All-Zero Codeword QC-LDPC System

The document describes an all-zero codeword QC-LDPC (Quasi-Cyclic Low-Density Parity-Check) system program designed for channel coding applications with customizable parameters. This system employs QC-LDPC codes characterized by their block-circulant parity-check matrices, where the all-zero codeword serves as a fundamental reference for encoding and decoding validation. The implementation typically involves matrix generation algorithms that create structured parity-check matrices using cyclic shifts of identity matrices, enabling efficient encoding through linear algebraic operations. In practical applications, the system performs channel coding by transforming information bits into codewords using generator matrices derived from the parity-check structure. The decoding process commonly utilizes iterative message-passing algorithms like belief propagation, where variable nodes and check nodes exchange probability messages to correct transmission errors. The parameter customization allows adjustment of code rate, block length, and iteration counts through configuration files or API interfaces. This QC-LDPC system finds extensive applications in wireless communications (5G NR standards), satellite communications, and optical fiber transmission systems. The architecture supports performance optimization through SNR threshold tuning and iteration control algorithms. Research and enhancement of this system focus on improving error-correction capability using optimized scheduling strategies and reduced-complexity decoding implementations, thereby providing robust channel coding solutions for modern communication infrastructure.