Noncatastrophic convolutional codes over a finite ring

Detalhes bibliográficos
Autor(a) principal: Napp, Diego
Data de Publicação: 2022
Outros Autores: Pinto, Raquel, Rocha, Conceição
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/34319
Resumo: Noncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. When these polynomials have coefficients in a finite field, these encoders have been characterized as polynomial left prime matrices. In this paper, we study the notion of noncatastrophicity in the context of convolutional codes when the polynomial matrices have entries in the finite ring Zpr. In particular, we study the notion of zero left prime in order to fully characterize noncatastrophic encoders over the finite ring Zpr. The second part of the paper is devoted to investigate free and column distance of convolutional codes that are free finitely generated Zpr-modules. We introduce the notion of b-degree and provide new bounds on the free distances and column distance. We show that this class of convolutional codes is optimal with respect to the column distance and to the free distance if and only if its projection on Zp is.
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spelling Noncatastrophic convolutional codes over a finite ringConvolutional codesNoncatastrophicityFinite ringsFinite support convolutional codesNoncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. When these polynomials have coefficients in a finite field, these encoders have been characterized as polynomial left prime matrices. In this paper, we study the notion of noncatastrophicity in the context of convolutional codes when the polynomial matrices have entries in the finite ring Zpr. In particular, we study the notion of zero left prime in order to fully characterize noncatastrophic encoders over the finite ring Zpr. The second part of the paper is devoted to investigate free and column distance of convolutional codes that are free finitely generated Zpr-modules. We introduce the notion of b-degree and provide new bounds on the free distances and column distance. We show that this class of convolutional codes is optimal with respect to the column distance and to the free distance if and only if its projection on Zp is.World Scientific2022-07-27T09:15:07Z2023-01-01T00:00:00Z2023-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/34319eng0219-498810.1142/S0219498823500299Napp, DiegoPinto, RaquelRocha, Conceiçãoinfo: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:RCAAP2024-02-22T12:05:14Zoai:ria.ua.pt:10773/34319Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:05:13.916102Repositório 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 Noncatastrophic convolutional codes over a finite ring
title Noncatastrophic convolutional codes over a finite ring
spellingShingle Noncatastrophic convolutional codes over a finite ring
Napp, Diego
Convolutional codes
Noncatastrophicity
Finite rings
Finite support convolutional codes
title_short Noncatastrophic convolutional codes over a finite ring
title_full Noncatastrophic convolutional codes over a finite ring
title_fullStr Noncatastrophic convolutional codes over a finite ring
title_full_unstemmed Noncatastrophic convolutional codes over a finite ring
title_sort Noncatastrophic convolutional codes over a finite ring
author Napp, Diego
author_facet Napp, Diego
Pinto, Raquel
Rocha, Conceição
author_role author
author2 Pinto, Raquel
Rocha, Conceição
author2_role author
author
dc.contributor.author.fl_str_mv Napp, Diego
Pinto, Raquel
Rocha, Conceição
dc.subject.por.fl_str_mv Convolutional codes
Noncatastrophicity
Finite rings
Finite support convolutional codes
topic Convolutional codes
Noncatastrophicity
Finite rings
Finite support convolutional codes
description Noncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. When these polynomials have coefficients in a finite field, these encoders have been characterized as polynomial left prime matrices. In this paper, we study the notion of noncatastrophicity in the context of convolutional codes when the polynomial matrices have entries in the finite ring Zpr. In particular, we study the notion of zero left prime in order to fully characterize noncatastrophic encoders over the finite ring Zpr. The second part of the paper is devoted to investigate free and column distance of convolutional codes that are free finitely generated Zpr-modules. We introduce the notion of b-degree and provide new bounds on the free distances and column distance. We show that this class of convolutional codes is optimal with respect to the column distance and to the free distance if and only if its projection on Zp is.
publishDate 2022
dc.date.none.fl_str_mv 2022-07-27T09:15:07Z
2023-01-01T00:00:00Z
2023-01
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/10773/34319
url http://hdl.handle.net/10773/34319
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0219-4988
10.1142/S0219498823500299
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 World Scientific
publisher.none.fl_str_mv World Scientific
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
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