LDPC Parity Check Message Scaling for Min-Sum Decoding
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Solution Overview
Problem
Current LDPC decoding methods face challenges in achieving an ideal compromise between decoding performance, data rate, implementation complexity, and energy consumption, particularly in high-speed communication systems like space communications, where error correction power, throughput, and hardware complexity are critical.
Innovation Solution
A method for calculating parity check messages in LDPC decoding that involves determining the first and second smallest absolute values of variable messages, comparing their differences with thresholds to determine correction values, and scaling data to prevent saturation, which supports different coding rates and reduces error rate floors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the Min-Sum algorithm is used to replace hyperbolic tangent calculations, then computational complexity is reduced, but error correction performance deteriorates due to overestimation of parity check message amplitudes
Solution Approach 1:
The patent introduces a normalization factor that dynamically adjusts the amplitude of parity check messages based on the degree of the parity check node. This parameter change compensates for the overestimation inherent in the Min-Sum algorithm, restoring error correction performance while maintaining the computational simplicity of the Min-Sum approach.
Solution Approach 2:
The patent implements a feedback mechanism where the degree of each parity check node is used to determine the normalization factor. This feedback loop allows the system to adaptively correct the amplitude of messages based on the structural properties of the LDPC code, improving reliability without increasing computational complexity significantly.
2Reliability
If BP-SPA algorithm is used for decoding, then error correction performance is improved, but computational complexity increases due to use of hyperbolic tangents, logarithms and exponentials
Solution Approach 1:
The patent replaces the computationally expensive functions (hyperbolic tangents, logarithms, exponentials) with simpler Min-Sum operations followed by a lightweight normalization step. This substitution uses cheaper computational operations that achieve comparable performance for the specific application of LDPC decoding.
Solution Approach 2:
By changing the functional approach from transcendental functions to algebraic operations with normalization, the patent achieves a balance between performance and complexity suitable for practical implementation.
3Device complexity
If data quantization is applied to reduce hardware complexity, then implementation complexity is reduced, but error rate floor increases due to saturation of data
Solution Approach 1:
The patent applies preliminary scaling to the a posteriori estimation variables before they are used in subsequent decoding iterations. This preventive scaling ensures that the variables remain within the dynamic range of the quantized representation, avoiding saturation and the associated error rate floor while maintaining fixed-point arithmetic benefits.
Solution Approach 2:
The patent introduces dynamic scaling factors that adjust the range of quantized variables based on the decoding progress and message amplitudes. This dynamic adaptation allows the system to maintain precision where needed while preserving the simplicity of fixed-point arithmetic.
Data Source
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AI summary
The invention relates to an LDPC decoding method. The method involves performing iterations until a stop criterion is satisfied. Each iteration involves: - computing variable messages (αn,m), - computing (112) parity check messages (βm,n), - computing a posteriori estimation variables. Computing (112) a parity check message (βm,n) for a parity check node (CNm) involves: - determining (141, 142) the two smallest values (Mini1, Min2) among the absolute values of the variable messages associated with said parity check node (CNm), - comparing (143) a difference between said values with a threshold, - determining (145) a correction value according to the result of the comparison, - computing (146) the parity check message according to the correction value.