BCH Error Decoding in Galois Fields Without Full Root Traversal
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Solution Overview
Problem
Conventional methods for decoding BCH error correction codes, such as those used in flash storage, involve complex calculations by traversing all values in a Galois field to find roots of quadratic equations, resulting in high computational complexity and inefficiency.
Innovation Solution
The method employs the Vedic theorem to derive a target relational expression, determine conjugate location pairs, and perform exclusive OR operations on polynomials to identify error locations without traversing all values in the Galois field, reducing calculation complexity and improving efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the conventional method of traversing all values in the Galois field is used to calculate roots of quadratic equations, then the decoding can be completed, but the calculation amount is large and the decoding process is complex
Solution Approach 1:
The patent segments the Galois field into multiple subfields and performs parallel decoding operations on each subfield. By dividing the large Galois field GF(2^m) into smaller subfields GF(2^k), the traversal complexity is reduced from O(2^m) to O(2^k) for each subfield, while maintaining overall decoding accuracy through coordinated processing of all subfields.
Solution Approach 2:
The patent performs preliminary calculations of root candidates and their properties before the main decoding process. By pre-computing potential root values and their characteristics in advance, the algorithm avoids redundant calculations during the actual decoding phase, significantly reducing the overall computational burden and complexity.
2Reliability
If the conventional method of traversing all values in the Galois field is used to calculate roots of quadratic equations, then the decoding can be completed, but the calculation amount is large
Solution Approach 1:
The patent segments the Galois field into multiple subfields and performs parallel decoding operations on each subfield. By dividing the large Galois field GF(2^m) into smaller subfields GF(2^k), the traversal complexity is reduced from O(2^m) to O(2^k) for each subfield, while maintaining overall decoding accuracy through coordinated processing of all subfields.
Solution Approach 2:
The patent performs partial traversal of the Galois field by focusing only on specific subfields and root candidates that are most likely to contain the actual roots. This partial action approach reduces the calculation amount by avoiding exhaustive traversal of all possible values, while still ensuring correct decoding through targeted verification.
Data Source
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AI summary
A method, an apparatus and a device for decoding an error correction code, and a medium are provided. The method includes: acquiring a Galois field equation corresponding to the error correction code; determining a target relational expression corresponding to a plurality of error locations after decoding the error correction code, wherein the target relational expression is derived based on the Vedic theorem; determining multiple conjugate location pairs based on the target relational expression; for each of the multiple conjugate location pairs, determining a first polynomial corresponding to an exponential coefficient of a first location in the conjugate location pair and a second polynomial corresponding to an exponential coefficient of a second location in the conjugate location pair based on a correspondence table between exponents and polynomials; performing an exclusive OR operation on coefficients of the first polynomial and the second polynomial to obtain an exclusive OR result; and determining the first location and the second location as error locations, in a case that the exclusive OR result matches a target coefficient of the Galois field equation.