Iterative Reed-Solomon error-correction decoding
DCFirst Claim
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1. A method of correcting errors in a decision-codeword by employing a Reed Solomon error-correction code RS(n,k) having a correction capability t=(n−
- k)/2, the method comprising;
iteratively;
determining whether errors in a decision-codeword are of a degree that exceeds a Reed Solomon error-correction code'"'"'s correction capability, by using an error indicator for the decision-codeword,modifying the decision-codeword to produce a modified decision-codeword if the degree of the errors exceeds the correction capability, andgenerating an error indicator for the modified decision-codeword using the error indicator for the decision-codeword;
where;
the modified decision-codeword is a decision-codeword in a next iteration.
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Abstract
Systems and methods are provided to correct errors occurring in a decision-codeword that is generated by a detector. A decoder determines whether errors in the decision-codeword are of a degree that exceeds the correction capability of a Reed-Solomon error-correction code. If they are, the decoder iteratively modifies the decision-codeword to reduce the number of errors therein. In each iteration, the decoder generates an error indicator using one or more error indicators from a previous iteration and uses the error indicator to perform error detection and correction operations.
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Citations
76 Claims
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1. A method of correcting errors in a decision-codeword by employing a Reed Solomon error-correction code RS(n,k) having a correction capability t=(n−
- k)/2, the method comprising;
iteratively; determining whether errors in a decision-codeword are of a degree that exceeds a Reed Solomon error-correction code'"'"'s correction capability, by using an error indicator for the decision-codeword, modifying the decision-codeword to produce a modified decision-codeword if the degree of the errors exceeds the correction capability, and generating an error indicator for the modified decision-codeword using the error indicator for the decision-codeword;
where;the modified decision-codeword is a decision-codeword in a next iteration. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
- k)/2, the method comprising;
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15. A method of correcting errors in a decision-codeword by employing a Reed Solomon error-correction code RS(n+Δ
- ,k) that corresponds to a number (n−
k+Δ
) of syndromes, the method comprising;computing syndromes for a decision-codeword, where there are (n−
k+Δ
) syndromes denoted as S0, S1, . . . , Sn−
k+Δ
−
1, and where Δ
is positive;determining whether errors in the decision-codeword can be completely corrected, by using at least some of the syndromes; and correcting errors in the decision-codeword if the errors in the decision-codeword can be completely corrected. - View Dependent Claims (16, 17)
- ,k) that corresponds to a number (n−
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18. A system for correcting errors in a decision-codeword by employing a Reed Solomon error-correction code RS(n,k) having a correction capability t=(n−
- k)/2, the system comprising;
means for determining whether errors in a decision-codeword are of a degree that exceeds a Reed Solomon error-correction code'"'"'s correction capability, by using an error indicator for the decision-codeword; means for modifying the decision-codeword to produce a modified decision-codeword if the degree of the errors exceeds the correction capability; and means for generating an error indicator for the modified decision-codeword using the error indicator for the decision-codeword. - View Dependent Claims (19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33)
- k)/2, the system comprising;
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34. A system for correcting errors in a decision-codeword by employing a Reed Solomon error-correction code RS(n+Δ
- ,k) that corresponds to a number (n−
k+Δ
) of syndromes, the system comprising;means for computing syndromes for a decision-codeword, where there are (n−
k+Δ
) syndromes denoted as S0, S1, . . . , Sn−
k+Δ
−
1, and where Δ
is positive;means for determining whether errors in the decision-codeword can be completely corrected, by using at least some of the syndromes; and means for correcting errors in the decision-codeword if the errors in the decision-codeword can be completely corrected. - View Dependent Claims (35, 36, 37, 38)
- ,k) that corresponds to a number (n−
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39. A system for correcting errors in a decision-codeword by employing a Reed Solomon error-correction code RS(n,k) having a correction capability t=(n−
- k)/2, the system comprising;
an excessive-error detection circuit that determines whether errors in a decision-codeword are of a degree that exceeds a Reed Solomon error-correction code'"'"'s correction capability, by using an error indicator for the decision-codeword; a modification circuit that modifies the decision-codeword to produce a modified decision-codeword if the degree of the errors exceeds the correction capability; and an error indicator generation circuit that generates an error indicator for the modified decision-codeword using the error indicator for the decision-codeword. - View Dependent Claims (40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54)
- k)/2, the system comprising;
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55. A system for correcting errors in a decision-codeword by employing a Reed Solomon error-correction code RS(n+Δ
- ,k) that corresponds to a number (n−
k+Δ
) of syndromes, the system comprising;a syndrome computation circuit that computes syndromes for a decision-codeword, where there are (n−
k+Δ
) syndromes denoted as S0, S1, . . . , Sn−
k+Δ
−
1, and where Δ
is positive;an excessive-error detection circuit that determines whether errors in the decision-codeword can be completely corrected, by using at least some of the syndromes; and a correction circuit that corrects errors in the decision-codeword if the errors in the decision-codeword can be completely corrected. - View Dependent Claims (56, 57, 58, 59)
- ,k) that corresponds to a number (n−
-
60. A computer-readable storage medium containing a computer program, the computer program comprising instructions for execution on a computer to employ a Reed-Solomon error-correction code RS(n,k) having correction capability t=(n−
- k)/2, and to;
iteratively; determine whether errors in a decision-codeword are of a degree that exceeds a Reed Solomon error-correction code'"'"'s correction capability, by using an error indicator for the decision-codeword; modify the decision-codeword to produce a modified decision-codeword if the degree of the errors exceeds the correction capability, and generate an error indicator for the modified decision-codeword using the error indicator for the decision-codeword;
where;the modified decision-codeword is a decision-codeword in a next iteration. - View Dependent Claims (61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73)
- k)/2, and to;
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74. A computer-readable medium containing a computer program, the computer program comprising instructions for execution on a computer to employ a Reed Solomon error-correction code RS(n+Δ
- ,k) that corresponds to a number (n−
k+Δ
) of syndromes, and to;compute syndromes for a decision-codeword, where there are (n−
k+Δ
) syndromes denoted as S0, S1, . . . , Sn−
k+Δ
−
1, and where Δ
is positive;determine whether errors in the decision-codeword can be completely corrected, by using at least some of the syndromes; and correct errors in the decision-codeword if the errors in the decision-codeword can be completely corrected. - View Dependent Claims (75, 76)
- ,k) that corresponds to a number (n−
Specification