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2017 | OriginalPaper | Chapter

Input-State-Output Representations of Concatenated 2D Convolutional Codes

Authors : Diego Napp, Raquel Pinto, Rita Simões

Published in: CONTROLO 2016

Publisher: Springer International Publishing

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Abstract

In this paper we investigate a novel model of concatenation of a pair of two-dimensional (2D) convolutional codes. We consider finite-support 2D convolutional codes and choose the so-called Fornasini-Marchesini input-state-output (ISO) model to represent these codes. More concretely, we interconnect in series two ISO representations of two 2D convolutional codes and derive the ISO representation of the obtained 2D convolutional code. We provide necessary condition for this representation to be minimal. Moreover, structural properties of modal reachability and modal observability of the resulting 2D convolutional codes are investigated.

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next chapter MDP Periodically Time-Varying Convolutional Codes

Climent, J.-J., Napp, D., Pinto, R., Simões, R.: Series concatenation of 2D convolutional codes. In: Proceedings IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS) (2015)

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Rocha, P.: Structure and representation of \(2\)-d systems. Ph.D. Dissertation, University of Groningen, Groningen, The Netherlands (1990)

Fornasini, E., Valcher, M.E.: Algebraic aspects of two-dimensional convolutional codes. IEEE Trans. Inf. Theory 40(4), 1068–1082 (1994)MathSciNetCrossRefMATH

Fornasini, E., Marchesini, G.: Structure and properties of two-dimensional systems. In: Tzafestas, S.G. (ed.) Multidimensional Systems, Techniques and Applications, pp. 37–88 (1986)

Valcher, M.E., Fornasini, E.: On 2D finite support convolutional codes: an algebraic approach. Multidimension. Syst. Signal Process. 5, 231–243 (1994)MathSciNetCrossRefMATH

Napp, D., Perea, C., Pinto, R.: Input-state-output representations and constructions of finite support 2D convolutional codes. Adv. Math. Commun. 4(4), 533–545 (2010)MathSciNetCrossRefMATH

Climent, J.-J., Herranz, V., Perea, C.: A first approximation of concatenated convolutional codes from linear systems theory viewpoint. Linear Algebra Appl 425, 673–699 (2007)MathSciNetCrossRefMATH

Title: Input-State-Output Representations of Concatenated 2D Convolutional Codes
Authors: Diego Napp
Raquel Pinto
Rita Simões
Publisher: Springer International Publishing
Book: CONTROLO 2016
Print ISBN: 978-3-319-43670-8

Electronic ISBN: 978-3-319-43671-5

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-43671-5_1