On multidimensional convolutional codes and controllability properties of multidimensional systems over finite rings

Zerz, Eva

doi:10.1002/asjc.169

Cited by 18 publications

(14 citation statements)

References 16 publications

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“…The available representations let us describe the dynamics of the encoders of the codes or constructing convolutional codes with certain good properties such as observability. Recently, the study of convolutional codes over nite elds has been developed through these relations based on rst order representations and input/state/output (I/S/O) representations and references therein [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Feedback equivalence of convolutional codes over finite rings

DeCastro-García

2017

Open Mathematics

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Abstract:The approach to convolutional codes from the linear systems point of view provides us with e ective tools in order to construct convolutional codes with adequate properties that let us use them in many applications. In this work, we have generalized feedback equivalence between families of convolutional codes and linear systems over certain rings, and we show that every locally Brunovsky linear system may be considered as a representation of a code under feedback convolutional equivalence.

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Section: Introductionmentioning

confidence: 99%

Feedback equivalence of convolutional codes over finite rings

DeCastro-García

2017

Open Mathematics

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“…Several attempts aiming at the construction and implementation of this type of codes have been presented in [1], [2], [4], [11], [17], [19], [20], [24], [34].…”

Section: Introductionmentioning

confidence: 99%

Maximum Distance Separable 2D Convolutional Codes

Climent

Napp

Perea

et al. 2016

IEEE Trans. Inform. Theory

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Maximum Distance Separable (MDS) block codes and MDS one-dimensional (1D) convolutional codes are the most robust codes for error correction within the class of block codes of a fixed rate and 1D convolutional codes of a certain rate and degree, respectively. In this paper we generalize this concept to the class of two-dimensional (2D) convolutional codes. For that we introduce a natural bound on the distance of a 2D convolutional code of rate k/n and degree δ, which generalizes the Singleton bound for block codes and the generalized Singleton bound for 1D convolutional codes. Then we prove the existence of 2D convolutional codes of rate k/n and degree δ that reach such bound when n ≥ kif k | δ, by presenting a concrete constructive procedure. Index Terms2D convolutional code, generalized Singleton bound, maximum distance separable code, superregular matrix, circulant Cauchy matrix.

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“…However, they were not very developed on the subsequent years. Recently, these codes have been a matter of interest by several authors [2,3,14,15,24].…”

Section: Introductionmentioning

confidence: 99%

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

Pinho

Pinto

Rocha

2012

Des. Codes Cryptogr.

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In this paper, two-dimensional convolutional codes constituted by sequences in (F n ) Z 2 where F is a finite field, are considered. In particular, we restrict to codes with rate 1 n and we investigate the problem of minimal dimension for realizations of such codes by separable Roesser models. The encoders which allow to obtain such minimal realizations, called R-minimal encoders, are characterized.

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On multidimensional convolutional codes and controllability properties of multidimensional systems over finite rings

Cited by 18 publications

References 16 publications

Feedback equivalence of convolutional codes over finite rings

Feedback equivalence of convolutional codes over finite rings

Maximum Distance Separable 2D Convolutional Codes

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

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