LDPC BP Decoding Implementation in MATLAB

This MATLAB implementation demonstrates BP (Belief Propagation) decoding for Low-Density Parity-Check (LDPC) codes operating over an AWGN channel. The program begins by constructing an AWGN channel model in MATLAB to simulate additive white Gaussian noise during signal transmission. The implementation includes LDPC encoding procedures followed by the development of a comprehensive BP decoding algorithm that processes received signals to recover original transmitted information. Key implementation aspects include: - AWGN channel modeling using MATLAB's built-in random number generation functions - LDPC code construction with sparse parity-check matrix representation - BP decoding algorithm implementation with iterative message passing between variable and check nodes - Log-likelihood ratio (LLR) calculations for soft-decision decoding - Convergence checking and iteration control mechanisms The decoder employs probability propagation techniques where messages are iteratively passed between variable nodes and check nodes in the Tanner graph representation. Each iteration updates belief probabilities until convergence criteria are met or maximum iterations are reached. This implementation provides practical insights into AWGN channel characteristics, LDPC code properties, and the operational principles of belief propagation decoding algorithms for achieving reliable communication systems. The code structure includes modular functions for channel simulation, encoding, decoding, and performance evaluation, making it suitable for both educational purposes and practical communication system development.