JP4777258B2 - ガロア体乗算のためのルックアップテーブルを使用するリード・ソロモン符号の符号化および復号化 - Google Patents

ガロア体乗算のためのルックアップテーブルを使用するリード・ソロモン符号の符号化および復号化 Download PDF

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JP4777258B2
JP4777258B2 JP2006543834A JP2006543834A JP4777258B2 JP 4777258 B2 JP4777258 B2 JP 4777258B2 JP 2006543834 A JP2006543834 A JP 2006543834A JP 2006543834 A JP2006543834 A JP 2006543834A JP 4777258 B2 JP4777258 B2 JP 4777258B2
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remainder
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galois field
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リベロル，ボリス
リー，ユーン，ヤン
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アナログ・デバイシズ・インコーポレーテッド
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    • 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
    • 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
    • H03M13/65—Purpose and implementation aspects
    • H03M13/6502—Reduction of hardware complexity or efficient processing
    • H03M13/6505—Memory efficient implementations
    • 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
    • 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
    • H03M13/158—Finite field arithmetic processing
    • 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
    • H03M13/159—Remainder calculation, e.g. for encoding and syndrome calculation
    • 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
    • H03M13/65—Purpose and implementation aspects
    • H03M13/6569—Implementation on processors, e.g. DSPs, or software implementations

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  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Algebra (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Error Detection And Correction (AREA)
  • Detection And Correction Of Errors (AREA)
JP2006543834A 2003-12-12 2004-11-16 ガロア体乗算のためのルックアップテーブルを使用するリード・ソロモン符号の符号化および復号化 Expired - Fee Related JP4777258B2 (ja)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
US10/735,423 2003-12-12
US10/735,423 US7162679B2 (en) 2003-12-12 2003-12-12 Methods and apparatus for coding and decoding data using Reed-Solomon codes
PCT/US2004/038272 WO2005062472A1 (en) 2003-12-12 2004-11-16 Encoding and decoding of reed-solomon codes using look-up tables for galois field multiplications

Publications (3)

Publication Number Publication Date
JP2007514371A JP2007514371A (ja) 2007-05-31
JP2007514371A5 JP2007514371A5 (cg-RX-API-DMAC7.html) 2008-01-10
JP4777258B2 true JP4777258B2 (ja) 2011-09-21

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US (1) US7162679B2 (cg-RX-API-DMAC7.html)
JP (1) JP4777258B2 (cg-RX-API-DMAC7.html)
KR (1) KR20060125837A (cg-RX-API-DMAC7.html)
CN (1) CN1894857A (cg-RX-API-DMAC7.html)
WO (1) WO2005062472A1 (cg-RX-API-DMAC7.html)

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KR100933139B1 (ko) 2006-02-22 2009-12-21 삼성전자주식회사 통신 시스템에서 신호 수신 장치 및 방법
US7814398B2 (en) * 2006-06-09 2010-10-12 Seagate Technology Llc Communication channel with Reed-Solomon encoding and single parity check
EP2074787B1 (en) * 2006-10-19 2012-08-15 QUALCOMM Incorporated Beacon coding in wireless communications systems
JP4749383B2 (ja) * 2007-05-17 2011-08-17 三菱電機株式会社 符号化装置、暗号化装置及びプログラム
TWI334277B (en) * 2007-06-06 2010-12-01 Lite On Technology Corp Method for calculating syndrome efficiently in reed-solomon decoding and machine readable storage medium storing instructions for performing the method
EP2283417B1 (en) * 2008-05-12 2014-01-29 QUALCOMM Incorporated Implementation of arbitrary galois field arithmetic on a programmable processor
CN101814922B (zh) 2009-02-23 2013-06-19 国际商业机器公司 基于bch码的多位错纠错方法和装置以及存储系统
US8347192B1 (en) * 2010-03-08 2013-01-01 Altera Corporation Parallel finite field vector operators
US8682950B2 (en) * 2010-05-28 2014-03-25 Microsoft Corporation Computer-implemented symbolic polynomial factorization
CN102104446B (zh) * 2011-02-28 2013-01-30 华为技术有限公司 编码包转发方法、编码包接收处理方法和转发节点
JP2014010415A (ja) * 2012-07-03 2014-01-20 Nec Soft Ltd 分散情報管理システム、分散情報管理装置、分散情報保持装置、分散情報管理方法およびプログラム
US10148285B1 (en) 2012-07-25 2018-12-04 Erich Schmitt Abstraction and de-abstraction of a digital data stream
CN103023512B (zh) * 2013-01-18 2016-01-20 苏州威士达信息科技有限公司 Atsc系统rs编码中常系数矩阵的生成装置和方法
CN103095418B (zh) * 2013-01-18 2016-01-20 北京广讯科技有限责任公司 Cmmb系统rs编码中常系数矩阵的生成装置和方法
US9362953B2 (en) * 2013-08-02 2016-06-07 Infineon Technologies Ag Efficient error correction of multi-bit errors
US10795858B1 (en) 2014-02-18 2020-10-06 Erich Schmitt Universal abstraction and de-abstraction of a digital data stream
US10171109B2 (en) * 2017-01-23 2019-01-01 Hefei High-Dimensional Data Technology Co., Ltd. Fast encoding method and device for Reed-Solomon codes with a small number of redundancies
KR102975474B1 (ko) 2019-12-23 2026-06-10 삼성전자주식회사 메모리 컨트롤러 및 메모리 시스템
US11184029B1 (en) * 2020-05-28 2021-11-23 Samsung Electronics Co., Ltd. Low power ECC for eUFS
US11438013B2 (en) * 2020-07-15 2022-09-06 Samsung Electronics Co., Ltd. Low-power error correction code computation in GF (2R)
US12001279B2 (en) * 2022-10-20 2024-06-04 Micron Technology, Inc. Error protection for managed memory devices
CN119382721A (zh) * 2023-07-27 2025-01-28 华为技术有限公司 编译码方法、编码器、译码器及计算机存储介质

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US4763332A (en) * 1987-03-02 1988-08-09 Data Systems Technology Corp. Shared circuitry for the encoding and syndrome generation functions of a Reed-Solomon code
US4847801A (en) * 1987-10-26 1989-07-11 Cyclotomics, Inc. Compact galois field multiplier
JP2000295116A (ja) * 1999-03-15 2000-10-20 Texas Instr Inc <Ti> 誤り修正符号化方法
JP2003529233A (ja) * 1999-08-27 2003-09-30 モトローラ・インコーポレイテッド データを符号化及び復号化する方法及び装置

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JPS61203728A (ja) * 1985-03-07 1986-09-09 Fujitsu Ltd 拡大体における求積回路
US4763332A (en) * 1987-03-02 1988-08-09 Data Systems Technology Corp. Shared circuitry for the encoding and syndrome generation functions of a Reed-Solomon code
US4847801A (en) * 1987-10-26 1989-07-11 Cyclotomics, Inc. Compact galois field multiplier
JP2000295116A (ja) * 1999-03-15 2000-10-20 Texas Instr Inc <Ti> 誤り修正符号化方法
JP2003529233A (ja) * 1999-08-27 2003-09-30 モトローラ・インコーポレイテッド データを符号化及び復号化する方法及び装置

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US20050149832A1 (en) 2005-07-07
US7162679B2 (en) 2007-01-09
WO2005062472A1 (en) 2005-07-07
KR20060125837A (ko) 2006-12-06
CN1894857A (zh) 2007-01-10
JP2007514371A (ja) 2007-05-31

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