Realization of 2D (2,2)-periodic encoders by means of 2D periodic separable Roesser models

• Autorzy: Napp Diego , Pereira Ricardo , Pinto Raquel , Rocha Paula

Identyfikatory

DOI

10.2478/amcs-2019-0039

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

periodic 2D system; convolutional codes; realization problems

PL

układ dwuwymiarowy; kod splotowy; problem realizacji

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2019
• Tom: Vol. 29, no. 3
• Strony: 527--539
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Napp Diego

• CIDMA, Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal

autor

Pereira Ricardo

• CIDMA, Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal

autor

Pinto Raquel

• CIDMA, Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal

autor

Rocha Paula

• SYSTEC, Faculty of Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto, Portugal

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).