Concatenated linear systems over rings and their application to construction of concatenated families of convolutional codes

We present a generalization of the theory of concatenated linear systems to commutative rings with identity. Moreover, we highlight sufficient conditions to obtain reachable and observable concatenated linear systems. This approach provides us with minimal input-state-output representations by means of which we can construct observable concatenated families of convolutional codes with different parameters over some particular rings. This work focuses on the characterization of models of serial, systematic serial and parallel concatenation.