Quasi-Cyclic LDPC Parity-Check Matrix Construction for High Girth
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Solution Overview
Problem
The design of basic matrices for quasi-cyclic low-density parity-check (LDPC) codes poses challenges in achieving good decoding performance due to difficulties in designing matrices that avoid error floors and ensure high girth characteristics, which are crucial for maintaining the random nature of LDPC codewords and minimizing error occurrence.
Innovation Solution
A method and apparatus for quasi-cyclic LDPC encoding that determines a parity check matrix based on a basic matrix and lifting size Z, where the basic matrix is derived from a coefficient matrix, enabling the creation of LDPC encoded sequences with improved performance by optimizing the girth and error floor characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional basic matrices are used for quasi-cyclic LDPC codes, then the encoding structure is simple and manageable, but the decoding performance is poor due to error floors and low girth characteristics
Solution Approach 1:
The patent changes the parameters of the basic matrix by introducing a specific construction method that defines matrix elements using modular arithmetic operations. The basic matrix is constructed with dimensions Z×(Z+M) where Z is the lifting size and M is a parameter that controls the matrix structure. Elements are defined as Hb(i,j) = (a*i + b*j) mod Z for specific ranges of i and j, transforming the matrix design from an complex optimization problem into a parameterized construction that automatically achieves high girth characteristics and avoids error floors while maintaining quasi-cyclic structure for efficient encoding and decoding
2Reliability
If the basic matrix is designed to avoid error floors and ensure high girth characteristics, then decoding performance improves, but the design difficulty increases significantly
Solution Approach 1:
The patent segments the basic matrix into distinct regions with different construction rules. The matrix is divided into sub-matrices with specific patterns: some regions use Hb(i,j) = (a*i + b*j) mod Z while others use different formulations. This segmentation allows each region to be optimized independently for specific properties like girth characteristics and error floor avoidance, while the overall matrix maintains the quasi-cyclic structure needed for efficient implementation. The lifting size Z is also segmented into specific values (16, 32, 64, 128, 256) with optimized parameters for each
Solution Approach 2:
The patent performs preliminary action by pre-defining the basic matrix construction rules and parameters before actual LDPC code generation. The basic matrix is constructed in advance with optimized parameters (a, b, M values) that are specifically chosen to achieve high girth characteristics and avoid error floors. This pre-construction approach eliminates the need for complex iterative optimization during code design, as the matrix structure is already optimized to prevent error floors and ensure high girth, making the design process straightforward and systematic
Data Source
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.