RS Decoding Lookup Tables for Faster Error Validation
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Solution Overview
Problem
Conventional RS error correction algorithms require significant memory for lookup tables, leading to slow data processing and limited application, and lack validation of error codes, resulting in low stability and security.
Innovation Solution
A RS error correction decoding method that uses a lookup table f(αj) for power exponents of α in GF(2m) to calculate coefficients of the generator and remainder polynomials, reducing memory usage and incorporating an additional redundant code for error validation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a lookup table with 2^m elements is used for RS error correction calculation, then the error correction capability is improved, but the memory occupation increases and data processing speed decreases
Solution Approach 1:
The patent segments the large lookup table into multiple smaller sub-lookup tables. Instead of using a single 2^m element table, the algorithm divides it into several tables with fewer elements each, allowing parallel or sequential access that reduces memory access time and improves processing speed while maintaining the same error correction capability.
Solution Approach 2:
The patent transforms the one-dimensional large lookup table into a multi-dimensional structure by creating multiple sub-lookup tables organized in a hierarchical or distributed manner. This dimensional transformation allows the system to access required data through multiple smaller tables rather than one large table, reducing memory access latency and improving processing throughput.
2Reliability
If a lookup table with 2^m elements is used for RS error correction calculation, then the error correction capability is improved, but the memory occupation increases
Solution Approach 1:
The patent segments the large lookup table into multiple smaller sub-lookup tables. Instead of using a single 2^m element table, the algorithm divides it into several tables with fewer elements each, reducing the peak memory occupation while maintaining the same error correction capability through distributed storage and access.
Solution Approach 2:
The patent implements a strategy where not all lookup table elements are loaded into memory simultaneously. Instead, only the necessary sub-lookup tables are loaded based on the current processing requirements, and other tables are discarded from active memory and recovered when needed, thereby reducing overall memory occupation while preserving full error correction capability.
3Device complexity
If conventional RS error correction algorithm is used, then the error correction process is simple, but the stability and correctness of the system is low due to lack of error checking
Solution Approach 1:
The patent introduces a feedback mechanism where the error correction process includes verification steps. After correcting errors using the RS algorithm, the system performs checking operations to verify the correctness of the correction, creating a feedback loop that enhances system stability and reliability without significantly complicating the overall algorithm structure.
Solution Approach 2:
The patent performs preliminary error checking and validation operations before finalizing the error correction process. By incorporating verification steps in advance, the system ensures the stability and correctness of the error correction without requiring complex post-processing, thus maintaining algorithm simplicity while improving reliability.
Data Source
AI summary
A decoding method includes that when encoding at a sending terminal, for a m-order primitive polynomial P(x), a primitive field element in galois field GF(2m) is represented by α; a lookup table f(αj) for different power exponents of α is established, where the value of j is selected from all the integers ranging from 0 to 2m−1, with a total number of 2m; a generator polynomial G(x) is expanded to obtain a polynomial with respect to x, with coefficients being an addition or subtraction of the power exponents of α; a remainder polynomial R(x), obtained by dividing code word polynomial Q(x) by the generator polynomial G(x), is a polynomial with respect to x, with coefficients being an addition or subtraction of the power exponents of α; and the coefficients of the generator polynomial G(x) and the remainder polynomial R(x) are both calculated using data found in the lookup table f(αj).