State-space realizations of periodic convolutional codes
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , , |
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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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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 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
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 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
SIAM |
publisher.none.fl_str_mv |
SIAM |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137716655357952 |