Chien Search Skipping in Reed-Solomon Chase Decoding
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Solution Overview
Problem
Existing Chase-type decoders for Reed-Solomon codes are computationally inefficient due to the dominance of Chien search operations in high-rate codes, which can lead to incorrect error locator polynomials being passed to the Chien search, especially when errors exceed the code's correction capability.
Innovation Solution
The proposed solution involves skipping the Chien search when the error locator polynomial's length exceeds a threshold, selecting candidate polynomials based on reliability, and performing a Chien search only when necessary, thereby reducing computational time and improving the accuracy of error location determination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Chien search is performed on all error locator polynomials, then error location accuracy is maintained, but computational time increases significantly
Solution Approach 1:
The patent changes the parameter of error locator polynomial degree as a decision criterion. When the degree exceeds a threshold (t), the system skips Chien search and directly declares decoding failure. This parameter-based filtering resolves the contradiction by avoiding unnecessary computational operations on polynomials that cannot yield valid results, thus reducing computational time while maintaining accuracy for valid cases.
Solution Approach 2:
The patent applies partial action by performing Chien search only on a subset of error locator polynomials (those with degree ≤ t) rather than all generated polynomials. This selective approach eliminates wasted computational effort on excessive polynomials that exceed the code's error correction capability, thereby reducing overall computational time while preserving complete error location accuracy for decodable cases.
2Reliability
If Chase decoding flips and erases bits to correct excessive errors, then error correction capability is improved, but incorrect error locator polynomials are generated leading to wasted Chien search operations
Solution Approach 1:
The patent performs preliminary validation by checking the degree of error locator polynomials before executing Chien search. This preliminary action filters out invalid polynomials generated by Chase decoding's bit flipping and erasing operations, preventing wasted computational resources on incorrect polynomials and improving overall decoding efficiency while maintaining the ability to correct excessive errors.
Solution Approach 2:
The patent introduces feedback through the degree check mechanism that informs the decoding process whether to proceed with Chien search or declare failure. This feedback loop prevents the system from wasting productivity on incorrect error locator polynomials generated during Chase decoding, allowing the system to adaptively respond to the validity of each polynomial and maintain high error correction capability without efficiency loss.
3Speed
If threshold t is set low, then computational speed increases by skipping more Chien searches, but risk of false negatives increases
Solution Approach 1:
The patent optimizes the threshold parameter t to achieve the best balance between speed and reliability. By setting t appropriately (where t ≤ τ and 2t ≤ d-1), the system ensures that all correctable error patterns are captured (maintaining reliability) while filtering out enough invalid polynomials to achieve significant speed improvement. This parameter optimization resolves the contradiction by finding the optimal operating point.
Solution Approach 2:
The patent applies local quality by making the threshold t adaptable to specific code parameters and error patterns. Rather than using a fixed universal threshold, the system can adjust t locally based on the code's error correction capability τ and minimum distance d, ensuring optimal performance for each specific decoding scenario while maintaining the speed-accuracy balance.
Data Source
AI summary
Data is processed by obtaining a length of an error locator polynomial. It is determined whether the length of the error locator polynomial is greater than a threshold. In the event the length of the error locator polynomial is greater than the threshold, performance of a Chien search on the error locator polynomial is skipped. In the event the length of the error locator polynomial is less than or equal to than the threshold, the Chien search is performed on the error locator polynomial to determine one or more roots of the error locator polynomial, where the roots correspond to one or more error locations.