A first approximation of concatenated convolutional codes from linear systems theory viewpoint

This article focuses on the characterization of two models of concatenated convolutional codes from the perspective of linear systems theory. We present an input-state-output representation of these models and study the conditions for obtaining a minimal input-state-output representation and non-catastrophic concatenated convolutional code. We also establish conditions so that the concatenated codes are observable and give a lower bound for their free distances.