MATLAB Implementation of LDPC Encoding and Belief Propagation Iterative Decoding

In this project, we demonstrate how to implement LDPC (Low-Density Parity-Check) encoding and Belief Propagation (BP) iterative decoding using MATLAB. LDPC encoding is a powerful error correction technique that enhances data transmission reliability by adding redundant information through sparse parity-check matrices. The BP iterative decoding method employs message-passing algorithms between variable and check nodes to progressively approximate the original transmitted information. We will provide comprehensive explanations of both LDPC encoding principles and BP decoding algorithms, including key implementation aspects such as: - Construction of sparse parity-check matrices using various methods (e.g., Gallager construction, progressive edge growth) - Encoding implementation through generator matrix derivation or direct encoding algorithms - BP decoding implementation with log-likelihood ratio (LLR) message updates - Iteration control and convergence criteria handling - Performance metrics calculation including bit error rate (BER) analysis The complete MATLAB program example includes modular functions for matrix generation, encoding processes, decoding iterations, and performance evaluation. The code demonstrates practical implementation techniques such as sparse matrix optimization for computational efficiency, message scheduling strategies, and early termination conditions to reduce decoding latency. This implementation serves as an educational tool for understanding channel coding fundamentals and provides a foundation for further optimization in communication system applications.