On a Class of Systematic IIR Convolutional Codes and its Properties

Abstract

In this paper, an important class of convolutional encoders, i.e. the systematic IIR convolutional encoder $C_conv (2, 1, 2)$, is considered. We obtain state diagram and modified state diagram for this class. Moreover, we examine generating function and minimum free distance. It is shown that the maximum value of the minimum free distance for this class of encoders is equal to 5 which can only be achieved in two cases.