LDPC Min-Sum Decoding Algorithm

The Min-Sum decoding algorithm for LDPC codes is a widely used error-correction decoding method. This implementation covers both the construction of the parity-check matrix H and a series of decoding steps. The algorithm operates through iterative calculations on received codewords, typically implemented using message passing between variable nodes and check nodes. Key functions include initializing log-likelihood ratios (LLRs), performing min-sum approximations for check node updates, and applying threshold-based decisions for bit estimation. The min-sum approach reduces computational complexity by approximating the computationally expensive product operation in belief propagation with minimum operations. This algorithm significantly minimizes decoding error probability and finds extensive applications in wireless communications, digital broadcasting, and storage systems. The code implementation typically features configurable iteration limits, early termination checks, and performance monitoring capabilities.