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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
Lévy, B.C.: \(2\)d-polynomial and rational matrices and their applications for the modelling of \(2\)-d dynamical systems. Ph.D. Dissertation, Department of Electrical Engineering, Stanford University, Stanford, CA (1981)
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)
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)
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)
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)
Acknowledgments
The three authors were supported by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA), and The Portuguese Foundation for Science and Technology (FCT—Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2013.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Napp, D., Pinto, R., Simões, R. (2017). Input-State-Output Representations of Concatenated 2D Convolutional Codes. In: Garrido, P., Soares, F., Moreira, A. (eds) CONTROLO 2016. Lecture Notes in Electrical Engineering, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-319-43671-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-43671-5_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43670-8
Online ISBN: 978-3-319-43671-5
eBook Packages: EngineeringEngineering (R0)