Convolutional Codes Over Finite Abelian Groups: Some Basic Results

Abelian groups provide the most natural structure to represent codes over phase modulation signals. Convolutional codes over finite Abelian groups are introduced and the properties of linear encoders for this class of codes are analyzed. Through the structure theorem for finitely generated Abelian groups this analysis can be reduced to the study of of convolutional codes over the ring Zn. We can in this way introduce the concept of encoding group and to compare it with the more classical input group introduced in [6]. In the last part of the paper the state space realization of a convolutional code and of a convolutional encoder is investigated.