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Title: Realization of 2D (2,2)-periodic encoders by means of 2D periodic separable Roesser models
Author: Pereira, Ricardo
Napp, Diego
Pinto, Raquel
Rocha, Paula
Keywords: Periodic 2D systems
Convolutional codes
Issue Date: Sep-2019
Publisher: University of Zielona Gora Press
Abstract: 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. In comparison to the literature on one-dimensional (1D) time-invariant convolutional codes, there exists only relatively few results on the realization problem for the 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 minimility and present necessary conditions for these representations to be minimal. Our results immediately lead to constructive algorithms to build these representations.
Peer review: yes
DOI: 10.2478/amcs-2019-0039
ISSN: 1641-876X
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Appears in Collections:CIDMA - Artigos
DMat - Artigos
SCG - Artigos

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