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

Pinho, Telma; Pinto, Raquel; Rocha, Paula

doi:10.1007/s10623-012-9768-1

Cited by 5 publications

(5 citation statements)

References 14 publications

(20 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Early on there was the river pollution modeling Fornasini (1991) that established a role for the Fornasini-Marchesini model but with limited follow up. Also there continues to be research conducted on the use of 2D systems analysis for convolutional codes, see, e.g., Pinto, Pinto, and Rocha (2014), Valcher and Fornasini (1994) (where the second reference uses the Roesser model but links back to the 2D realization problem discussed in Section 7).…”

Section: Applicationsmentioning

confidence: 99%

Control systems analysis for the Fornasini-Marchesini 2D systems model – progress after four decades

Gałkowski

Rogers

2018

International Journal of Control

View full text Add to dashboard Cite

The development of a control systems theory for multidimensional linear systems, i.e., systems with more than one independent variable is an area where a very significant volume of research is based on representations for the underlying dynamics introduced in the 1970s. One of these is the Fornasini-Marchesini state-space model published in 1978. This paper reviews the significant developments in the succeeding four decades in both theory and application, where the second area includes examples where this model description is an enabler the analysis of other classes of systems.

show abstract

Section: Applicationsmentioning

confidence: 99%

Control systems analysis for the Fornasini-Marchesini 2D systems model – progress after four decades

Gałkowski

Rogers

2018

International Journal of Control

View full text Add to dashboard Cite

show abstract

“…Two-dimensional (2D) convolutional codes naturally extend the notion of 1D convolutional codes, see for instance [5,14,22,30]. We are going to consider convolutional codes whose codewords belong to…”

Section: Two-dimensional (2d) Convolutional Codesmentioning

confidence: 99%

MDS 2D convolutional codes with optimal 1D horizontal projections

Almeida

Napp

Pinto

2017

Des. Codes Cryptogr.

Self Cite

View full text Add to dashboard Cite

Two dimensional (2D) convolutional codes is a class of codes that generalizes standard one-dimensional (1D) convolutional codes in order to treat two dimensional data. In this paper we present a novel and concrete construction of 2D convolutional codes with the particular property that their projection onto the horizontal lines yield optimal (in the sense of [2]) 1D convolutional codes with a certain rate and certain Forney indices. Moreover, using this property we show that the proposed constructions are indeed Maximum Distance Separable (MDS), i.e., are 2D convolutional codes having the maximum possible distance among all 2D convolutional codes with the same parameters. The key idea is to use a particular type of superregular matrices to build the generator matrix.

show abstract

“…However, the general problem of a minimal state space realization of multidimensional systems has not been solved even for 2-dimensional systems. Nevertheless, for some special cases, minimal state space realization methods have been derived; see the works of Zerz (2000), Pinho et al (2014), Pinho (2016), Napp et al (2010), Galkowski (1996; and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we continue this thread of research by considering periodic 2D convolutional codes and the corresponding minimal state space realization problem. Although some results have been obtained in the context of time-invariant 2D convolutional codes (Pinho et al, 2014;Fornasini et al, 2015) and 1D periodic convolutional codes (Climent et al, 2009), this problem remains unexplored in the context of periodic 2D convolutional codes. Here we aim at deriving state Roesser 2D state space representations (Aleixo and Rocha, 2017;Kaczorek, 2001) from a (2,2)-periodic two-dimensional generator matrix.…”

Section: Introductionmentioning

confidence: 99%

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

Napp

Pereira

Pinto

et al. 2019

International Journal of Applied Mathematics and Computer Science

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 5 publications

References 14 publications

Control systems analysis for the Fornasini-Marchesini 2D systems model – progress after four decades

Control systems analysis for the Fornasini-Marchesini 2D systems model – progress after four decades

MDS 2D convolutional codes with optimal 1D horizontal projections

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

Contact Info

Product

Resources

About