Flexible Construction of Girth-Six QC-LDPC Codes: Algorithmic Implementation and Performance Analysis

This article provides a comprehensive guide to constructing girth-six QC-LDPC codes with enhanced flexibility. As these codes gain widespread adoption in communication systems, understanding their construction and characteristics becomes crucial. We begin with an overview of fundamental QC-LDPC concepts, including parity-check matrix structure and circulant permutation matrices. The core implementation involves constructing base matrices with carefully designed offset values to avoid short cycles, typically implemented through combinatorial optimization algorithms. For flexibility enhancement, we introduce parameterized construction methods using Python/ MATLAB code snippets that allow dynamic adjustment of code length and rate through modular matrix expansion techniques. The performance impact of flexibility is analyzed through simulation results comparing bit-error-rate curves under different constraint conditions. Finally, we summarize key findings and propose future research directions including machine learning-assisted construction algorithms and hardware-efficient implementations.