Composite-Field Syndrome Calculation Circuit for Faster ECC
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Solution Overview
Problem
Existing error-correction systems face increased circuit size and decreased operating frequency due to the need for basis conversion from Galois field to composite field representation for syndrome calculation, which complicates error-detection and error-correction processing.
Innovation Solution
A syndrome calculation circuit that integrates matrix product calculation to generate syndrome bits in a composite field by multiplying input data bits with a basis conversion matrix and a parity check matrix, reducing circuit size and enhancing processing speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If basis conversion from Galois field to composite field is performed for syndrome calculation, then error-correction capability is improved, but circuit size increases and operating frequency decreases
Solution Approach 1:
The patent merges the basis conversion function and syndrome calculation function into a single integrated circuit. The syndrome calculation circuit directly computes syndrome bits in composite field representation by multiplying input data bits with a parity check matrix, eliminating the need for separate basis conversion circuits. This integration reduces circuit size while maintaining error-correction capability.
Solution Approach 2:
The patent changes the computational parameter from Galois field representation to composite field representation directly in the syndrome calculation process. By performing matrix multiplication in composite field and applying basis conversion during the calculation rather than as a separate step, the circuit achieves both error-correction capability and reduced complexity.
2Reliability
If basis conversion from Galois field to composite field is performed for syndrome calculation, then error-correction capability is improved, but operating frequency decreases
Solution Approach 1:
The patent merges the basis conversion function and syndrome calculation function into a single integrated circuit. The syndrome calculation circuit directly computes syndrome bits in composite field representation by multiplying input data bits with a parity check matrix, eliminating the need for separate basis conversion circuits. This integration reduces circuit size while maintaining error-correction capability.
Solution Approach 2:
The patent performs basis conversion preparation in advance by designing the parity check matrix in composite field representation. This preliminary setup allows the syndrome calculation to directly produce composite field syndrome bits without requiring subsequent basis conversion operations, thereby increasing operating frequency.
3Measurement precision
If separate basis conversion circuit and syndrome calculation circuit are used, then processing accuracy is maintained, but circuit complexity increases
Solution Approach 1:
The patent merges the basis conversion function and syndrome calculation function into a single integrated circuit. The syndrome calculation circuit directly computes syndrome bits in composite field representation by multiplying input data bits with a parity check matrix, eliminating the need for separate basis conversion circuits. This integration reduces circuit size while maintaining error-correction capability.
Data Source
AI summary
A syndrome calculation circuit includes a matrix product calculation circuit. The matrix product calculation circuit is configured to generate syndrome bits in a composite field by calculating a matrix product of input data bits and a first arithmetic matrix. The first arithmetic matrix is a matrix product of a basis conversion matrix for converting a data string from a Galois field to the composite field and a second arithmetic matrix, which is at least a part of a parity check matrix.