QC-LDPC Permutation Matrix Lifting for Low-Rate Code Design
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Solution Overview
Problem
Current QC-LDPC codes in communication systems, such as the 802.11n standard for WiFi, lack low code rates like 1/6, 1/4, and 1/3, which are essential for low signal-to-noise ratio and long-distance transmission environments, limiting their performance and implementation.
Innovation Solution
A method for constructing permutation matrices for QC-LDPC codes with low code rates by designing base matrices with specific row weights and lifting factors, allowing for the creation of check matrices that support 1/6, 1/4, and 1/3 code rates, enabling improved performance in challenging transmission conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If QC-LDPC codes with low code rates (1/6, 1/4, 1/3) are designed from scratch, then decoding performance in low signal-to-noise ratio environments is improved, but device complexity and development costs increase
Solution Approach 1:
The patent makes existing QC-LDPC code structures serve multiple functions by configuring them with different lifting factors and row weights to achieve multiple low code rates (1/6, 1/4, 1/3). Instead of designing separate code structures for each code rate, a unified base matrix structure is used that can be adapted to generate codes with different code rates through parameter configuration, thereby reducing overall system complexity while maintaining decoding performance.
Solution Approach 2:
The patent changes key parameters of the existing QC-LDPC code structure, specifically the lifting factor and row weight, to transform a single code structure into multiple code variants with different code rates. By adjusting these parameters, the same base matrix can generate codes optimized for different low signal-to-noise ratio environments without requiring fundamentally different code designs.
2Device complexity
If existing QC-LDPC code structures are reused for low code rates, then device complexity is reduced, but the ability to support specific low code rates (1/6, 1/4, 1/3) is limited
Solution Approach 1:
The patent systematically varies the lifting factor and row weight parameters of the base matrix to generate QC-LDPC codes with specific low code rates of 1/6, 1/4, and 1/3. This parameter adjustment approach enables the existing code structure to adapt to different code rate requirements while maintaining structural simplicity.
Solution Approach 2:
The unified base matrix structure is designed to perform multiple code rate functions simultaneously. By configuring the lifting factor and row weight appropriately, the same structural framework can support multiple low code rates, making the system versatile without increasing complexity.
3Adaptability or versatility
If new code structures are developed for low code rates, then code rate adaptability is improved, but manufacturing and development costs increase
Solution Approach 1:
The patent creates a universal base matrix structure that can generate multiple low code rate variants (1/6, 1/4, 1/3) through parameter configuration. This approach eliminates the need to develop and manufacture separate code structures for each code rate, significantly reducing development costs while maintaining full code rate adaptability.
Solution Approach 2:
Instead of developing new code structures, the patent achieves code rate adaptability by changing parameters (lifting factor, row weight) of an existing structure. This parameter-based approach is much more cost-effective than structural redesign while still providing support for multiple low code rates.
Data Source
AI summary
There are provided a method for constructing a permutation matrix or a check matrix, a processing device, a storage medium and a coding method. The method of constructing a permutation matrix includes: obtaining a base matrix used for the permutation matrix; and lifting the base matrix to obtain the permutation matrix, which includes: obtaining a protograph of the base matrix; and obtaining each macro-cycle in the protograph, and for each macro-cycle in the protograph, determining a size of a short cycle corresponding to the macro-cycle in a Tanner graph of the check matrix corresponding to the permutation matrix by an equivalent cyclic value ECS of the macro-cycle, and determining whether at least one cyclic value in the macro-cycle needs to be set according to the size of the short cycle.