System and method for multi-dimensional encoding and decoding
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.
1. A method for using a cyclic redundancy check (CRC) to evaluate error corrections, the method comprising:
receiving a set of data and initial CRC values associated therewith,
correcting the set of data by changing a sub-set of the data;
computing intermediate CRC values for the entire uncorrected set of data in parallel with said correcting;
computing supplemental CRC values for only the sub-set of changed data after said correcting;
combining the intermediate and supplemental CRC values to generate CRC values for the entire corrected set of data; and
evaluating the validity of the corrected set of data by comparing the combined CRC values with the initial CRC values.
2. The method of claim 1 , wherein the corrected set of data is validated if the combined CRC values substantially match the initial CRC values and invalidated if the combined CRC values do not substantially match the initial CRC values.
3. The method of claim 1 , wherein a single clock cycle is used after said correcting to evaluate the validity of the corrected set of data for each data bit corrected in the corrected set of data.
4. The method of claim 1 , wherein the sub-set of changed data is defined by an error vector only having non-zero values at jth indices associated with changed bits in the sub-set of changed data.
5. The method of claim 4 comprising operating on the error vector to generate the supplemental CRC values at each jth index.
6. The method of claim 4 comprising incrementing the values at each jth index at each register of a linear feedback shift-register by a primitive element in a finite field to achieve the supplemental CRC values at each jth index in the finite field.
7. The method of claim 6 comprising incrementing the values at each jth index at each register of the linear feedback shift-register by powers of two in a binary field to achieve the supplemental CRC values at each jth index in the binary field.
8. The method of claim 1 , wherein errors are potentially induced while transferring the set of received data and the initial CRC values are computed before said transferring.
9. The method of claim 1 , wherein the set of data and initial CRC values are encoded together.
10. A system for using a cyclic redundancy check (CRC) to evaluate error corrections, the system comprising:
a memory to store a set of data and initial CRC values associated therewith; and
a processor to receive the set of data and associated initial CRC values, correct the set of data by changing a sub-set of the data, compute intermediate CRC values for the entire uncorrected set of data in parallel with said correcting, compute supplemental CRC values for only the sub-set of changed data after said correcting; combine the intermediate and supplemental CRC values to generate CRC values for the entire corrected set of data, and evaluate the validity of the corrected set of data by comparing the combined CRC values with the initial CRC values.
11. The system of claim 10 , wherein the processor validates the corrected set of data if the combined CRC values substantially match the initial CRC values and invalidates the corrected set of data if the combined CRC values do not substantially match the initial CRC values.
12. The system of claim 10 , wherein the processor uses a single clock cycle after said correcting to evaluate the validity of the corrected set of data for each data bit corrected in the corrected set of data.
13. The system of claim 10 , wherein the sub-set of changed data is defined by an error vector only having non-zero values at jth indices associated with changed bits in the sub-set of changed data.
14. The system of claim 13 , wherein the processor operates on the error vector to generate the supplemental CRC values at each jth index.
15. The system of claim 13 , wherein the processor increments the values at each jth index at each register of a linear feedback shift-register by a primitive element in a finite field to achieve the supplemental CRC values at each jth index in the finite field.
16. The system of claim 15 , wherein the processor increments the values at each jth index at each register of the linear feedback shift-register by powers of two in a binary field to achieve the supplemental CRC values at each jth index in the binary field.