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