Implementation of LDPC Low-Density Parity-Check Codes with MATLAB Simulation

This text introduces a MATLAB simulation program designed for AWGN channels, implementing the Low-Density Parity-Check (LDPC) algorithm. LDPC codes have gained significant attention in recent years due to their straightforward implementation, excellent performance, and low bit error rates. The simulation typically involves generating sparse parity-check matrices using construction methods like Gallager codes or progressive-edge growth, followed by iterative decoding algorithms such as belief propagation or min-sum. Notably, LDPC codes are widely adopted in communication systems including satellite communications, digital television, and Blu-ray discs. Therefore, mastering LDPC encoding techniques - including matrix generation, encoding procedures, and log-likelihood ratio based decoding - is crucial for professionals in the communication field. The code implementation demonstrates key aspects like syndrome checking, convergence thresholds, and performance comparisons with theoretical limits.