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

Definitions

• the invention relates to a modified Reed-Solomon error correction encoder.
• ECC's error correction codes
• ECC symbols are then appended to the data string to form ECC symbols.
• ECC symbols are then appended to the data string to form
• data symbols to be read are retrieved from the disks and mathematically decoded.
• Stored digital data can contain multiple errors.
• ECC used for the correction of multiple errors is a Reed-Solomon code
• Reed-Solomon codes see Peterson and Weldon, Error Correction Codes! . To correct multiple errors in strings of data symbols, Reed-Solomon codes efficiently and
• the remainder of the system operates with 8-bit symbols or bytes, or symbols that are
• the system must include an interface to translate the symbols between the 8-bit
• An ECC based on GF(2 ⁇ ) can protect a string of up to 253 8-bit data symbols or
• EDCs 8-bit-symbol error detection codes
• bit-symbol error detection codes over GF(2 16 ) are used.
• the 8-bit-symbol codes are easy
• An error detection code based on GF(2 0) has sufficient code word length, i.e.
• bit symbols are, in general, not arranged for manipulation of 10-bit symbols.
• decoder adds the complexity of another step to the EDC cross check process. Further,
• the code word bytes can later be
• the appended pseudo data bytes are modified such that encoding the
• Such a system can also be used to encode data over
• the encoder forms a preliminary EDC
• redundancy symbols that have i+1 selected bits set to all Os or all Is, and in "R" (w+i+1)-
• bit pseudo redundancy symbols which are appended to the modified EDC symbols.
• the encoding system next complements the modified EDC symbols with the i+1
• the decoder decodes the entire EDC code word
• the decoder may decode the EDC code word as (w+i)-bit symbols, or it may decode the
• EDC code word as (w+i+l)-bit symbols and use less complex circuitry to perform certain
• Galois fields GF(2 +I ) can be generated by an
• the field elements can then be express as powers of h(x) modulo p(x), where h(x)
• the error correction system uses (w+i+l)-bit representations of the elements of GF(2 W+1 ), to simplify the circuitry that
• Fig. 1 is a functional block diagram of an encoding system constructed in
• Fig. 2 is a flow chart of the operations of the encoder of Fig. 1;
• Fig. 3 is a functional block diagram of a decoding system constructed in
• Fig. 4 is a flow chart of the operations of the decoder of Fig. 3.
• Fig. 5 is a functional block diagram of a portion of a syndrome processor depicted
• the Galois Field, GF(2 + ') can be generated by an irreducible
• Each element of GF(2 10 ) can thus be expressed as a power of x 3 +x+l modulo p(x).
• element of GF(2 m ) is instead represented by a degree m polynomial, that is, by an (m+1)-
• bit symbol the element is associated with two distinct, but related symbols b(x) and c(x),
• b(x) b 10 b 9 b 8 b 7 b 6 b 5 b 4 b 3 b 2 b, b 0 ,
• b(x) b 10 b 9 b 8 b 7 b 6 b 5 b 4 b 3 b 2 b, b 0
• an encoding system 10 includes a Reed Solomon encoder 12
• multipliers 15-17 are implemented with a minimum number of exclusive-OR gates.
• the encoding system next determines if the preliminary EDC code word requires
• processor 26 determines if the leading i+1 bits are all set to the same value. In the
• the system determines in processor 26 if in each EDC redundancy symbol the
• bits in positions x 9 and x 8 are set to the same bit value as the bit in position x 10 .
• the EDC modifier code word is essentially a combination of one or more
• the processor 26 also produces R pseudo redundancy symbols P,, P 2 .
• step 208 determines if the first i+1 coefficients of an EDC redundancy symbol are all Os.
• step 212 If the i+1 bits are all Is, the system first complements the
• the modifying code words are:
• ⁇ ⁇ ⁇ 251 *x 3 + ⁇ 551 *x 2 + ⁇ 6I6 *x + ⁇ 446
• the modifying code words r c which are selected to have constant terms that have their
• i+1 bits set to all Os are preferably selected using the system and techniques discussed in
• the modifying code word r 0 which is used to modify bit 8 of the coefficient of x 1 ,
• each of the remaining code word symbols all zeros as the respective bits 10, 9 and 8.
• modifying code word rw which is used to modify bit 9 of the coefficient of x 1 , has a
• r 5 which are used to modify the coefficient of x 3 , similarly have bit 8 or bit 9 of the
• the modifying code words are stored in modifier table 30. Alternatively, only the
• the table 30 may thus contain for each code word the coefficient of x 3 .
• the encoder 12 encodes the data to produce the following
• the system complements the symbols to set the i+1 bits to all zeros.
• the system first complements the coefficients of x 3 and x 1 and then
• a decoder 300 cross checks the sector symbols by
• the decoder 300 includes three registers 301, 302, 303, which at the end of the encoding
• the system appends i+1,
• each of the adders 310, 311, 312, which also receive, respectively, the products from
• the registers 301-303 contain the syndromes s 64 , s 65 and s 66 .
• a syndrome processor 308 determines a sector is error-free if the EDC syndromes
• s 64 , s 65 and s 66 are all either all zeros or equal to p(x), and the ECC syndromes produced in
• an error correction processor 310 corrects the errors
• step 404 reconstructs EDC syndromes s' k based on the error locations, eloc,, and error values, eval,, determined by the ECC (step 404). First, the system determines partial reconstructed EDC syndromes s' k based on the error locations, eloc,, and error values, eval,, determined by the ECC (step 404). First, the system determines partial reconstructed EDC syndromes s' k based on the error locations, eloc,, and error values, eval, determined by the ECC (step 404). First, the system determines partial reconstructed
• the syndrome processor 308 raises the 10-bit element ⁇
• a table 316 that produces eloc upper, and ⁇ eloClower has just 32 entries.
• the table thus contains entries for ⁇ ° to ⁇ 31 and
• entry table can thus be used in place of a 2 10 entry table, saving not only storage space but
• the value ( ⁇ eloc > P er ,) 32 is then a permulation of ⁇ 0Qu PP er ,. This permulation can be
• partial syndromes s' 65 , and s' 66 can be readily determined as:
• multipliers 324-326 using multipliers 324-326, adders 330-333 and permutation hardware 328.
• step 1 To determine if the corrected sector is error-free, the syndrome processor, in step
• the encoder and decoder of Figs. 1 and 3 may use another code over GF(2 10 ),
• the decoder uses small look-up tables, and

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• 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)
• Detection And Correction Of Errors (AREA)

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• 1997
  • 1997-01-23 US US08/786,894 patent/US5948117A/en not_active Expired - Lifetime
• 1998
  • 1998-01-23 JP JP53474898A patent/JP3989558B2/ja not_active Expired - Fee Related
  • 1998-01-23 EP EP98902705A patent/EP0906665A4/en not_active Withdrawn
  • 1998-01-23 AU AU59299/98A patent/AU5929998A/en not_active Abandoned
  • 1998-01-23 WO PCT/US1998/001356 patent/WO1998035451A1/en not_active Ceased

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