Variable-Length LDPC Encoding Using Grouped Exponential Matrices
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Solution Overview
Problem
Current quasi-cyclic LDPC codes can only support code length increases by integral multiples, leading to performance variations across different code lengths and the presence of small cycles, which affects the overall performance of the LDPC code.
Innovation Solution
A method and device for encoding and decoding LDPC codes with variable lengths by constructing a base exponential matrix, grouping code lengths, correcting and extending the matrix to support continuous changes in code lengths, ensuring no small cycles occur, and optimizing cycle distribution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If quasi-cyclic LDPC code is used with integral multiple code length increases, then device complexity is reduced and storage is simplified, but code length adaptability is limited and performance varies across different code lengths
Solution Approach 1:
The patent segments the code length adaptation process into discrete groups, where each group corresponds to a specific base exponential matrix configuration. By dividing the code length range into segments and assigning optimized matrices to each segment, the system achieves both manageable complexity and good adaptability within each segment.
Solution Approach 2:
The patent changes the parameter of code length by selecting different base exponential matrices for different code length ranges. Instead of using a single fixed matrix structure, the system adjusts the matrix parameters according to the required code length, enabling flexible adaptation while maintaining implementation simplicity.
2Ease of manufacture
If quasi-cyclic LDPC code with fixed matrix structure is used, then encoding and decoding processes are simplified, but small cycles appear in the Tanner graph affecting code performance
Solution Approach 1:
The patent applies local quality by optimizing the base exponential matrix structure specifically for different code length groups. Each group's matrix is designed with local structural characteristics that avoid small cycles in the Tanner graph, while maintaining the overall quasi-cyclic property for encoding simplicity.
Solution Approach 2:
The patent performs preliminary action by pre-optimizing the base exponential matrices for different code length groups before actual encoding. The matrices are designed in advance to eliminate small cycles and improve girth, so that when encoding is performed, the simplified quasi-cyclic structure is already in place without introducing performance-degrading cycles.
3Reliability
If independent LDPC code design is performed for each code length, then code performance is optimized for each length, but device complexity and construction effort increase significantly
Solution Approach 1:
The patent makes the base exponential matrix universal by designing it to serve multiple code length groups simultaneously. A single base matrix structure can be used across several code lengths by adjusting parameters within that structure, reducing construction complexity while maintaining good performance across different code lengths.
Solution Approach 2:
The patent merges the design of multiple code length configurations into a unified base exponential matrix structure. Instead of independently designing matrices for each code length, the system combines the requirements of multiple code lengths into a single matrix design that serves all groups, reducing overall construction effort while maintaining performance.
Data Source
AI summary
A method for encoding or decoding an LDPC code with variable code lengths is provided in an embodiment of the present invention. The method includes: obtaining a base exponential matrix of an LDPC code and grouping code lengths during construction of the base exponential matrix; correcting the base exponential matrix according to a grouping correction factor to obtain an exponential matrix of the group corresponding to the grouping correction factor; extending the exponential matrix by using an extension factor of a code length in the group to obtain an LDPC matrix corresponding to the code length; and implementing encoding or decoding by using the LDPC matrix.