Parallel inversionless error and erasure processing

1. A method for decoding, comprising:

obtaining a syndrome polynomial;

obtaining erasure locations, if any, wherein the syndrome polynomial and the erasure locations are associated with Reed-Solomon encoded information to be error and erasure decoded; and

using a processor to simultaneously generate a complementary error evaluator polynomial and an error locator polynomial using the syndrome polynomial and erasure locations, wherein simultaneously generating is performed in a unified manner without separately removing erasure related information and performing error-only decoding using the erasure-removed information.

2. A method as recited in claim 1 , wherein simultaneously generating is performed in an inversionless manner.

3. A method as recited in claim 1 further comprising determining one or more error locations using the complementary error evaluator polynomial and the error locator polynomial.

4. A method for decoding, comprising:

obtaining a syndrome polynomial;

obtaining erasure locations, if any, wherein the syndrome polynomial and the erasure locations are associated with Reed-Solomon encoded information to be error and erasure decoded;

using a processor to simultaneously generate a complementary error evaluator polynomial and an error locator polynomial me polynomial and erasure locations; and

using the processor to determine one or more error locations using the complementary error evaluator polynomial and the error locator polynomial, including

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5. A system for decoding, comprising:

an interface configured to:

obtain a syndrome polynomial; and

obtain erasure locations, if any, wherein the syndrome polynomial and the erasure locations are associated with Reed-Solomon encoded information to be error and erasure decoded; and

a processor configured to:

simultaneously generate a complementary error evaluator polynomial and an error locator polynomial using the syndrome polynomial and erasure locations; and

determine one or more error locations using the complementary error evaluator polynomial and the error locator polynomial, including

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6. A system as recited in claim 5 , wherein the processor is configured to simultaneously generate a complementary error evaluator polynomial and an error locator polynomial in an inversionless manner.

7. A system as recited in claim 5 , wherein the processor is further configured to determine one or more error locations using the complementary error evaluator polynomial and the error locator polynomial.

8. A system as recited in claim 5 , wherein the system is systolic.

9. A system for decoding, comprising:

an interface configured to:

obtain a syndrome polynomial; and

obtain erasure locations, if any, wherein the syndrome polynomial and the erasure locations are associated with Reed-Solomon encoded information to be error and erasure decoded; and

a processor configured to: simultaneously generate a complementary error evaluator polynomial and an error locator polynomial using the syndrome polynomial and erasure locations, wherein simultaneously generating is performed in a unified manner without separately removing erasure related information and performing error-only decoding using the erasure-removed information.

10. A computer program product for decoding, the computer program product being embodied in a non-transitory computer readable storage medium and comprising computer instructions for:

obtaining a syndrome polynomial;

obtaining erasure locations, if any, wherein the syndrome polynomial and the erasure locations are associated with Reed-Solomon encoded information to be error and erasure decoded; and

simultaneously generating a complementary error evaluator polynomial and an error locator polynomial using the syndrome polynomial and erasure locations, wherein simultaneously generating is perform in a unified manner without separately removing erasure related information and performing error-only decoding using the erasure-removed information.

11. A computer program product as recited in claim 10 , wherein the computer instructions for simultaneously generating are configured to perform it in an inversionless manner.

12. A computer program product as recited in claim 10 , the computer program product further comprising computer instructions for determining one or more error locations using the complementary error evaluator polynomial and the error locator polynomial.

13. A computer program product for decoding, the computer program product being embodied in a non-transitory computer readable storage medium and comprising computer instructions for:

obtaining a syndrome polynomial;

obtaining erasure locations, if any, wherein the syndrome polynomial and the erasure locations are associated with Reed-Solomon encoded information to be error and erasure decoded;

simultaneously generating a complementary error evaluator polynomial and an error locator polynomial using the syndrome polynomial and erasure locations; and

determining one or more error locations using the complementary error evaluator polynomial and the error locator polynomial, including

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