A matrix based list decoding algorithm for linear 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/10773/30499 |
Resumo: | In this paper we address the problem of list decoding of linear codes over an integer residue ring Zq, where q is a power of a prime p. The proposed procedure exploits a particular matrix representation of the linear code over Zpr , called the standard form, and the p-adic expansion of the to-be-decoded vector. In particular, we focus on the erasure channel in which the location of the errors is known. This problem then boils down to solving a system of linear equations with coefficients in Zpr . From the parity-check matrix representations of the code we recursively select certain equations that a codeword must satisfy and have coefficients only in the field p^{r−1}Zpr . This yields a step by step procedure obtaining a list of the closest codewords to a given received vector with some of its coordinates erased. We show that such an algorithm actually computes all possible erased coordinates, that is, the provided list is minimal. |
id |
RCAP_091f3d4d3a5fef2344c60245c6e6e322 |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/30499 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
A matrix based list decoding algorithm for linear codes over integer residue ringsFinite ringsLinear codes over finite ringsErasure channelDecoding algorithmsMatrix representationsParity-check matrixIn this paper we address the problem of list decoding of linear codes over an integer residue ring Zq, where q is a power of a prime p. The proposed procedure exploits a particular matrix representation of the linear code over Zpr , called the standard form, and the p-adic expansion of the to-be-decoded vector. In particular, we focus on the erasure channel in which the location of the errors is known. This problem then boils down to solving a system of linear equations with coefficients in Zpr . From the parity-check matrix representations of the code we recursively select certain equations that a codeword must satisfy and have coefficients only in the field p^{r−1}Zpr . This yields a step by step procedure obtaining a list of the closest codewords to a given received vector with some of its coordinates erased. We show that such an algorithm actually computes all possible erased coordinates, that is, the provided list is minimal.Elsevier2021-02-05T13:02:44Z2023-04-01T00:00:00Z2021-04-01T00:00:00Z2021-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/30499eng0024-379510.1016/j.laa.2020.09.031Napp, DiegoPinto, RaquelSaçıkara, ElifToste, Marisainfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:57:33Zoai:ria.ua.pt:10773/30499Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:02:00.036460Repositório 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 |
A matrix based list decoding algorithm for linear codes over integer residue rings |
title |
A matrix based list decoding algorithm for linear codes over integer residue rings |
spellingShingle |
A matrix based list decoding algorithm for linear codes over integer residue rings Napp, Diego Finite rings Linear codes over finite rings Erasure channel Decoding algorithms Matrix representations Parity-check matrix |
title_short |
A matrix based list decoding algorithm for linear codes over integer residue rings |
title_full |
A matrix based list decoding algorithm for linear codes over integer residue rings |
title_fullStr |
A matrix based list decoding algorithm for linear codes over integer residue rings |
title_full_unstemmed |
A matrix based list decoding algorithm for linear codes over integer residue rings |
title_sort |
A matrix based list decoding algorithm for linear codes over integer residue rings |
author |
Napp, Diego |
author_facet |
Napp, Diego Pinto, Raquel Saçıkara, Elif Toste, Marisa |
author_role |
author |
author2 |
Pinto, Raquel Saçıkara, Elif Toste, Marisa |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Napp, Diego Pinto, Raquel Saçıkara, Elif Toste, Marisa |
dc.subject.por.fl_str_mv |
Finite rings Linear codes over finite rings Erasure channel Decoding algorithms Matrix representations Parity-check matrix |
topic |
Finite rings Linear codes over finite rings Erasure channel Decoding algorithms Matrix representations Parity-check matrix |
description |
In this paper we address the problem of list decoding of linear codes over an integer residue ring Zq, where q is a power of a prime p. The proposed procedure exploits a particular matrix representation of the linear code over Zpr , called the standard form, and the p-adic expansion of the to-be-decoded vector. In particular, we focus on the erasure channel in which the location of the errors is known. This problem then boils down to solving a system of linear equations with coefficients in Zpr . From the parity-check matrix representations of the code we recursively select certain equations that a codeword must satisfy and have coefficients only in the field p^{r−1}Zpr . This yields a step by step procedure obtaining a list of the closest codewords to a given received vector with some of its coordinates erased. We show that such an algorithm actually computes all possible erased coordinates, that is, the provided list is minimal. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-02-05T13:02:44Z 2021-04-01T00:00:00Z 2021-04-01 2023-04-01T00:00:00Z |
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/10773/30499 |
url |
http://hdl.handle.net/10773/30499 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0024-3795 10.1016/j.laa.2020.09.031 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
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_ |
1799137675438981120 |