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US 6,643,819 B1Granted
Hybrid root-finding technique
AssigneeMaxtor Corporation
InventorLih-Jyh Weng
Life of this patent
Estimating the term…
Abstract
A root finding mechanism uses an affine polynomial to find the roots of an error locator polynomial. The affine polynomial is produced from the error locator polynomial and field elements for generating roots of the affine polynomial are determined. Gray code is used to select the field elements used to generate the different roots of the affine polynomial. The roots are tested as possible true roots of the error locator polynomial.
Claims16
An apparatus for processing an erroneous code word comprising:
- an error locator polynomial generator to determine an error locator polynomial associated with the erroneous code word;
- circuitry to find field elements for generating roots of a least affine multiple of the error locator polynomial;
- an error locator polynomial root determination unit to use a Gray code sequence to select linear combinations of one or more of the field elements to generate the roots of the least affine multiple and evaluate such roots as true roots of the error locator polynomial;
- wherein the error locator polynomial root determination unit operates on the error locator polynomial in a form that includes coefficients which comprise linearized polynomials, the error locator polynomial root determination unit providing values of the linearized polynomials for each of the field elements;
- and
- wherein, during each root generation, the error locator polynomial root determination unit uses the Gray code sequence to select a linear combination of one or more of the values for each of the linearized polynomials so that such values are selected when the field elements for which such values are provided are selected.
3 more elements
A method for processing an erroneous code word comprising:
- determining an error locator polynomial associated with the erroneous code word;
- finding field elements for generating roots of a least affine multiple of the error locator polynomial;
- using a Gray code sequence to select linear combinations of one or more of the field elements to generate the roots of the least affine multiple;
- providing the error locator polynomial in a form that includes coefficients which comprise linearized polynomials;
- providing values of the linearized polynomials for each of the field elements;
- and
- during each root generation, using the Gray code sequence to select a linear combination of one or more of the values for each of the linearized polynomials so that such values are selected when the field elements for which such values are provided are selected;
- and
- evaluating the roots as the true roots of the error locator polynomial.
6 more elements
An apparatus for processing an erroneous code word comprising:
- an error locator polynomial generator to determine an error locator polynomial associated with the erroneous code word;
- circuitry to find field elements for generating roots of a least affine multiple of the error locator polynomial;
- an error locator polynomial root determination unit to use a binary code sequence to select linear combinations of one or more of the field elements to generate the roots of the least affine multiple and evaluate such roots as true roots of the error locator polynomial;
- wherein the error locator polynomial root determination unit operates on the error locator polynomial in a form that includes coefficients which comprise linearized polynomials, the error locator polynomial root determination unit providing values of the linearized polynomials for each of the field elements;
- and
- wherein, during each root generation, the error locator polynomial root determination unit uses the binary code sequence to select a linear combination of one or more of the values for each of the linearized polynomials so that such values are selected when the field elements for which such values are provided are selected.
3 more elements
A method for processing an erroneous code word comprising:
- determining an error locator polynomial associated with the erroneous code word;
- finding field elements for generating roots of a least affine multiple of the error locator polynomial;
- using a binary code sequence to select linear combinations of one or more of the field elements to generate the roots of the least affine multiple;
- providing the error locator polynomial in a form that includes coefficients which comprise linearized polynomials;
- providing values of the linearized polynomials for each of the field elements;
- and
- during each root generation, using the binary code sequence to select a linear combination of one or more of the values for each of the linearized polynomials so that such values are selected when the field elements for which such values are provided are selected;
- and
- evaluating the roots as the true roots of the error locator polynomial.
6 more elements
A disk drive unit comprising:
- a disk;
- a decoder;
- and
- a read/write controller connected to the disk and the decoder, the read/write controller reading an erroneous code word from the disk and providing the erroneous code word to the decoder;
- wherein the decoder comprises:
- an error locator polynomial generator to determine an error locator polynomial associated with the erroneous code word;
- circuitry to find field elements for generating roots of a least affine multiple of the error locator polynomial;
- an error locator polynomial root determination unit to use a binary code sequence to select linear combinations of one or more of the field elements to generate the roots of the least affine multiple and evaluate such roots as true roots of the error locator polynomial;
- wherein the error locator polynomial root determination unit operates on the error locator polynomial in a form that includes coefficients which comprise linearized polynomials, the error locator polynomial root determination unit providing values of the linearized polynomials for each of the field elements;
- and
- wherein, during each root generation, the error locator polynomial root determination unit uses the binary code sequence to select a linear combination of one or more of the values for each of the linearized polynomials so that such values are selected when the field elements for which such values are provided are selected.
8 more elements
Dependencies are inferred from the claim text.