Reed-Solomon Coding with Compact Lookup Tables and Data Validation
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Solution Overview
Problem
Conventional RS error correction methods require large memory for lookup tables, leading to slow data processing and limited application, and lack validation of error-corrected data, resulting in low security and stability.
Innovation Solution
A lookup table f(αj) with 2m exponents of the primitive field element α is established for calculating coefficients of the generator and remainder polynomials, reducing memory usage and incorporating an additional redundant code for data validation during encoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional RS error correction methods use large lookup tables for Galois field operations, then decoding accuracy is maintained, but memory consumption increases and data processing speed decreases
Solution Approach 1:
The patent divides the traditional single large lookup table into multiple smaller lookup tables, each storing specific Galois field operation results (multiplication, division, exponentiation). This segmentation reduces the memory footprint of each individual table while collectively maintaining all necessary decoding functionality, thus resolving the contradiction between maintaining decoding accuracy and reducing memory consumption
Solution Approach 2:
The patent transforms the memory storage structure by organizing lookup tables in a multi-dimensional manner, where tables are arranged by operation type and can be selectively accessed. This dimensional organization allows the system to load only necessary table segments into memory, reducing overall memory consumption while preserving complete decoding capability through structured access patterns
2Adaptability or versatility
If conventional RS error correction methods use large lookup tables, then complete Galois field operations are supported, but data processing speed is limited
Solution Approach 1:
The patent pre-calculates and stores results of complex Galois field operations (multiplication, division, exponentiation) in separate lookup tables before runtime. During actual decoding, the system simply retrieves pre-computed results rather than performing time-consuming calculations, significantly improving data processing speed while maintaining full Galois field operation capability through the organized table structure
Solution Approach 2:
The patent creates multiple copies of essential lookup table segments that can be loaded into different memory regions or cache levels. This copying strategy allows parallel access to identical operational data, improving processing speed through concurrent operations while the modular table design keeps each copy compact, thus balancing versatility with productivity
3Productivity
If conventional RS error correction algorithms do not validate error codes after correction, then processing is faster, but system stability and correctness are reduced
Solution Approach 1:
The patent implements a feedback mechanism where the decoded data undergoes validation checking using the syndrome calculation results. The system feeds back the correction results to a validation stage that verifies whether the corrected data satisfies the expected error-free conditions. This feedback loop ensures system stability and correctness while the efficient lookup table structure minimizes the overhead time, maintaining acceptable processing speed
Data Source
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AI summary
The present invention provides a RS error correction decoding method. In the method, 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). With the RS error correction decoding method, system memory is greatly saved, and the flexibility and convenience in applying the RS error correction code are improved.