Adjacent 2-Bit Error Correction Using H-Matrix Syndrome Links
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Solution Overview
Problem
Existing error correction methods, particularly those using Bose-Chaudhuri-Hocquenghem (BCH) codes, are inefficient in determining the zeroes of the locator polynomial, leading to high processing time for error correction.
Innovation Solution
A method is proposed that uses an H-matrix to process errors in a sequence of bits, where an error syndrome is determined and linked with components of the H-matrix, allowing for the correction of adjacent 2-bit errors by inverting error syndrome components based on the H-matrix columns.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the Chien algorithm is used to determine zeroes of the locator polynomial, then error correction capability is achieved, but processing time becomes excessively long
Solution Approach 1:
The patent segments the error correction problem by distinguishing between adjacent 2-bit errors and other error patterns. By checking specific syndrome conditions (s0 = s2 and s1 = s3 for adjacent errors), the algorithm can quickly identify and correct adjacent 2-bit errors without performing the complete time-consuming Chien algorithm, thus reducing overall processing time while maintaining error correction capability
Solution Approach 2:
The patent applies partial action by implementing a simplified correction approach for specific error cases (adjacent 2-bit errors) rather than applying the full Chien algorithm to all error patterns. This partial correction method checks only necessary syndrome components and applies correction only when specific conditions are met, significantly reducing processing time for the common case of adjacent errors while still providing comprehensive error correction through the full algorithm when needed
2Adaptability or versatility
If general error correction methods are used, then all types of errors can be corrected, but correction speed is reduced
Solution Approach 1:
The patent applies local quality by implementing different correction strategies for different error patterns. For adjacent 2-bit errors, it uses a specialized fast correction method that checks syndrome relationships and applies direct correction. For other error patterns, it falls back to the general Chien algorithm. This localized optimization maintains versatility in handling all error types while achieving high-speed correction for the specific case of adjacent errors
Data Source
AI summary
What is proposed is a solution for processing errors in a sequence of bits, wherein the sequence of bits, in the error-free case, forms a codeword of an error code, wherein the error code is based on an H-matrix or is able to be determined thereby, wherein an error syndrome is determined for the sequence of bits, wherein a link is determined between components of the error syndrome and parts of the H-matrix, and wherein two adjacent bits in the sequence of bits are corrected if the link adopts a predefined value.