Construction of Column-Weight Three Girth-Eight QC-LDPC Codes

This program constructs quasi-cyclic low-density parity-check (QC-LDPC) codes with column-weight three and girth-eight based on given row weights and sub-matrix sizes. The implementation uses a structured approach where the parity-check matrix is built from circulant permutation matrices, allowing efficient encoding and decoding. The algorithm dynamically adjusts row weights and sub-matrix dimensions to optimize code performance for specific applications. These customizable QC-LDPC codes find significant applications in digital communications and data storage systems. The code generation process involves verifying cycle properties to maintain the girth-eight constraint while ensuring the column-weight remains three. This coding scheme enhances data transmission reliability by reducing error rates and improving error correction capability, making it particularly valuable in modern communication systems where robust error performance is critical. The program's key functions include matrix dimension validation, circulant matrix generation, and girth verification through cycle detection algorithms. Users can modify parameters to generate codes tailored to specific channel conditions or performance requirements, with the implementation providing necessary checks to maintain code structural integrity.