List decoding of convolutional codes over integer residue rings
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
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/10773/31713 |
Resumo: | A convolutional code over is a -submodule of where stands for the ring of polynomials with coefficients in . In this paper, we study the list decoding problem of these codes when the transmission is performed over an erasure channel, that is, we study how much information one can recover from a codeword when some of its coefficients have been erased. We do that using the p-adic expansion of w and particular representations of the parity-check polynomial matrix of the code. From these matrix polynomial representations we recursively select certain equations that w must satisfy and have only coefficients in the field . We exploit the natural block Toeplitz structure of the sliding parity-check matrix to derive a step by step methodology to obtain a list of possible codewords for a given corrupted codeword w, that is, a list with the closest codewords to w. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
spelling |
List decoding of convolutional codes over integer residue ringsConvolutional codesFinite ringsErasure channelA convolutional code over is a -submodule of where stands for the ring of polynomials with coefficients in . In this paper, we study the list decoding problem of these codes when the transmission is performed over an erasure channel, that is, we study how much information one can recover from a codeword when some of its coefficients have been erased. We do that using the p-adic expansion of w and particular representations of the parity-check polynomial matrix of the code. From these matrix polynomial representations we recursively select certain equations that w must satisfy and have only coefficients in the field . We exploit the natural block Toeplitz structure of the sliding parity-check matrix to derive a step by step methodology to obtain a list of possible codewords for a given corrupted codeword w, that is, a list with the closest codewords to w.Elsevier2021-07-29T10:54:03Z2021-06-01T00:00:00Z2021-06info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/31713eng1071-579710.1016/j.ffa.2021.101815Lieb, JuliaNapp, DiegoPinto, Raquelinfo: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:RCAAP2024-02-22T12:00:56Zoai:ria.ua.pt:10773/31713Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:03:24.909383Repositório 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 |
List decoding of convolutional codes over integer residue rings |
title |
List decoding of convolutional codes over integer residue rings |
spellingShingle |
List decoding of convolutional codes over integer residue rings Lieb, Julia Convolutional codes Finite rings Erasure channel |
title_short |
List decoding of convolutional codes over integer residue rings |
title_full |
List decoding of convolutional codes over integer residue rings |
title_fullStr |
List decoding of convolutional codes over integer residue rings |
title_full_unstemmed |
List decoding of convolutional codes over integer residue rings |
title_sort |
List decoding of convolutional codes over integer residue rings |
author |
Lieb, Julia |
author_facet |
Lieb, Julia Napp, Diego Pinto, Raquel |
author_role |
author |
author2 |
Napp, Diego Pinto, Raquel |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Lieb, Julia Napp, Diego Pinto, Raquel |
dc.subject.por.fl_str_mv |
Convolutional codes Finite rings Erasure channel |
topic |
Convolutional codes Finite rings Erasure channel |
description |
A convolutional code over is a -submodule of where stands for the ring of polynomials with coefficients in . In this paper, we study the list decoding problem of these codes when the transmission is performed over an erasure channel, that is, we study how much information one can recover from a codeword when some of its coefficients have been erased. We do that using the p-adic expansion of w and particular representations of the parity-check polynomial matrix of the code. From these matrix polynomial representations we recursively select certain equations that w must satisfy and have only coefficients in the field . We exploit the natural block Toeplitz structure of the sliding parity-check matrix to derive a step by step methodology to obtain a list of possible codewords for a given corrupted codeword w, that is, a list with the closest codewords to w. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-07-29T10:54:03Z 2021-06-01T00:00:00Z 2021-06 |
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/10773/31713 |
url |
http://hdl.handle.net/10773/31713 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1071-5797 10.1016/j.ffa.2021.101815 |
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 |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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_ |
1799137689223561216 |