FR2400801A1 - Systeme de detection et de correction d'erreurs utilisant les codes reed-solomon - Google Patents

Systeme de detection et de correction d'erreurs utilisant les codes reed-solomon

Info

Publication number
FR2400801A1
FR2400801A1 FR7820116A FR7820116A FR2400801A1 FR 2400801 A1 FR2400801 A1 FR 2400801A1 FR 7820116 A FR7820116 A FR 7820116A FR 7820116 A FR7820116 A FR 7820116A FR 2400801 A1 FR2400801 A1 FR 2400801A1
Authority
FR
France
Prior art keywords
error
correction system
sigma
error detection
reed
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
FR7820116A
Other languages
English (en)
Other versions
FR2400801B1 (fr
Inventor
Chin L Chen
Mu Y Hsiao
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
International Business Machines Corp
Original Assignee
International Business Machines Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by International Business Machines Corp filed Critical International Business Machines Corp
Publication of FR2400801A1 publication Critical patent/FR2400801A1/fr
Application granted granted Critical
Publication of FR2400801B1 publication Critical patent/FR2400801B1/fr
Granted legal-status Critical Current

Links

Classifications

    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
    • H03M13/151—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
    • G11B20/10—Digital recording or reproducing
    • G11B20/18—Error detection or correction; Testing, e.g. of drop-outs
    • G11B20/1806—Pulse code modulation systems for audio signals
    • G11B20/1809—Pulse code modulation systems for audio signals by interleaving
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
    • G11B20/10—Digital recording or reproducing
    • G11B20/18—Error detection or correction; Testing, e.g. of drop-outs
    • G11B20/1833—Error detection or correction; Testing, e.g. of drop-outs by adding special lists or symbols to the coded information

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Signal Processing (AREA)
  • Algebra (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Theoretical Computer Science (AREA)
  • Multimedia (AREA)
  • Error Detection And Correction (AREA)
  • Detection And Correction Of Errors (AREA)

Abstract

Système de détection et de correction d'erreurs utilisant un polynôme de localisation d'erreurs sigma (x) et des syndromes d'erreurs Si . Un décodeur détermine si So Not= 0 et S2 + sigma S1 =0 et S3 + sigma S2 =0 lorsque sigma =S1 /S0 pour signaler qu'une erreur simple s'est produite dans un mot. S'il ne s'agit pas d'une erreur simple, le décodeur détermine s'il s'agit d'une erreur double et si tel n'est pas le cas détermine la présence éventuelle de trois ou de plus de trois erreurs. L'invention rend les détecteurs d'erreurs plus simples et plus rapide.
FR7820116A 1977-08-15 1978-06-29 Systeme de detection et de correction d'erreurs utilisant les codes reed-solomon Granted FR2400801A1 (fr)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US05/824,763 US4142174A (en) 1977-08-15 1977-08-15 High speed decoding of Reed-Solomon codes

Publications (2)

Publication Number Publication Date
FR2400801A1 true FR2400801A1 (fr) 1979-03-16
FR2400801B1 FR2400801B1 (fr) 1983-03-18

Family

ID=25242256

Family Applications (1)

Application Number Title Priority Date Filing Date
FR7820116A Granted FR2400801A1 (fr) 1977-08-15 1978-06-29 Systeme de detection et de correction d'erreurs utilisant les codes reed-solomon

Country Status (5)

Country Link
US (1) US4142174A (fr)
JP (1) JPS5432240A (fr)
DE (1) DE2834963A1 (fr)
FR (1) FR2400801A1 (fr)
GB (1) GB1570169A (fr)

Cited By (7)

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Publication number Priority date Publication date Assignee Title
FR2481027A1 (fr) * 1980-04-16 1981-10-23 Sony Corp Procede et appareil de traitement de signaux numeriques
FR2485299A1 (fr) * 1980-06-20 1981-12-24 Sony Corp Procede de correction d'erreurs
FR2491278A1 (fr) * 1980-07-18 1982-04-02 Sony Corp Procede pour la correction d'erreurs dans une transmission de donnees, dans laquelle un bloc comprend n mots composes chacun de m bits
EP0053474A1 (fr) * 1980-11-28 1982-06-09 Sony Corporation Dispositif pour le traitement de signaux à modulation d'impulsions codées
EP0072640A1 (fr) * 1981-08-14 1983-02-23 Sony Corporation Méthodes pour la correction d'erreurs de données
EP0105499A2 (fr) * 1982-09-30 1984-04-18 Nec Corporation Méthode capable de décoder simultanément deux séquences reproduites
EP0136587A2 (fr) * 1983-09-06 1985-04-10 Kabushiki Kaisha Toshiba Circuit de correction d'erreur

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US4162480A (en) * 1977-01-28 1979-07-24 Cyclotomics, Inc. Galois field computer
US4360916A (en) * 1979-12-31 1982-11-23 Ncr Canada Ltd.-Ncr Canada Ltee. Method and apparatus for providing for two bits-error detection and correction
JPS57155667A (en) * 1981-03-23 1982-09-25 Sony Corp Arithmetic circuit of galois matter
US4413339A (en) * 1981-06-24 1983-11-01 Digital Equipment Corporation Multiple error detecting and correcting system employing Reed-Solomon codes
DE3176988D1 (en) * 1981-12-30 1989-03-16 Ibm Information system using error syndrome for special control
JPS58138140A (ja) * 1982-02-12 1983-08-16 Sansui Electric Co デジタル信号の誤り検出回路
JPS58219848A (ja) * 1982-06-15 1983-12-21 Toshiba Corp ガロア体における乗算装置
JPS58219850A (ja) * 1982-06-15 1983-12-21 Toshiba Corp 誤り位置検出回路
EP0096163B1 (fr) * 1982-06-15 1988-06-01 Kabushiki Kaisha Toshiba Appareil pour diviser les éléments d'un champ de Galois
JPS58219852A (ja) * 1982-06-15 1983-12-21 Toshiba Corp エラ−訂正回路
EP0096165B1 (fr) * 1982-06-15 1988-06-08 Kabushiki Kaisha Toshiba Appareil pour diviser les éléments d'un champ de Galois
JPS595759A (ja) * 1982-06-30 1984-01-12 Nec Home Electronics Ltd リード・ソロモン符号復号方式
GB2132393B (en) * 1982-12-17 1986-05-14 Sony Corp Methods and apparatus for correcting errors in binary data
US4504948A (en) * 1982-12-29 1985-03-12 International Business Machines Corporation Syndrome processing unit for multibyte error correcting systems
US4564945A (en) * 1983-06-20 1986-01-14 Reference Technology, Inc. Error-correction code for digital data on video disc
NL8302214A (nl) * 1983-06-22 1985-01-16 Philips Nv Dekodeerinrichting voor het dekoderen van kodewoorden die bloksgewijs middels een reed-solomon-code tegen meerdere symboolfouten per blok beschermd zijn, en uitleesinrichting voor optisch uitleesbare opslaglichamen welke uitleesinrichting voorzien is van zo een dekodeerinrichting.
US4556977A (en) * 1983-09-15 1985-12-03 International Business Machines Corporation Decoding of BCH double error correction - triple error detection (DEC-TED) codes
JPS6052736U (ja) * 1983-09-20 1985-04-13 株式会社ケンウッド Ｂｃｈ単一誤り訂正・二重誤り検出符号復号化回路
JPS6064529A (ja) * 1983-09-20 1985-04-13 Trio Kenwood Corp Ｂｃｈ単一誤り訂正・二重誤り検出符号復号化回路
US4646303A (en) * 1983-10-05 1987-02-24 Nippon Gakki Seizo Kabushiki Kaisha Data error detection and correction circuit
AU571908B2 (en) * 1983-10-28 1988-04-28 Laser Magnetic Storage International Co. Error correction apparatus
US4584686A (en) * 1983-12-22 1986-04-22 Optical Storage International Reed-Solomon error correction apparatus
JPS60130221A (ja) * 1983-12-16 1985-07-11 Hiroichi Okano ２重バイト誤り訂正３重バイト誤り検出リード・ソロモン符号の復号装置
KR930003997B1 (ko) * 1983-12-20 1993-05-19 소니 가부시끼가이샤 에러 정정부호의 복호방법 및 복호장치
WO1985003371A1 (fr) * 1984-01-21 1985-08-01 Sony Corporation Circuit de calcul de champs finis
US4675754A (en) * 1984-02-21 1987-06-23 Mitsubishi Denki Kabushiki Kaisha Magnetic recorder/reproducer
NL8400629A (nl) * 1984-02-29 1985-09-16 Philips Nv Snelle decodeur voor reed-solomon-codes, welke mede als encodeur te gebruiken is, alsmede opname/reproduktie-apparaat voorzien van zo een encodeur/decodeur.
US4597083A (en) * 1984-04-06 1986-06-24 Ampex Corporation Error detection and correction in digital communication systems
JPH0778748B2 (ja) * 1984-04-11 1995-08-23 三菱電機株式会社 ガロア体演算ユニット
JPS61126826A (ja) * 1984-11-22 1986-06-14 Hiroichi Okano 倍長単一誤り訂正２重誤り検出リ−ド・ソロモン符号の復号器
US4841300A (en) * 1986-06-18 1989-06-20 Mitsubishi Denki K.K. Error correction encoder/decoder
FR2605818B1 (fr) * 1986-10-27 1992-09-18 Thomson Csf Codeur-decodeur algebrique de codes en blocs reed solomon et bch, applicable aux telecommunications numeriques
US4875211A (en) * 1986-12-10 1989-10-17 Matsushita Electric Industrial Co., Ltd. Galois field arithmetic logic unit
US4782490A (en) * 1987-03-16 1988-11-01 Cythera Corporation Method and a system for multiple error detection and correction
JPS63158918A (ja) * 1987-12-11 1988-07-01 Sony Corp エラー訂正方法
US4890286A (en) * 1987-12-11 1989-12-26 Sanyo Electric Co., Ltd. Method and apparatus for decoding error correcting code
JPS6427322A (en) * 1988-04-21 1989-01-30 Sony Corp Arithmetic circuit for galois field
JP2810397B2 (ja) * 1989-02-16 1998-10-15 キヤノン株式会社 誤り訂正装置
EP0386506A3 (fr) * 1989-03-06 1991-09-25 International Business Machines Corporation Codage et décodage de symboles à correction d'erreurs à peu de frais
US5136592A (en) * 1989-06-28 1992-08-04 Digital Equipment Corporation Error detection and correction system for long burst errors
US5040179A (en) * 1989-08-18 1991-08-13 Loral Aerospace Corp. High data rate BCH encoder
US5280488A (en) * 1990-11-08 1994-01-18 Neal Glover Reed-Solomon code system employing k-bit serial techniques for encoding and burst error trapping
US5226043A (en) * 1990-12-27 1993-07-06 Raytheon Company Apparatus and method for data error detection and correction and address error detection in a memory system
JPH04358486A (ja) * 1991-06-04 1992-12-11 Toshiba Corp 高能率符号化信号処理装置
JP3093494B2 (ja) * 1992-11-18 2000-10-03 株式会社東芝 多様性信号処理装置
US5561608A (en) * 1992-11-18 1996-10-01 Kabushiki Kaisha Toshiba Multisystem adaptable type signal processing and recording/reproducing apparatus
JPH0828672B2 (ja) * 1993-03-25 1996-03-21 博一 岡野 倍長単一誤り訂正２重誤り検出リード・ソロモン符号の復号器
US5778009A (en) * 1995-06-14 1998-07-07 Quantum Corporation Dedicated ALU architecture for 10-bit Reed-Solomon error correction module
US5754563A (en) * 1995-09-11 1998-05-19 Ecc Technologies, Inc. Byte-parallel system for implementing reed-solomon error-correcting codes
US6308295B1 (en) 1996-10-08 2001-10-23 Arizona Board Of Regents Parallel spectral reed-solomon encoder and decoder
KR100213254B1 (ko) * 1996-10-18 1999-08-02 윤종용 에러 정정 방법 및 장치
JPH113573A (ja) * 1997-04-15 1999-01-06 Mitsubishi Electric Corp 拡大リードソロモン符号の誤り訂正復号方法と誤り訂正復号装置、１次伸長拡大リードソロモン符号の誤り訂正方法と誤り訂正装置、および２次伸長拡大リードソロモン符号の誤り訂正方法と誤り訂正装置
JPH1117557A (ja) * 1997-05-01 1999-01-22 Mitsubishi Electric Corp 誤り訂正方法及び誤り訂正装置
JP3850512B2 (ja) * 1997-05-07 2006-11-29 日本テキサス・インスツルメンツ株式会社 リードソロモン復号装置
US6405339B1 (en) * 1999-08-31 2002-06-11 International Business Machines Corporation Parallelized programmable encoder/syndrome generator
US6662338B1 (en) 1999-09-30 2003-12-09 Stmicroelectronics, Inc. Parity- sensitive Viterbi detector and method for recovering information from a read signal
US6492918B1 (en) * 1999-09-30 2002-12-10 Stmicroelectronics, Inc. Code word having data bits and code bits and method for encoding data
US6694476B1 (en) 2000-06-02 2004-02-17 Vitesse Semiconductor Corporation Reed-solomon encoder and decoder
US6738942B1 (en) 2000-06-02 2004-05-18 Vitesse Semiconductor Corporation Product code based forward error correction system
CN100576785C (zh) * 2002-04-25 2009-12-30 Pmc-斯尔若以色列有限公司 以太网中的前向纠错编码
US6954892B2 (en) * 2002-06-06 2005-10-11 National Chiao Tung University Method for calculating syndrome polynomial in decoding error correction codes
US8832523B2 (en) * 2006-03-03 2014-09-09 Ternarylogic Llc Multi-state symbol error correction in matrix based codes
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US7171591B2 (en) * 2003-12-23 2007-01-30 International Business Machines Corporation Method and apparatus for encoding special uncorrectable errors in an error correction code
US7243293B2 (en) * 2003-12-23 2007-07-10 International Business Machines Corporation (18, 9) Error correction code for double error correction and triple error detection
EP1681770A1 (fr) * 2005-01-18 2006-07-19 Koninklijke Philips Electronics N.V. Code de correction d'erreurs
US7475329B2 (en) * 2005-02-16 2009-01-06 Hitachi Global Storage Technologies Netherlands B.V. Techniques for performing Galois field logarithms for detecting error locations that require less storage space
US7219289B2 (en) * 2005-03-15 2007-05-15 Tandberg Data Corporation Multiply redundant raid system and XOR-efficient method and apparatus for implementing the same
US7676733B2 (en) * 2006-01-04 2010-03-09 Intel Corporation Techniques to perform forward error correction for an electrical backplane
US9203436B2 (en) * 2006-07-12 2015-12-01 Ternarylogic Llc Error correction in multi-valued (p,k) codes
JP4891704B2 (ja) * 2006-08-28 2012-03-07 株式会社東芝 半導体記憶装置
JP5259343B2 (ja) * 2008-10-31 2013-08-07 株式会社東芝 メモリ装置

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Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2481027A1 (fr) * 1980-04-16 1981-10-23 Sony Corp Procede et appareil de traitement de signaux numeriques
FR2485299A1 (fr) * 1980-06-20 1981-12-24 Sony Corp Procede de correction d'erreurs
FR2491278A1 (fr) * 1980-07-18 1982-04-02 Sony Corp Procede pour la correction d'erreurs dans une transmission de donnees, dans laquelle un bloc comprend n mots composes chacun de m bits
EP0053474A1 (fr) * 1980-11-28 1982-06-09 Sony Corporation Dispositif pour le traitement de signaux à modulation d'impulsions codées
EP0072640A1 (fr) * 1981-08-14 1983-02-23 Sony Corporation Méthodes pour la correction d'erreurs de données
EP0105499A2 (fr) * 1982-09-30 1984-04-18 Nec Corporation Méthode capable de décoder simultanément deux séquences reproduites
EP0105499A3 (en) * 1982-09-30 1986-12-30 Nec Corporation Method capable of simultaneously decoding two reproduced sequences
EP0136587A2 (fr) * 1983-09-06 1985-04-10 Kabushiki Kaisha Toshiba Circuit de correction d'erreur
EP0136587A3 (en) * 1983-09-06 1987-05-27 Kabushiki Kaisha Toshiba Error correction circuit

Also Published As

Publication number Publication date
GB1570169A (en) 1980-06-25
JPS5620575B2 (fr) 1981-05-14
FR2400801B1 (fr) 1983-03-18
DE2834963A1 (de) 1979-03-01
JPS5432240A (en) 1979-03-09
US4142174A (en) 1979-02-27

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