Error correction in multi-valued (p,k) codes
First Claim
1. A method for correcting an n-valued symbol in error in an n-valued codeword of a (p,k) code having p n-valued symbols of which k n-valued symbols are information symbols and (p−
- k) symbols are check symbols with p>
1, n>
2 and k>
1, comprising;
receiving by a processor of the n-valued codeword that is a Reed-Solomon codeword wherein each n-valued symbol in the n-valued codeword is represented by a signal;
determining by the processor of a location of the n-valued symbol in error in the n-valued codeword based on check symbols in the n-valued codeword;
selecting by the processor of a pre-determined n-valued expression from a plurality of pre-determined expressions based on the location of the n-valued symbol in error; and
calculating by the processor a correct value of the n-valued symbol in error by evaluating the predetermined n-valued expressions which applies one or more of the p n-valued symbols not in error as an input variable and wherein the predetermined n-valued expression applies at least one n-valued logic function and outputs the correct value of the n-valued symbol in error.
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Accused Products
Abstract
Methods, apparatus and systems for error correction of n-valued symbols in (p,k) codewords including Reed Solomon codes of p n-valued symbols with n>2 and k information symbols have been disclosed. Coders and decoders using a Linear Feedback Shift Registers (LFSR) are applied. An LFSR can be in Fibonacci or Galois configuration. Errors can be corrected by execution of an n-valued expression in a deterministic way. Error correcting methods using Galois arithmetic are disclosed. Methods using Cramer'"'"'s rule are also disclosed. Deterministic error correction methods based on known symbols in error are provided, making first determining error magnitudes not necessary. An error location methods using up and down state tracking is provided. Methods and apparatus executing the methods with binary circuits are also disclosed. Systems using the error correcting methods, including communication systems and data storage systems are also provided.
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Citations
18 Claims
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1. A method for correcting an n-valued symbol in error in an n-valued codeword of a (p,k) code having p n-valued symbols of which k n-valued symbols are information symbols and (p−
- k) symbols are check symbols with p>
1, n>
2 and k>
1, comprising;receiving by a processor of the n-valued codeword that is a Reed-Solomon codeword wherein each n-valued symbol in the n-valued codeword is represented by a signal; determining by the processor of a location of the n-valued symbol in error in the n-valued codeword based on check symbols in the n-valued codeword; selecting by the processor of a pre-determined n-valued expression from a plurality of pre-determined expressions based on the location of the n-valued symbol in error; and calculating by the processor a correct value of the n-valued symbol in error by evaluating the predetermined n-valued expressions which applies one or more of the p n-valued symbols not in error as an input variable and wherein the predetermined n-valued expression applies at least one n-valued logic function and outputs the correct value of the n-valued symbol in error. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
- k) symbols are check symbols with p>
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12. An apparatus for correcting an n-valued symbol in error in an n-valued codeword of a (p,k) code having p n-valued symbols of which k n-valued symbols are information symbols and (p−
- k) symbols are check symbols with p>
1, n>
2 and k>
1, comprising;a processor executing instructions to perform the steps of; receiving the n-valued codeword that is a Reed-Solomon codeword wherein each n-valued symbol in the n-valued codeword is represented by a signal and an n-valued symbol is in error with an unknown location in the Reed-Solomon codeword; determining the location of the n-valued symbol in error in the n-valued Reed-Solomon codeword; selecting a predetermined n-valued expression based on the location of the n-valued symbol in error from a plurality of predetermined expressions; and determining a correct value of the n-valued symbol in error by evaluating the predetermined n-valued expression which applies one or more of the p n-valued symbols not in error directly as an input variable and wherein the pre-determined n-valued expression applies at least one n-valued logic function and outputs the correct value of the n-valued symbol in error. - View Dependent Claims (13, 14)
- k) symbols are check symbols with p>
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15. A system for processing a (p,k) codeword having p n-valued symbols of which k n-valued symbols are information symbols and (p−
- k) symbols are check symbols with p>
1, n>
2 and k>
1, the codeword having a symbol in error, comprising;a receiver which receives the p symbols of the (p,k) codeword; a processor performing the steps of; receiving the (p,k) codeword that is a Reed-Solomon codeword wherein each n-valued symbol in the n-valued codeword is represented by a signal and an n-valued symbol is in error with an unknown location in the Reed-Solomon codeword; determining the location of the n-valued symbol in error in the Reed-Solomon codeword; and calculating a correct value of the n-valued symbol in error by non-iteratively evaluating a single predetermined n-valued expression that is selected from a plurality of at least three predetermined n-valued expressions based on the location of the n-valued symbol in error, the selected single predetermined n-valued expression outputting the correct value. - View Dependent Claims (16, 17, 18)
- k) symbols are check symbols with p>
Specification