State space and polynomial matrix parametrization of minimal convolutional encoders

The paper discusses the possibility of characterizing some important properties of convolutional codes and its encoders and syndrome formers by means of matrix fraction descriptions and state space models. A complete parametrization is then provided for all minimal encoders and minimal syndrome formers of a given code. Finally state feedback and static precompensation (resp.output injection and postcompensation) allow to synthesize all minimal encoders (resp. minimal syndrome formers), when a minimal one is available.