WO1999045911A8 - Universal reed-solomon coder-decoder - Google Patents

Universal reed-solomon coder-decoder

Info

Publication number
WO1999045911A8
WO1999045911A8 PCT/US1999/005493 US9905493W WO9945911A8 WO 1999045911 A8 WO1999045911 A8 WO 1999045911A8 US 9905493 W US9905493 W US 9905493W WO 9945911 A8 WO9945911 A8 WO 9945911A8
Authority
WO
WIPO (PCT)
Prior art keywords
decoder
block size
decoding
approach
solomon coder
Prior art date
Application number
PCT/US1999/005493
Other languages
French (fr)
Other versions
WO1999045911A9 (en
WO1999045911A2 (en
WO1999045911A3 (en
Inventor
Xinyu Ma
Girish Chandran
Original Assignee
Tiernan Communications Inc
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 Tiernan Communications Inc filed Critical Tiernan Communications Inc
Priority to AU31852/99A priority Critical patent/AU3185299A/en
Publication of WO1999045911A2 publication Critical patent/WO1999045911A2/en
Publication of WO1999045911A9 publication Critical patent/WO1999045911A9/en
Publication of WO1999045911A3 publication Critical patent/WO1999045911A3/en
Publication of WO1999045911A8 publication Critical patent/WO1999045911A8/en

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
    • H03M13/1515—Reed-Solomon 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
    • H03M13/154—Error and erasure correction, e.g. by using the error and erasure locator or Forney polynomial
    • 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
    • H03M13/29—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2933—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using a block and a convolutional code
    • H03M13/2936—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using a block and a convolutional code comprising an outer Reed-Solomon code and an inner convolutional code

Landscapes

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

Abstract

A generalized Reed-Solomon coding is characterized by the codeword block size n, the information block size k and the generator polynomial g(x), which is a function of β and r according to the equation: g(x)=(x+βr)(x+βr+1)(x+βr+2)(x+βr+3)(x+βr+4)...(x+βr+2t-1) where β is an element of the Galois field and r is the initial exponent for β. For decoding, an approach to finding error patterns uses a modified general form that takes advantage of properties of the generating polynomial. With the disclosed universal RS encoding-decoding approach, a user only needs to specify four parameters, namely those values (n, k, β, r), and any RS coding design specification can be met using a single framework.
PCT/US1999/005493 1998-03-12 1999-03-12 Universal reed-solomon coder-decoder WO1999045911A2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU31852/99A AU3185299A (en) 1998-03-12 1999-03-12 Universal reed-solomon coder-decoder

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US7774098P 1998-03-12 1998-03-12
US60/077,740 1998-03-12

Publications (4)

Publication Number Publication Date
WO1999045911A2 WO1999045911A2 (en) 1999-09-16
WO1999045911A9 WO1999045911A9 (en) 2000-01-20
WO1999045911A3 WO1999045911A3 (en) 2000-04-06
WO1999045911A8 true WO1999045911A8 (en) 2000-05-18

Family

ID=22139792

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/US1999/005493 WO1999045911A2 (en) 1998-03-12 1999-03-12 Universal reed-solomon coder-decoder

Country Status (2)

Country Link
AU (1) AU3185299A (en)
WO (1) WO1999045911A2 (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6385751B1 (en) * 1998-12-30 2002-05-07 Texas Instruments Incorporated Programmable, reconfigurable DSP implementation of a Reed-Solomon encoder/decoder

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1989002123A1 (en) * 1987-08-24 1989-03-09 Digital Equipment Corporation High bandwidth reed-solomon encoding, decoding and error correcting circuit

Also Published As

Publication number Publication date
WO1999045911A9 (en) 2000-01-20
AU3185299A (en) 1999-09-27
WO1999045911A2 (en) 1999-09-16
WO1999045911A3 (en) 2000-04-06

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