Quasi-Cyclic Check Matrix Layout for High-Girth LDPC Codes
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Solution Overview
Problem
Conventional LDPC code encoders face challenges in designing parity check matrices with high girth values (g ≧ 6, 8, 10) due to lack of regularity and extensibility, leading to increased complexity and uncertainty about the optimality of generated codes.
Innovation Solution
A check matrix generating device and method that configures a regular quasi-cyclic matrix by combining cyclic permutation matrices with specific row and column arrangements, allowing for the generation of parity check matrices with improved performance and regularity, enabling the design of LDPC codes with higher girth values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional LDPC code encoders use quasi-cyclic codes with cyclic permutation matrices, then the encoding structure is established, but the design lacks regularity and extensibility, leading to increased complexity and uncertainty about code optimality
Solution Approach 1:
The patent applies parameter changes by systematically varying the shift amounts (pj,l values) in the cyclic permutation matrices to achieve different girth values. By changing these parameters while maintaining the quasi-cyclic structure, the invention generates parity check matrices with girth ≥6, ≥8, or ≥10, thereby improving code reliability without fundamentally changing the encoder architecture.
Solution Approach 2:
The patent segments the parity check matrix into multiple cyclic permutation matrices of size p×p, where each matrix corresponds to a specific position in the quasi-cyclic structure. This segmentation allows independent optimization of each permutation matrix while maintaining overall regularity, reducing design complexity through modular construction.
2Reliability
If the girth value of the parity check matrix is increased to improve decoding performance, then code reliability improves, but the design complexity increases due to lack of regularity in conventional approaches
Solution Approach 1:
The patent systematically changes the shift parameters (pj,l values) of cyclic permutation matrices to control and increase the girth value. By establishing specific relationships between these parameters, the invention achieves girth ≥6, ≥8, or ≥10 while maintaining the regular quasi-cyclic structure, thereby improving decoding performance without proportionally increasing design complexity.
Solution Approach 2:
The patent creates a universal design framework where the same quasi-cyclic encoder structure can generate parity check matrices with different girth values by simply adjusting the permutation parameters. This multi-functionality allows a single encoder design to achieve various performance levels, reducing the need for multiple specialized designs.
3Productivity
If conventional methods are used to generate parity check matrices, then the encoding process can proceed, but there is uncertainty about the optimality of the generated codes due to lack of regularity
Solution Approach 1:
The patent establishes explicit parameter relationships for the cyclic permutation matrices that guarantee minimum girth values. These parameter specifications provide a systematic method to assess code optimality based on measurable structural properties, eliminating uncertainty about code quality while maintaining efficient encoding capability.
Data Source
AI summary
When arranging J cyclic permutation matrices I(pj,l) with p rows and q columns (0≦j≦J−1, 0≦l≦L−1) in a row direction and also arranging L cyclic permutation matrices I(pj,l) in a column direction so as to generate a regular quasi-cyclic matrix having uniform row and column weights, a quasi-cyclic matrix generating unit 31 configures the regular quasi-cyclic matrix by combining cyclic permutation matrices I(pj,l) in each of which matrix elements whose row number is r (0≦r≦p−1) and whose column number is (r+pj,l) mod p are “1”s, and other matrix elements are “0”s in such a way that a plurality of cyclic permutation matrices I(pj,l) arranged at, e.g., the 1st row differ from one another.