Exact and experimental algorithms for a Huffman-based error detecting code
Autor(a) principal: | |
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Data de Publicação: | 2006 |
Outros Autores: | , |
Tipo de documento: | Relatório |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRJ |
Texto Completo: | http://hdl.handle.net/11422/1924 |
Resumo: | Even codes are binary pre fix codes, in which each encoding contains an even number of 1's. They are Huffman based codes with the additional property of being able to detect the ocurrence of an odd number of 1-bit errors in the message. They have been de ned motivated by a problem posed by Hamming in 1980. Even codes have been studied for the case in which the symbols have uniform probabilities. In the present work, it is considered the general situation of arbitrary probabilities. An exact algorithm for constructing an optimal even code is described. The algorithm has complexity O(n3), where n is the number of symbols. Further, two heuristics for constructing nearly optimal even codes are presented, which require O(n log n) time. The cost of the even code constructed by the second heuristics is at most 16,7% higher than the cost of a Huffman code, for the same probabilities. However, computer experiments suggest that, for practical purposes, this value seems to be much less: about 5% or less, for n large enough. This corresponds to the overhead in the size of the encoded message, for having the ability to detect errors. Concerning undetected errors, we obtain bounds on the probability of the trees to produce k consecutive wrong symbols, which suggest that such probability is small, for large messages. |
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Pinto, Paulo Eustáquio DuarteProtti, FábioSzwarcfiter, Jayme Luiz2017-05-09T14:13:10Z2023-11-30T03:00:27Z2006-02-23PINTO, P. E.D. ; PROTTI, F. SZWARCFITER, J. L. Exact and experimental algorithms for a Huffman-based error detecting code. Rio de Janeiro: NCE, UFRJ, 2006. 25 p. (Relatório Técnico, 01/06)http://hdl.handle.net/11422/1924Even codes are binary pre fix codes, in which each encoding contains an even number of 1's. They are Huffman based codes with the additional property of being able to detect the ocurrence of an odd number of 1-bit errors in the message. They have been de ned motivated by a problem posed by Hamming in 1980. Even codes have been studied for the case in which the symbols have uniform probabilities. In the present work, it is considered the general situation of arbitrary probabilities. An exact algorithm for constructing an optimal even code is described. The algorithm has complexity O(n3), where n is the number of symbols. Further, two heuristics for constructing nearly optimal even codes are presented, which require O(n log n) time. The cost of the even code constructed by the second heuristics is at most 16,7% higher than the cost of a Huffman code, for the same probabilities. However, computer experiments suggest that, for practical purposes, this value seems to be much less: about 5% or less, for n large enough. This corresponds to the overhead in the size of the encoded message, for having the ability to detect errors. Concerning undetected errors, we obtain bounds on the probability of the trees to produce k consecutive wrong symbols, which suggest that such probability is small, for large messages.Submitted by Elaine Almeida (elaine.almeida@nce.ufrj.br) on 2017-05-09T14:13:10Z No. of bitstreams: 1 01_06_000649951.pdf: 321859 bytes, checksum: 804b0231b95ffd874ceaeccc5ec6989b (MD5)Made available in DSpace on 2017-05-09T14:13:10Z (GMT). No. of bitstreams: 1 01_06_000649951.pdf: 321859 bytes, checksum: 804b0231b95ffd874ceaeccc5ec6989b (MD5) Previous issue date: 2006-02-23engRelatório técnico NCECNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAOCompressão de dados (Ciência da computação)Detecção de errosCódigos de HuffmanExact and experimental algorithms for a Huffman-based error detecting codeinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/report0106abertoBrasilInstituto Tércio Pacitti de Aplicações e Pesquisas Computacionaisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJORIGINAL01_06_000649951.pdf01_06_000649951.pdfapplication/pdf321859http://pantheon.ufrj.br:80/bitstream/11422/1924/1/01_06_000649951.pdf804b0231b95ffd874ceaeccc5ec6989bMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81853http://pantheon.ufrj.br:80/bitstream/11422/1924/2/license.txtdd32849f2bfb22da963c3aac6e26e255MD52TEXT01_06_000649951.pdf.txt01_06_000649951.pdf.txtExtracted texttext/plain47097http://pantheon.ufrj.br:80/bitstream/11422/1924/3/01_06_000649951.pdf.txta1a0572994831595265810b542117f90MD5311422/19242023-11-30 00:00:27.373oai:pantheon.ufrj.br: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Repositório de PublicaçõesPUBhttp://www.pantheon.ufrj.br/oai/requestopendoar:2023-11-30T03:00:27Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false |
dc.title.pt_BR.fl_str_mv |
Exact and experimental algorithms for a Huffman-based error detecting code |
title |
Exact and experimental algorithms for a Huffman-based error detecting code |
spellingShingle |
Exact and experimental algorithms for a Huffman-based error detecting code Pinto, Paulo Eustáquio Duarte CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Compressão de dados (Ciência da computação) Detecção de erros Códigos de Huffman |
title_short |
Exact and experimental algorithms for a Huffman-based error detecting code |
title_full |
Exact and experimental algorithms for a Huffman-based error detecting code |
title_fullStr |
Exact and experimental algorithms for a Huffman-based error detecting code |
title_full_unstemmed |
Exact and experimental algorithms for a Huffman-based error detecting code |
title_sort |
Exact and experimental algorithms for a Huffman-based error detecting code |
author |
Pinto, Paulo Eustáquio Duarte |
author_facet |
Pinto, Paulo Eustáquio Duarte Protti, Fábio Szwarcfiter, Jayme Luiz |
author_role |
author |
author2 |
Protti, Fábio Szwarcfiter, Jayme Luiz |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Pinto, Paulo Eustáquio Duarte Protti, Fábio Szwarcfiter, Jayme Luiz |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
topic |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Compressão de dados (Ciência da computação) Detecção de erros Códigos de Huffman |
dc.subject.por.fl_str_mv |
Compressão de dados (Ciência da computação) Detecção de erros Códigos de Huffman |
description |
Even codes are binary pre fix codes, in which each encoding contains an even number of 1's. They are Huffman based codes with the additional property of being able to detect the ocurrence of an odd number of 1-bit errors in the message. They have been de ned motivated by a problem posed by Hamming in 1980. Even codes have been studied for the case in which the symbols have uniform probabilities. In the present work, it is considered the general situation of arbitrary probabilities. An exact algorithm for constructing an optimal even code is described. The algorithm has complexity O(n3), where n is the number of symbols. Further, two heuristics for constructing nearly optimal even codes are presented, which require O(n log n) time. The cost of the even code constructed by the second heuristics is at most 16,7% higher than the cost of a Huffman code, for the same probabilities. However, computer experiments suggest that, for practical purposes, this value seems to be much less: about 5% or less, for n large enough. This corresponds to the overhead in the size of the encoded message, for having the ability to detect errors. Concerning undetected errors, we obtain bounds on the probability of the trees to produce k consecutive wrong symbols, which suggest that such probability is small, for large messages. |
publishDate |
2006 |
dc.date.issued.fl_str_mv |
2006-02-23 |
dc.date.accessioned.fl_str_mv |
2017-05-09T14:13:10Z |
dc.date.available.fl_str_mv |
2023-11-30T03:00:27Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/report |
format |
report |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
PINTO, P. E.D. ; PROTTI, F. SZWARCFITER, J. L. Exact and experimental algorithms for a Huffman-based error detecting code. Rio de Janeiro: NCE, UFRJ, 2006. 25 p. (Relatório Técnico, 01/06) |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/11422/1924 |
identifier_str_mv |
PINTO, P. E.D. ; PROTTI, F. SZWARCFITER, J. L. Exact and experimental algorithms for a Huffman-based error detecting code. Rio de Janeiro: NCE, UFRJ, 2006. 25 p. (Relatório Técnico, 01/06) |
url |
http://hdl.handle.net/11422/1924 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Relatório técnico NCE |
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info:eu-repo/semantics/openAccess |
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openAccess |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto Tércio Pacitti de Aplicações e Pesquisas Computacionais |
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Universidade Federal do Rio de Janeiro (UFRJ) |
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UFRJ |
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UFRJ |
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Repositório Institucional da UFRJ |
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