Minimal State-Space Representation of Convolutional Product Codes

Joan-Josep Climent, Diego Napp, Raquel Pinto and Verónica Requena
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Joan-Josep Climent: Departament de Matemàtiques, Universitat d’Alacant, E-03690 Alacant, Spain
Diego Napp: Departament de Matemàtiques, Universitat d’Alacant, E-03690 Alacant, Spain
Raquel Pinto: CIDMA—Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Verónica Requena: Departament de Matemàtiques, Universitat d’Alacant, E-03690 Alacant, Spain

Mathematics, 2021, vol. 9, issue 12, 1-16

Abstract: In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.

Keywords: convolutional code; generator matrix; state-space representation; minimal representation; product code (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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