arXiv subjects

Miguel V. Carriegos

Publications and source records attributed to Miguel V. Carriegos.

6 recordsLinked to original sources

arXiv2026

Decoding convolutional codes over finite rings. A linear dynamical systems approach

Observable convolutional codes defined over Zpr with the Predictable Degree Property admit minimal input/state/output representations that preserve structural properties under scalar restriction. We make use of this fact to present Rosenthal's decoding algorithm for these convolutional codes. When combined with the Greferath-Vellbinger algorithm and a modified version of the Torrecillas-Lobillo-Navarro algorithm, the decoding problem of convolutional codes over Zpr reduces to selecting two decoding algorithms for linear block codes over a field. Finally, we analyze both the theoretical and practical error-correction capabilities of the combined algorithm as well as its time complexity.

cs.IT↗

arXiv2024

Construction of observable and MDP convolutional codes with good decodable properties for erasure channels by I/S/O representations

This paper addresses the construction of observable convolutional codes that exhibit good performance with the available decoding algorithms for erasure channels. Our construction is based on the use of input/state/output (I/S/O) representations and the invariance of certain properties of linear systems under various group actions.

cs.IT↗

arXiv2016

Linear representations of convolutional codes over rings

In this paper we extend the relation between convolutional codes and linear systems over finite fields to certain commutative rings through first order representations . We introduce the definition of rings with representations as those for which these representations always exist, and we show that finite products of finite fields belong to this class. We develop the input/state/output representations for convolutional codes over these rings, and we show how to use them to construct observable convolutional codes as in the classical case.

math.OC↗

arXiv2016

A note on the kernel of a pair of linear maps

The kernel of a pair of linear systems is studied in the framework of commutative ring theory with applications to behavioral perspective of linear systems

math.AC↗

arXiv2015

Partitions of elements in a monoid and its applications to systems theory

The feedback class of a locally Brunovsky linear system is fully determined by the decomposition of state space as direct sum of system invariants [4]. In this paper we attack the problem of enumerating all feedback classes of locally Brunovsky systems over a $n$-dimensional state space and translate to the combinatorial problem of enumerating all the partitions of integer $n$ in some abelian semigroup. The problem of computing the number $ν(n,k)$ of all the partitions of integer $n$ into $k$ different summands is pointed out.

math.AC↗

arXiv2013

On the K-theory of feedback actions on linear systems

A categorical approach to linear control systems is introduced. Feedback actions on linear systems arises as a symmetric monoidal category. Stable feedback isomorphisms generalize enlargement of pairs of matrices. Subcategory of locally Brunovsky linear systems is studied and the stable feedback isomorphisms of locally Brunovsky linear systems are characterized by the K_0 group of the (monoidal) category. Hence a link from linear dynamical systems to algebraic K-theory is stablished.

math.AC↗