System and method for multi-dimensional encoding and decoding
First Claim
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1. A method for decoding comprising:
- receiving data encoded by a component codeword configured to correct up to a maximum number of errors (q) in the data;
generating an error locator polynomial (ELP) of a predetermined order (r) defining the locations in the component codeword of up to (r) errors, wherein;
if the maximum number of errors (q) that the component codeword is configured to correct is equal to the predetermined order (r), the ELP includes (r) roots corresponding to up to (r) errors to be corrected by the component codeword and if the maximum number of errors (q) that the component codeword is configured to correct is less than the predetermined order (r), the ELP includes (q) roots corresponding to up to (q) errors to be corrected by the component codeword and (r-q) virtual roots added to generate the ELP of the predetermined order (r); and
correcting up to (q) errors at locations in the component code defined by the (q) roots of the ELP.
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Abstract
A system and method for using a cyclic redundancy check (CRC) to evaluate error corrections. A set of data and initial CRC values associated therewith may be received. The set of data by changing a sub-set of the data may be corrected. Intermediate CRC values may be computed for the entire uncorrected set of data in parallel with said correcting. Supplemental CRC values may be computed for only the sub-set of changed data after said correcting. The intermediate and supplemental CRC values may be combined to generate CRC values for the entire corrected set of data. The validity of the corrected set of data may be evaluated by comparing the combined CRC values with the initial CRC values.
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Citations
20 Claims
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1. A method for decoding comprising:
- receiving data encoded by a component codeword configured to correct up to a maximum number of errors (q) in the data;
generating an error locator polynomial (ELP) of a predetermined order (r) defining the locations in the component codeword of up to (r) errors, wherein;
if the maximum number of errors (q) that the component codeword is configured to correct is equal to the predetermined order (r), the ELP includes (r) roots corresponding to up to (r) errors to be corrected by the component codeword and if the maximum number of errors (q) that the component codeword is configured to correct is less than the predetermined order (r), the ELP includes (q) roots corresponding to up to (q) errors to be corrected by the component codeword and (r-q) virtual roots added to generate the ELP of the predetermined order (r); and
correcting up to (q) errors at locations in the component code defined by the (q) roots of the ELP. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
- receiving data encoded by a component codeword configured to correct up to a maximum number of errors (q) in the data;
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11. A system for decoding comprising:
- a memory to store data encoded by a component codeword configured to correct up to a maximum number of errors (q) in the data; and
a decoder configured to correct up to a maximum number of errors (r) in the data, the decoder to generate an error locator polynomial (ELP) of a predetermined order (r) defining the locations in the component codeword of up to (r) errors, wherein if the maximum number of errors (q) that the component codeword is configured to correct is equal to the predetermined order (r), the ELP includes (r) roots corresponding to up to (r) errors to be corrected by the component codeword and if the maximum number of errors (q) that the component codeword is configured to correct is less than the predetermined order (r), the ELP includes (q) roots corresponding to up to (q) errors to be corrected by the component codeword and (r-q) virtual roots added to generate the ELP of the predetermined order (r), and the decoder to correct up to (q) errors at locations in the component code defined by the (q) roots of the ELP. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20)
- a memory to store data encoded by a component codeword configured to correct up to a maximum number of errors (q) in the data; and
Specification