LDPC Offset BP Decoding with Corrected Row LLR Approximation
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Solution Overview
Problem
The Offset BP-based decoding method for LDPC codes has low precision and inadequate decoding performance due to its approximate arithmetic operations, which are influenced by variables, leading to a high number of arithmetic operations and reduced circuit implementation efficiency.
Innovation Solution
A decoding method that approximates the row arithmetic operation of the Sum-Product decoding method using an Offset BP-based approach by setting the row LLR as the minimum of column LLRs minus an offset, thereby improving precision and reducing arithmetic operations, while maintaining a similar circuit scale to the Offset BP-based method.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Sum-Product decoding method is used, then decoding performance is high, but the amount of arithmetic operations is large and circuit implementation is difficult
Solution Approach 1:
The patent changes the parameter representation from natural logarithms (Sum-Product) to base-2 logarithms. This transformation allows the use of binary arithmetic operations instead of complex floating-point operations, significantly reducing circuit complexity while maintaining decoding performance. The row LLR and column LLR calculations are reformulated using bitwise operations and lookup tables based on the base-2 logarithmic transformation.
2Productivity
If Offset BP-based decoding method is used, then the amount of arithmetic operations is reduced, but decoding performance deteriorates due to low precision approximate arithmetic operations
Solution Approach 1:
The patent introduces a correction parameter γ (gamma) that is added to the minimum absolute value of column LLRs during row processing. This correction term compensates for the approximation error inherent in Offset BP methods. By dynamically adjusting γ based on the minimum LLR magnitude, the method maintains high decoding performance while preserving the computational efficiency of approximate arithmetic operations.
Solution Approach 2:
The patent implements a feedback mechanism where the correction parameter γ is determined based on the minimum absolute value of column LLRs from the previous iteration. This feedback loop allows the system to adaptively adjust the correction amount, ensuring that approximation errors are compensated without requiring full Sum-Product decoding complexity. The correction is applied iteratively to improve decoding accuracy.
3Reliability
If variable offset parameter is used, then decoding performance is improved, but the amount of arithmetic operations increases
Solution Approach 1:
The patent pre-calculates and stores correction parameters γ in lookup tables before the actual decoding process. These pre-computed values are based on the minimum LLR magnitudes and are prepared in advance to avoid real-time complex calculations. During decoding, the system simply retrieves the appropriate γ value from the lookup table and applies it, maintaining computational efficiency while achieving high decoding performance through the variable correction parameter.
Data Source
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AI summary
In row calculation, a value which is obtained by subtracting an offset according to a minimum of the absolute values of column LLRs from the minimum of the absolute values of the column LLRs is set as a row LLR corresponding to a column of the column LLRs. An object of the present invention is to provide a decoding method and a decoding device that can approximate a row arithmetic operation based on a Sum-Product decoding method with a high degree of precision by using an Offset BP-based decoding method, thereby improving the performance of decoding of an error correcting code.