Series concatenation of 2D convolutional codes by means of input-state-output representations

Abstract

In this paper we investigate the properties of two-dimensional ($2$D) convolutional codes which are obtained from series concatenation of two $2$D convolutional codes. For this purpose we confine ourselves to dealing with finite-support $2$D convolutional codes and make use of the so-called Fornasini-Marchesini input-state-output (ISO) model representations. Within these ISO representations we study when the structural properties of modal reachability and modal observability of the two given ISO representations carry over to the resulting $2$D convolutional code. Moreover, we provide necessary conditions for obtaining a systematic concatenated convolutional code. Finally, we present a lower bound on its free distance.