Quasi-Cyclic LDPC Basic Matrix Design for High-Girth Encoding
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Solution Overview
Problem
The design of basic matrices for quasi-cyclic low-density parity-check (LDPC) codes poses challenges, leading to poor performance and an error floor, with existing solutions failing to effectively address the difficulty in achieving high girth characteristics necessary for improved decoding performance.
Innovation Solution
A method and apparatus for designing quasi-cyclic LDPC encoding that involves determining a parity check matrix based on a basic matrix coefficient and lifting size, utilizing a set of lifting sizes and coefficient matrices to support multiple code lengths, and adjusting coefficients to maintain girth characteristics without affecting the code's performance, thereby improving encoding and decoding efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If basic matrix design for quasi-cyclic LDPC codes is optimized to improve girth characteristics, then decoding performance is improved, but design complexity and difficulty increase
Solution Approach 1:
The patent applies universality by creating a unified basic matrix design that supports multiple lifting sizes (different code lengths) while maintaining good girth characteristics. The basic matrix is designed to be versatile, working across different code configurations without requiring separate designs for each code length, thus improving reliability while managing design complexity through a single unified approach.
Solution Approach 2:
The patent utilizes parameter changes by systematically varying the lifting size parameter to generate different code lengths from a single basic matrix. By changing the lifting size parameter, the same basic matrix structure can produce codes of different lengths while maintaining the essential girth characteristics needed for good decoding performance, thereby avoiding the complexity of designing separate matrices for each code length.
2Adaptability or versatility
If multiple lifting sizes are supported with different basic matrices, then code length flexibility is improved, but storage requirements and system complexity increase
Solution Approach 1:
The patent implements universality by designing a single basic matrix that can serve multiple lifting sizes. Instead of storing separate basic matrices for different code lengths, the system uses one universal basic matrix with a predefined structure that adapts to various lifting sizes, significantly reducing storage requirements while maintaining code length flexibility.
Solution Approach 2:
The patent applies the nested doll principle by having a hierarchical structure where a single basic matrix contains the essential pattern that can be expanded to different code lengths through lifting. The basic matrix serves as a compact core structure that generates larger code structures when expanded, allowing the system to store only the small basic matrix while supporting multiple code lengths through expansion operations.
3Reliability
If girth characteristics are optimized in basic matrix design, then error floor performance is reduced, but encoding and decoding complexity increases
Solution Approach 1:
The patent applies local quality by focusing optimization efforts on specific local structures within the basic matrix that most critically affect girth characteristics. Rather than uniformly complicating the entire matrix design, the invention identifies and optimizes only the critical local regions that have the greatest impact on error floor performance, thereby achieving reliability improvement with minimal increase in overall complexity.
Data Source
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AI summary
Provided is a design method and apparatus for quasi-cyclic low-density parity-check (LDPC) encoding. The method includes: performing LDPC encoding on a K-bit information sequence to be encoded according to a parity check matrix of a quasi-cyclic LDPC code to obtain an N-bit LDPC encoded sequence, where the parity check matrix is determined according to a basic matrix and a lifting size Z, and the basic matrix is determined according to the lifting size Z and a coefficient matrix, where K is a positive integer, N is an integer greater than K, and Z is a positive integer.