Techniques for correcting errors and erasures using a single-shot generalized minimum distance key equation solver
First Claim
1. A system for correcting errors in a codeword, the system comprising:
- a channel that sorts reliability numbers of symbols in the codeword to create an ordered list of candidate erasure locations; and
a generalized minimum distance decoder that iteratively processes the ordered list of candidate erasure locations and at least two syndromes of the codeword using a single-shot key equation solver to generate an error locator polynomial and an error evaluator polynomial,wherein the generalized minimum distance decoder processes the least reliable candidate erasure locations first within the ordered list of candidate erasure locations.
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Abstract
A system corrects errors in a codeword. The system includes a channel that sorts reliability numbers of symbols in the codeword to create an ordered list of candidate erasure locations. The system also includes a generalized minimum distance decoder that iteratively processes the ordered list of candidate erasure locations and at least two syndromes of the codeword using a single-shot key equation solver to generate an error locator polynomial and an error evaluator polynomial. The generalized minimum distance decoder processes the least reliable candidate erasure locations first within the ordered list of candidate erasure locations.
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Citations
20 Claims
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1. A system for correcting errors in a codeword, the system comprising:
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a channel that sorts reliability numbers of symbols in the codeword to create an ordered list of candidate erasure locations; and a generalized minimum distance decoder that iteratively processes the ordered list of candidate erasure locations and at least two syndromes of the codeword using a single-shot key equation solver to generate an error locator polynomial and an error evaluator polynomial, wherein the generalized minimum distance decoder processes the least reliable candidate erasure locations first within the ordered list of candidate erasure locations. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A method for correcting errors in a codeword, the method comprising:
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generating reliability numbers for symbols in the codeword; sorting the reliability numbers to generate a sorted list of candidate erasure locations for the symbols in the codeword; and iteratively processing the sorted list of candidate erasure locations and at least two syndromes of the codeword to generate an error locator polynomial and an error evaluator polynomial using a single-shot generalized minimum distance key equation solver, wherein the reliability numbers are arranged such that the single-shot generalized minimum distance key equation solver processes the least reliable candidate erasure locations first within the sorted list of candidate erasure locations. - View Dependent Claims (9, 10, 11, 12, 13, 14)
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15. A hard disk drive that corrects errors in a codeword read from a magnetic disk, the hard disk drive comprising:
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a channel that sorts reliability numbers of symbols in the codeword to create an ordered list of candidate erasure locations; and a decoder using a single-shot generalized minimum distance key equation solver to iteratively process the ordered list of candidate erasure locations and at least two syndromes of the codeword to generate an error locator polynomial and an error evaluator polynomial, wherein the single-shot generalized minimum distance key equation solver processes the least reliable candidate erasure locations first within the ordered list of candidate erasure locations. - View Dependent Claims (16, 17, 18, 19, 20)
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Specification