Rita Simões

Characterizations of global reachability of 2D structured systems

The new concept of 2D structured system is defined and characterizations of global reachability are obtained. This paper extends well known results for the 1D case, according to which a structured system (Aλ, Bλ) is (generically) reachable if and only if its graph is spanned by a cactus, or, equivalently, if and only if the pair (Aλ, Bλ) is full generically row rank and irreducible.

Series concatenation of 2D convolutional codes

In this paper we study two-dimensional (2D) con-volutional codes which are obtained from series concatenation of two 2D convolutional codes. In this preliminary work we confine ourselves to dealing with finite-support 2D convolutional codes and make use of the so-called Fornasini-Marchesini input-state-output (ISO) model representations. In particular, we show that the series concatenation of two 2D convolutional codes is again a 2D convolutional code and we explicitly compute an ISO representation of the code. Within these ISO representations we study when the structural properties of reachability and observability of the two given ISO representations carry over to the resulting 2D convolutional code.

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 obtained 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.

Row and column rank partitions under small perturbations

The concept of rank partition of a family of vectors v 1, … , vm is a generalization of that has been useful for studying problems in Multilinear Algebra, namely, establishing conditions for non-vanishing decomposable symmetrized tensors and conditions for the equality of decomposable symmetrized tensors. A previous paper has described the rank partitions that can be obtained with arbitrarily small perturbations of the vectors v 1, … , vm . The purpose of the present article is to describe the pairs of row rank partitions and column rank partitions that can be obtained with arbitrarily small perturbations of a matrix.

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

ABSTRACT In this paper, we investigate the properties of two-dimensional (2D) convolutional codes which are obtained from series concatenation of two 2D convolutional codes. For this purpose, we confine ourselves to dealing with finite-support 2D convolutional codes and make use of the 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 2D convolutional code. Moreover, we provide necessary conditions for obtaining a systematic concatenated convolutional code. Finally, we present a lower bound on its free distance.

On Minimality of ISO Representation of Basic 2D Convolutional Codes

In this paper we study the minimality of input-state-output (ISO) representations of basic two-dimensional (2D) convolutional codes. For that we consider the Fornasini-Marchesini ISO representations of such codes. We define the novel property of strongly modally reachable representations and we show that such representations are minimal representations of a basic 2D convolutional code. Moreover, we prove that the dimension of such minimal representations equals the complexity of the code.

Burst Erasure Correction of 2D Convolutional Codes

In this paper we address the problem of decoding 2D convolutional codes over the erasure channel. In particular, we present a procedure to recover bursts of erasures that are distributed in a diagonal line. To this end we introduce the notion of balls around a burst of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main result reduces the decoding problem of 2D convolutional codes to a problem of decoding a set of associated 1D convolutional codes.