Coding Theory and Applications pp 185-193 | Cite as
Minimal Realizations of Syndrome Formers of a Special Class of 2D Codes
Abstract
In this paper we consider a special class of 2D convolutional codes (composition codes) with encoders G(d1, d2) that can be decomposed as the product of two 1D encoders, i.e., \(G(d_{1},d_{2}) = G_{2}(d_{2})G_{1}(d_{1})\). In case that \(G_{1}(d_{1})\) and \(G_{2}(d_{2})\) are prime we provide constructions of syndrome formers of the code, directly from \(G_{1}(d_{1})\) and \(G_{2}(d_{2})\). Moreover we investigate the minimality of 2D state-space realization by means of a separable Roesser model of syndrome formers of composition codes, where \(G_{2}(d_{2})\) is a quasi-systematic encoder.
Keywords
Encoders and syndrome forms 2D composition codes 2D state-space modelsNotes
Acknowledgements
This work was supported by Portuguese funds through the CIDMA – Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundac̣ão para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013.
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