Composite-Field Syndrome Calculation With Integrated Basis Conversion
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Solution Overview
Problem
Existing error-correction systems face increased circuit size and reduced operating frequency due to the need for separate syndrome calculation and basis conversion processes in Galois field to composite field representation for error-detection and correction.
Innovation Solution
A syndrome calculation circuit that integrates matrix product calculation to generate syndrome bits in a composite field by combining the basis conversion and syndrome calculation processes, reducing circuit size and enhancing processing speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If separate syndrome calculation and basis conversion processes are used, then error-correction functionality is achieved, but circuit size increases and operating frequency decreases
Solution Approach 1:
The patent combines the syndrome calculation circuit and basis conversion circuit into a single integrated circuit. The syndrome calculation unit calculates syndrome values from input data, and the basis conversion unit simultaneously converts these syndrome values from Galois field representation to composite field representation. This merging eliminates the need for separate circuits, reducing overall circuit size and complexity while maintaining error-correction functionality.
2Reliability
If separate syndrome calculation and basis conversion processes are used, then error-correction functionality is achieved, but operating frequency decreases
Solution Approach 1:
The integrated circuit performs syndrome calculation and basis conversion in a unified architecture, allowing simultaneous execution of both operations. This eliminates the sequential processing required in separate circuits, reducing total processing time and enabling higher operating frequencies while maintaining reliable error-correction functionality.
3Reliability
If basis conversion from Galois field to composite field is performed, then error-correction processing is enabled, but the number of XOR gates and stages increases
Solution Approach 1:
The patent implements a specialized basis conversion unit with an optimized structure that performs field conversion using a minimal set of XOR gates arranged in efficient stages. The conversion unit is designed to handle the specific mathematical requirements of Galois field to composite field transformation with the least necessary computational resources, reducing the number of XOR gates and stages compared to generic implementation approaches.
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.