LDPC Base Matrix Construction for Girth and Error Floor Control
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Solution Overview
Problem
Current Low Density Parity Check (LDPC) codes constructed using identity matrices and cyclic shift matrices do not effectively consider girth and code size relationships, leading to a slowed decrease in bit error rate (BER) at high signal noise ratios (SNR) and the presence of an error floor, degrading performance.
Innovation Solution
A method for constructing base matrices of LDPC codes that maximizes girth and minimizes the number of shortest cycles, using the Bit-Filling algorithm and quasi-lower triangular structures, to eliminate the error floor and accelerate the BER curve decrease, while allowing for variable code sizes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If LDPC codes are constructed using identity matrices and cyclic shift matrices without considering girth and code size relationships, then the construction process is simple, but the BER decreases slowly at high SNR and an error floor appears, degrading performance
Solution Approach 1:
The patent changes the construction parameters by introducing girth constraints and code size relationships into the matrix construction process. Specifically, it modifies the base matrix construction to ensure that the resulting parity check matrix has optimal girth properties, which directly addresses the error floor issue while maintaining construction feasibility
Solution Approach 2:
The patent performs preliminary optimization during the base matrix construction phase by pre-calculating and storing base matrices with optimized girth properties for different code sizes. This preliminary action ensures that when actual encoding is needed, the performance is already optimized without requiring complex real-time adjustments
2Reliability
If the base matrix is optimized to maximize girth and minimize shortest cycles, then the error floor is eliminated and BER performance improves, but the storage capacity and algorithm complexity increase
Solution Approach 1:
The patent segments the overall matrix construction into two independent parts: a base matrix that contains the structural optimization for girth and cycle properties, and an extension factor that scales the code size. This segmentation allows the complex optimization to be performed once on the small base matrix, while larger codes are generated by simple extension, reducing both storage and computational complexity
Solution Approach 2:
The patent applies partial optimization by focusing only on the critical base matrix portion that determines girth properties, rather than optimizing the entire large-scale parity check matrix. The extension operations that follow require minimal additional optimization, achieving most of the performance benefit with limited computational effort
3Ease of operation
If a unique base matrix is used for variable code sizes, then the encoder and decoder are uniquely determined and implementation is simplified, but the ability to adapt to different code sizes is constrained
Solution Approach 1:
The patent creates a universal base matrix construction methodology that can generate optimal base matrices for any code size through the extension factor mechanism. The same base construction algorithm and storage structure can serve multiple code sizes, making the system universally applicable while maintaining implementation simplicity through standardized procedures
Data Source
AI summary
The invention relates to a base matrix, a encoder/decoder of Low Density Parity Check (LDPC) codes and a generation method thereof. The encoder/decoder is determined uniquely by the parity check matrix of the LDPC codes. With different code sizes, said parity check matrix can be obtained by expanding different base matrixes, and also can be obtained by expanding a unique base matrix after correction. Elements of said base matrix must meet an inequation in which the girth value is up to the standard, e.g. when girth≧6, for any element i, j, k, l in the matrix which forms the short loop having a length of 4 in anticlockwise, there are always mod(i−j+k−l, z) unequal to 0. By this invention, the girth of the constructed base matrix is made as large as possible, the amount of the shortest loops is as few as possible when it is the same girth, thus the curve of bit error ratio (BER) is dropped quickly, the error floor of the LDPC codes is eliminated effectively, and the optimal performance of the LDPC codes is obtained.