Quasi-Cyclic LDPC Matrix Layout to Eliminate Four-Cycles
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Solution Overview
Problem
Current methods for designing Low Density Parity Check (LDPC) codes are inefficient, relying on brute force approaches to construct and compare parity check matrices, which hinders the development of LDPC codes with different properties needed for various communication systems.
Innovation Solution
The method involves constructing LDPC codes using cyclic shifted identity (CSI) sub-matrices within the parity check matrix, ensuring the absence of four-cycles by defining cyclic shift values through specific functions and algorithms, allowing for efficient generation and comparison of LDPC codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If brute force approaches are used to construct and compare parity check matrices, then LDPC codes can be designed, but the design process becomes inefficient and time-consuming
Solution Approach 1:
The parity check matrix is segmented into multiple sub-matrices, where each sub-matrix can be independently constructed and optimized. This segmentation allows for systematic design of LDPC codes with specific properties (such as avoiding four-cycles) while maintaining computational efficiency, resolving the contradiction between reliable code design and design efficiency.
Solution Approach 2:
The invention employs parameter-based construction methods where cyclic shift values and sub-matrix dimensions are systematically varied to generate different LDPC code variants. By changing these parameters according to specific rules (such as using different cyclic shifts to avoid four-cycles), the method efficiently generates codes with desired error correction properties without exhaustive brute force search.
2Ease of manufacture
If four-cycles are present in the LDPC code structure, then construction is simpler, but error correction performance deteriorates
Solution Approach 1:
The invention applies local quality control by specifically targeting and eliminating four-cycles in local sub-matrix configurations while maintaining the overall sparse structure. By controlling the cyclic shift parameters of individual sub-matrices, the method locally prevents harmful four-cycle formations without compromising the global code construction simplicity, thus improving error correction performance while maintaining ease of construction.
Solution Approach 2:
The method introduces asymmetry in the cyclic shift values of sub-matrices to break the symmetry that creates four-cycles. By using asymmetric shift patterns (where adjacent sub-matrices have different shift values), the construction avoids four-cycles while maintaining systematic and simple construction procedures, resolving the contradiction between construction simplicity and performance.
3Reliability
If traditional LDPC codes are used, then latency constraints may be violated, but communication systems require error correction
Solution Approach 1:
The invention employs dynamic code construction where the parity check matrix structure can be adaptively configured based on communication system requirements. By dynamically selecting sub-matrix dimensions, cyclic shift values, and code rates, the system can optimize the balance between error correction capability and decoding latency, allowing LDPC codes to meet real-time communication constraints while maintaining reliability.
Data Source
AI summary
Quasi-cyclic LDPC (Low Density Parity Check) code construction is presented that ensures no four cycles therein (e.g., in the bipartite graphs corresponding to the LDPC codes). Each LDPC code has a corresponding LDPC matrix that is composed of square sub-matrices, and based on the size of the sub-matrices of a particular LDPC matrix, then sub-matrix-based cyclic shifting is performed as not only a function of sub-matrix size, but also the row and column indices, to generate CSI (Cyclic Shifted Identity) sub-matrices. When the sub-matrix size is prime (e.g., each sub-matrix being size q×q, where q is a prime number), then it is guaranteed that no four cycles will exist in the resulting bipartite graph corresponding to the LDPC code of that LDPC matrix. When q is a non-prime number, an avoidance set can be used and/or one or more sub-matrices can be made to be an all zero-valued sub-matrix.