LDPC Check Matrix Encoding with Flexible Lifting Factors
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing computing methods for check matrices of LDPC codes require optimization to maintain a low bit-error-rate floor and reduce storage space while ensuring flexible code lengths.
Innovation Solution
An encoding method using a matrix with a lifting factor z, where submatrices include cyclic shift matrices based on an identity matrix, with cyclic shift values determined by specific functions to optimize performance and reduce bit-error-rate floor, and storage requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing computing methods for check matrices are used, then code flexibility is maintained, but bit-error-rate floor performance deteriorates and storage space increases
Solution Approach 1:
The patent applies parameter changes by modifying the cyclic shift values in the check matrix through mathematical transformations. Specifically, it uses functions involving the maximum lifting factor zmax to transform the original check matrix into an equivalent form with optimized cyclic shift parameters, achieving lower bit-error-rate floors while reducing storage requirements for the matrix representation.
Solution Approach 2:
The patent segments the check matrix into block matrices of size z×z, where each block is either an all-zero matrix or a cyclic shift matrix. This segmentation allows independent optimization of each block's cyclic shift value, enabling the system to achieve better error floor performance while maintaining flexible code lengths through the lifting factor mechanism.
2Quantity of substance
If lifting factor z is increased to reduce storage space, then storage requirements decrease, but code length flexibility and performance optimization are limited
Solution Approach 1:
The patent achieves universality by designing a check matrix structure that can support multiple code lengths through the lifting factor mechanism. The same base check matrix template can be used for different code lengths by adjusting the lifting factor z, allowing the system to maintain adaptability while using a compact stored representation that reduces space requirements.
Solution Approach 2:
The patent introduces dynamics by allowing the lifting factor z to be adjusted based on code length requirements. The check matrix structure dynamically adapts to different code lengths while maintaining the optimized cyclic shift pattern, enabling flexible code length support without sacrificing the storage space reductions achieved through the optimized representation.
3Reliability
If cyclic shift values are optimized to reduce bit-error-rate floor, then reliability improves, but computational complexity increases
Solution Approach 1:
The patent uses copying by storing only the essential parameters of the check matrix (such as the base pattern and lifting factor) rather than the complete expanded matrix. The actual check matrix is generated on-demand by copying and expanding the stored template with the appropriate lifting factor, reducing storage space while maintaining the ability to compute optimized cyclic shift values for reliable decoding.
Data Source
AI summary
The present disclosure relates 10 encoding methods, communication methods and apparatus. In one example method, a first information sequence is encoded by using a first matrix to obtain a second information sequence, where the first matrix meets a function related to a lifting factor and an element in Emax(H). The second information sequence is outputted.