Periodic state-space representations of periodic convolutional codes
Autor(a) principal: | |
---|---|
Data de Publicação: | 2018 |
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/10773/23899 |
Resumo: | In this paper we study the representation of periodically time-varying convolutional codes by means of periodic input-state-output models. In particular, we focus on period two and investigate under which conditions a given two-periodic convolutional code (obtained by alternating two time-invariant encoders) can be represented by a periodic input-state-output system. We first show that one cannot expect, in general, to obtain a periodic input-state-output representation of a periodic convolutional code by means of the individual realizations of each of the associated time-invariant codes. We, however, provide sufficient conditions for this to hold in terms of the column degrees of the associated column reduced generator matrices. Moreover, we derive a sufficient condition to obtain a periodic state-space realization that is minimal. Finally, examples to illustrate the results are presented. |
id |
RCAP_2987ec30ad1f9750ba6d650853396a6b |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/23899 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Periodic state-space representations of periodic convolutional codesConvolutional codesPeriodically time-varying codesInput-state- output representationsIn this paper we study the representation of periodically time-varying convolutional codes by means of periodic input-state-output models. In particular, we focus on period two and investigate under which conditions a given two-periodic convolutional code (obtained by alternating two time-invariant encoders) can be represented by a periodic input-state-output system. We first show that one cannot expect, in general, to obtain a periodic input-state-output representation of a periodic convolutional code by means of the individual realizations of each of the associated time-invariant codes. We, however, provide sufficient conditions for this to hold in terms of the column degrees of the associated column reduced generator matrices. Moreover, we derive a sufficient condition to obtain a periodic state-space realization that is minimal. Finally, examples to illustrate the results are presented.Springer Verlag2018-07-31T15:59:18Z2019-07-01T00:00:00Z2019-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/23899eng1936-244710.1007/s12095-018-0313-6Napp, DiegoPereira, 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:RCAAP2024-02-22T11:47:06Zoai:ria.ua.pt:10773/23899Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:57:47.640254Repositório 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 |
Periodic state-space representations of periodic convolutional codes |
title |
Periodic state-space representations of periodic convolutional codes |
spellingShingle |
Periodic state-space representations of periodic convolutional codes Napp, Diego Convolutional codes Periodically time-varying codes Input-state- output representations |
title_short |
Periodic state-space representations of periodic convolutional codes |
title_full |
Periodic state-space representations of periodic convolutional codes |
title_fullStr |
Periodic state-space representations of periodic convolutional codes |
title_full_unstemmed |
Periodic state-space representations of periodic convolutional codes |
title_sort |
Periodic state-space representations of periodic convolutional codes |
author |
Napp, Diego |
author_facet |
Napp, Diego Pereira, Ricardo Pinto, Raquel Rocha, Paula |
author_role |
author |
author2 |
Pereira, Ricardo Pinto, Raquel Rocha, Paula |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Napp, Diego Pereira, Ricardo Pinto, Raquel Rocha, Paula |
dc.subject.por.fl_str_mv |
Convolutional codes Periodically time-varying codes Input-state- output representations |
topic |
Convolutional codes Periodically time-varying codes Input-state- output representations |
description |
In this paper we study the representation of periodically time-varying convolutional codes by means of periodic input-state-output models. In particular, we focus on period two and investigate under which conditions a given two-periodic convolutional code (obtained by alternating two time-invariant encoders) can be represented by a periodic input-state-output system. We first show that one cannot expect, in general, to obtain a periodic input-state-output representation of a periodic convolutional code by means of the individual realizations of each of the associated time-invariant codes. We, however, provide sufficient conditions for this to hold in terms of the column degrees of the associated column reduced generator matrices. Moreover, we derive a sufficient condition to obtain a periodic state-space realization that is minimal. Finally, examples to illustrate the results are presented. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-07-31T15:59:18Z 2019-07-01T00:00:00Z 2019-07 |
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/10773/23899 |
url |
http://hdl.handle.net/10773/23899 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1936-2447 10.1007/s12095-018-0313-6 |
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 |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
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 |
|
_version_ |
1799137632556417024 |