Families of Convolutional Codes over Finite Fields: A Survey

The goal of this work is to give explicit interconnections between control theory and coding. It is well-known the existence of a closed relation between linear systems over finite fields and convolutional codes that allow to understand some properties of convolutional codes and to construct them. The connection between convolutional codes and linear systems permit to consider control as well as analyze observability of convolutional codes under linear systems point of view. An accurate look at the algebraic structure of convolutional codes using techniques of linear systems theory as well a study of input-state-output representation control systems. A particular property considered in control systems theory called output-controllability property is analyzed and used for solve the decoding process of this kind of codes.