Fast Syndrome Calculation via Intermediate Code-Domain Mapping
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Solution Overview
Problem
Existing error correction methods are inefficient, particularly in codes like Hamming, BCH, Reed-Muller, Simplex, Golay, and Goppa codes, where syndrome calculations are time-consuming and power-intensive, especially for multi-bit errors.
Innovation Solution
The method involves transitioning between code domains using linear mappings to perform syndrome calculations in one code domain and efficient error correction in another, leveraging known efficient algorithms, with specific matrix transformations to optimize syndrome calculation and correction processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If syndrome calculation is performed using traditional methods in error correcting codes, then error detection and correction capability is maintained, but computational complexity and power consumption increase significantly
Solution Approach 1:
The patent segments the syndrome calculation process by introducing an intermediate code domain transformation. Instead of directly calculating syndromes in the original code domain, the method divides the process into: (1) transforming received vectors to an intermediate code domain, (2) performing simplified syndrome calculation in the intermediate domain, and (3) transforming results back if needed. This segmentation reduces computational complexity at each stage while maintaining error correction capability.
Solution Approach 2:
The patent introduces an intermediate code domain as a mediator between the received code and the error correction process. By transforming the received vector through a linear mapping to an intermediate domain, the syndrome calculation becomes computationally simpler. The intermediate domain acts as a bridge that facilitates efficient processing while preserving the essential error detection and correction properties.
2Measurement precision
If syndrome calculation is performed using traditional methods, then error detection accuracy is maintained, but calculation time increases
Solution Approach 1:
The calculation process is segmented into transformation and syndrome calculation stages. The linear mapping to an intermediate code domain separates the complex syndrome calculation from the received vector, allowing pre-computation of transformation matrices and simplifying the actual syndrome calculation step, thereby reducing overall calculation time while maintaining accuracy.
Solution Approach 2:
The transformation matrices for mapping to and from the intermediate code domain are pre-computed and stored. This preliminary action eliminates the need to perform complex matrix operations during real-time error correction, significantly reducing calculation time while preserving error detection accuracy through the use of predetermined transformation relationships.
3Productivity
If efficient error correction algorithms are used in the original code domain, then correction speed is maintained, but syndrome calculation complexity remains high
Solution Approach 1:
The patent segments the overall error correction function into two distinct parts: a simple syndrome calculation in the intermediate code domain and the existing efficient error correction algorithm applied to transformed syndromes. This segmentation allows the use of simple, low-complexity syndrome calculation while preserving the efficiency of established error correction algorithms through the intermediate transformation.
Solution Approach 2:
The intermediate code domain serves as a mediator that transforms the received vector into a form where syndrome calculation is computationally simpler. The linear mappings to and from this intermediate domain enable the use of efficient error correction algorithms on transformed data, reducing device complexity while maintaining correction speed through the intermediary transformation process.
Data Source
AI summary
Error correction is proposed in which a syndrome calculation is carried out in a code domain of a second code and an efficient error correction algorithm is carried out in a code domain of a first code.