Realization of 2D (2,2)-Periodic Encoders by Means of 2D Periodic Separable Roesser Models

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Diego Napp (Author) Other; Ricardo Pereira (Author) Other; Raquel Pinto (Author) Other; Paula Rocha (Author) FEUP

Journal

Title: International Journal of Applied Mathematics and Computer Science

Vol. 29 No. 3

Pages: 527-539

ISSN: 1641-876X

Publisher: Walter De Gruyter

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00R-4WZ

DOI: 10.2478/amcs-2019-0039

Abstract (EN): It is well known that convolutional codes are linear systems when they are defined over a finite field. A fundamental issue in the implementation of convolutional codes is to obtain a minimal state representation of the code. Compared with the literature on one-dimensional (1D) time-invariant convolutional codes, there exist relatively few results on the realization problem for time-varying 1D convolutional codes and even fewer if the convolutional codes are two-dimensional (2D). In this paper we consider 2D periodic convolutional codes and address the minimal state space realization problem for this class of codes. This is, in general, a highly nontrivial problem. Here, we focus on separable Roesser models and show that in this case it is possible to derive, under weak conditions, concrete formulas for obtaining a 2D Roesser state space representation. Moreover, we study minimality and present necessary conditions for these representations to be minimal. Our results immediately lead to constructive algorithms to build these representations.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13