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http://hdl.handle.net/10773/26627
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 Realizations |
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 |
URI: | http://hdl.handle.net/10773/26627 |
DOI: | 10.2478/amcs-2019-0039 |
ISSN: | 1641-876X |
Publisher Version: | https://www.amcs.uz.zgora.pl/?action=paper&paper=1509 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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NappPerePintRoch19.pdf | 411.13 kB | Adobe PDF | View/Open |
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