BCH Error Decoding Using Vieta-Based Error Location Search
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Solution Overview
Problem
Conventional methods for decoding BCH error correction codes require traversing all values in a Galois field to calculate roots, resulting in a complex and computationally intensive process.
Innovation Solution
The method involves acquiring a Galois field equation, determining a target relational expression based on Vieta's formulas, and reducing the traversal range to determine error locations, thereby reducing the calculation amount and complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all values in the Galois field are traversed to calculate roots of the quadratic equation, then the error locations can be determined, but the calculation amount increases and the decoding process becomes complex
Solution Approach 1:
The patent segments the Galois field traversal into two parts: first traversing only half of the field values to find one error location, then using Vieta's formulas to calculate the second error location without traversal. This segmentation reduces the traversal scope while maintaining complete error location determination.
Solution Approach 2:
The patent performs preliminary action by deriving Vieta's formulas beforehand to establish the relationship between the two error locations. Once one error location is found through traversal, the second can be directly calculated using the pre-derived formulas, avoiding the need to traverse the entire field.
2Reliability
If all values in the Galois field are traversed to calculate roots, then complete error correction is achieved, but the calculation amount becomes large
Solution Approach 1:
The patent segments the error location determination into two stages: first determining one error location by traversing half the field values, then determining the second error location through mathematical calculation using Vieta's formulas. This segmentation maintains complete error correction capability while reducing the traversal workload by approximately half.
Solution Approach 2:
The patent changes the parameter of traversal range from the complete Galois field to half of the Galois field, combined with introducing the relational parameter from Vieta's formulas. This parameter change reduces the calculation amount while preserving the ability to determine both error locations accurately.
Data Source
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, where a total length of the error correction code is a predetermined number of digits; determining a target relational expression corresponding to a plurality of error locations after decoding the error correction code based on the Galois field equation, where the target relational expression is derived based on the Vieta's formulas; determining a first traversal range based on the target relational expression and the predetermined number of digits; determining a first error location from values included in the first traversal range; and determining a second error location based on the target relational expression and the first error location.