Input-state-output representations of concatenated 2D convolutional codes

In this paper we investigate a novel model of concatenation of a pair of two-dimensional (2D) convolutional codes. We consider finite-support 2D convolutional codes and choose the so-called Fornasini-Marchesini input-state-output (ISO) model to represent these codes. More concretely, we interconnect in series two ISO representations of two 2D convolutional codes and derive the ISO representation of the ob- tained 2D convolutional code. We provide necessary condition for this representation to be minimal. Moreover, structural properties of modal reachability and modal observability of the resulting 2D convolutional codes are investigated.

MDP periodically time-varying convolutional codes

In this paper we use some classical ideas from linear systems theory to analyse convolutional codes. In particular, we exploit input-state-output representations of periodic linear systems to study periodically time-varying convolutional codes. In this preliminary work we focus on the column distance of these codes and derive explicit necessary and sufficient conditions for an (n, 2, 1) periodically time-varying convolutional code to have Maximum Distance Profile (MDP).