Iterative ReedSolomon errorcorrection decoding
First Claim
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1. A method of correcting errors in a decisioncodeword by employing a Reed Solomon errorcorrection code RS(n,k) having a correction capability t=(n−
 k)/2, the method comprising;
iteratively;
determining whether errors in a decisioncodeword are of a degree that exceeds a Reed Solomon errorcorrection code'"'"'s correction capability, by using an error indicator for the decisioncodeword,modifying the decisioncodeword to produce a modified decisioncodeword if the degree of the errors exceeds the correction capability, andgenerating an error indicator for the modified decisioncodeword using the error indicator for the decisioncodeword;
where;
the modified decisioncodeword is a decisioncodeword in a next iteration.
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Abstract
Systems and methods are provided to correct errors occurring in a decisioncodeword that is generated by a detector. A decoder determines whether errors in the decisioncodeword are of a degree that exceeds the correction capability of a ReedSolomon errorcorrection code. If they are, the decoder iteratively modifies the decisioncodeword 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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76 Claims

1. A method of correcting errors in a decisioncodeword by employing a Reed Solomon errorcorrection code RS(n,k) having a correction capability t=(n−
 k)/2, the method comprising;
iteratively; determining whether errors in a decisioncodeword are of a degree that exceeds a Reed Solomon errorcorrection code'"'"'s correction capability, by using an error indicator for the decisioncodeword, modifying the decisioncodeword to produce a modified decisioncodeword if the degree of the errors exceeds the correction capability, and generating an error indicator for the modified decisioncodeword using the error indicator for the decisioncodeword;
where;the modified decisioncodeword is a decisioncodeword 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;

15. A method of correcting errors in a decisioncodeword by employing a Reed Solomon errorcorrection code RS(n+Δ
 ,k) that corresponds to a number (n−
k+Δ
) of syndromes, the method comprising;computing syndromes for a decisioncodeword, where there are (n−
k+Δ
) syndromes denoted as S_{0}, S_{1}, . . . , S_{n−k+Δ−1}, and where Δ
is positive;determining whether errors in the decisioncodeword can be completely corrected, by using at least some of the syndromes; and correcting errors in the decisioncodeword if the errors in the decisioncodeword can be completely corrected.  View Dependent Claims (16, 17)
 ,k) that corresponds to a number (n−

18. A system for correcting errors in a decisioncodeword by employing a Reed Solomon errorcorrection code RS(n,k) having a correction capability t=(n−
 k)/2, the system comprising;
means for determining whether errors in a decisioncodeword are of a degree that exceeds a Reed Solomon errorcorrection code'"'"'s correction capability, by using an error indicator for the decisioncodeword; means for modifying the decisioncodeword to produce a modified decisioncodeword if the degree of the errors exceeds the correction capability; and means for generating an error indicator for the modified decisioncodeword using the error indicator for the decisioncodeword.  View Dependent Claims (19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33)
 k)/2, the system comprising;

34. A system for correcting errors in a decisioncodeword by employing a Reed Solomon errorcorrection code RS(n+Δ
 ,k) that corresponds to a number (n−
k+Δ
) of syndromes, the system comprising;means for computing syndromes for a decisioncodeword, where there are (n−
k+Δ
) syndromes denoted as S_{0}, S_{1}, . . . , S_{n−k+Δ−1}, and where Δ
is positive;means for determining whether errors in the decisioncodeword can be completely corrected, by using at least some of the syndromes; and means for correcting errors in the decisioncodeword if the errors in the decisioncodeword can be completely corrected.  View Dependent Claims (35, 36, 37, 38)
 ,k) that corresponds to a number (n−

39. A system for correcting errors in a decisioncodeword by employing a Reed Solomon errorcorrection code RS(n,k) having a correction capability t=(n−
 k)/2, the system comprising;
an excessiveerror detection circuit that determines whether errors in a decisioncodeword are of a degree that exceeds a Reed Solomon errorcorrection code'"'"'s correction capability, by using an error indicator for the decisioncodeword; a modification circuit that modifies the decisioncodeword to produce a modified decisioncodeword if the degree of the errors exceeds the correction capability; and an error indicator generation circuit that generates an error indicator for the modified decisioncodeword using the error indicator for the decisioncodeword.  View Dependent Claims (40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54)
 k)/2, the system comprising;

55. A system for correcting errors in a decisioncodeword by employing a Reed Solomon errorcorrection 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 decisioncodeword, where there are (n−
k+Δ
) syndromes denoted as S_{0}, S_{1}, . . . , S_{n−k+Δ−1}, and where Δ
is positive;an excessiveerror detection circuit that determines whether errors in the decisioncodeword can be completely corrected, by using at least some of the syndromes; and a correction circuit that corrects errors in the decisioncodeword if the errors in the decisioncodeword can be completely corrected.  View Dependent Claims (56, 57, 58, 59)
 ,k) that corresponds to a number (n−

60. A computerreadable storage medium containing a computer program, the computer program comprising instructions for execution on a computer to employ a ReedSolomon errorcorrection code RS(n,k) having correction capability t=(n−
 k)/2, and to;
iteratively; determine whether errors in a decisioncodeword are of a degree that exceeds a Reed Solomon errorcorrection code'"'"'s correction capability, by using an error indicator for the decisioncodeword; modify the decisioncodeword to produce a modified decisioncodeword if the degree of the errors exceeds the correction capability, and generate an error indicator for the modified decisioncodeword using the error indicator for the decisioncodeword;
where;the modified decisioncodeword is a decisioncodeword in a next iteration.  View Dependent Claims (61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73)
 k)/2, and to;

74. A computerreadable medium containing a computer program, the computer program comprising instructions for execution on a computer to employ a Reed Solomon errorcorrection code RS(n+Δ
 ,k) that corresponds to a number (n−
k+Δ
) of syndromes, and to;compute syndromes for a decisioncodeword, where there are (n−
k+Δ
) syndromes denoted as S_{0}, S_{1}, . . . , S_{n−k+Δ−1}, and where Δ
is positive;determine whether errors in the decisioncodeword can be completely corrected, by using at least some of the syndromes; and correct errors in the decisioncodeword if the errors in the decisioncodeword can be completely corrected.  View Dependent Claims (75, 76)
 ,k) that corresponds to a number (n−
1 Specification