State-space realizations of periodic convolutional codes

Detalhes bibliográficos
Autor(a) principal: Fornasini, E.
Data de Publicação: 2022
Outros Autores: Napp, D., Pereira, Ricardo, Pinto, Raquel, Rocha, Paula
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/35025
Resumo: Convolutional codes are discrete linear systems over a finite field and can be defined as F[d]-modules, where F[d] is the ring of polynomials with coefficient in a finite field F. In this paper we study the algebraic properties of periodic convolutional codes of period 2 and their representation by means of input-state-output representations. We show that they can be described as F[d2]-modules and present explicit representation of the set of equivalent encoders. We investigate their statespace representation and present two different but equivalent types of state-space realizations for these codes. These novel representations can be implemented by realizing two linear time-invariant systems separately and switching the input (or the output) that is entering (or leaving) the system. We investigate their minimality and provide necessary and also sufficient conditions in terms of the reachability and observability properties of the two linear systems involved. The ideas presented here can be easily generalized for codes with period larger than 2.
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spelling State-space realizations of periodic convolutional codesPeriodic systemsConvolutional codesRealizationsConvolutional codes are discrete linear systems over a finite field and can be defined as F[d]-modules, where F[d] is the ring of polynomials with coefficient in a finite field F. In this paper we study the algebraic properties of periodic convolutional codes of period 2 and their representation by means of input-state-output representations. We show that they can be described as F[d2]-modules and present explicit representation of the set of equivalent encoders. We investigate their statespace representation and present two different but equivalent types of state-space realizations for these codes. These novel representations can be implemented by realizing two linear time-invariant systems separately and switching the input (or the output) that is entering (or leaving) the system. We investigate their minimality and provide necessary and also sufficient conditions in terms of the reachability and observability properties of the two linear systems involved. The ideas presented here can be easily generalized for codes with period larger than 2.SIAM2022-10-31T10:46:25Z2022-01-01T00:00:00Z2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/35025eng0363-012910.1137/21M1452172Fornasini, E.Napp, D.Pereira, RicardoPinto, RaquelRocha, Paulainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:07:34Zoai:ria.ua.pt:10773/35025Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:06:12.015633Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv State-space realizations of periodic convolutional codes
title State-space realizations of periodic convolutional codes
spellingShingle State-space realizations of periodic convolutional codes
Fornasini, E.
Periodic systems
Convolutional codes
Realizations
title_short State-space realizations of periodic convolutional codes
title_full State-space realizations of periodic convolutional codes
title_fullStr State-space realizations of periodic convolutional codes
title_full_unstemmed State-space realizations of periodic convolutional codes
title_sort State-space realizations of periodic convolutional codes
author Fornasini, E.
author_facet Fornasini, E.
Napp, D.
Pereira, Ricardo
Pinto, Raquel
Rocha, Paula
author_role author
author2 Napp, D.
Pereira, Ricardo
Pinto, Raquel
Rocha, Paula
author2_role author
author
author
author
dc.contributor.author.fl_str_mv Fornasini, E.
Napp, D.
Pereira, Ricardo
Pinto, Raquel
Rocha, Paula
dc.subject.por.fl_str_mv Periodic systems
Convolutional codes
Realizations
topic Periodic systems
Convolutional codes
Realizations
description Convolutional codes are discrete linear systems over a finite field and can be defined as F[d]-modules, where F[d] is the ring of polynomials with coefficient in a finite field F. In this paper we study the algebraic properties of periodic convolutional codes of period 2 and their representation by means of input-state-output representations. We show that they can be described as F[d2]-modules and present explicit representation of the set of equivalent encoders. We investigate their statespace representation and present two different but equivalent types of state-space realizations for these codes. These novel representations can be implemented by realizing two linear time-invariant systems separately and switching the input (or the output) that is entering (or leaving) the system. We investigate their minimality and provide necessary and also sufficient conditions in terms of the reachability and observability properties of the two linear systems involved. The ideas presented here can be easily generalized for codes with period larger than 2.
publishDate 2022
dc.date.none.fl_str_mv 2022-10-31T10:46:25Z
2022-01-01T00:00:00Z
2022
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dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/35025
url http://hdl.handle.net/10773/35025
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0363-0129
10.1137/21M1452172
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