MATLAB Implementation of LDPC Code Encoding and Decoding Using LU Decomposition and Belief Propagation Algorithms

This MATLAB implementation provides a comprehensive LDPC code encoding and decoding solution utilizing LU decomposition for linear system solving during encoding and Belief Propagation (BP) algorithm for iterative decoding. LDPC codes represent a powerful error correction technique capable of effectively detecting and correcting transmission errors through sparse parity-check matrices. The encoding process leverages LU decomposition to efficiently solve linear equations derived from the parity-check matrix, ensuring computational stability and numerical accuracy. For decoding, the BP algorithm iteratively updates probability messages between variable and check nodes, employing log-domain calculations to prevent numerical instability while maintaining decoding performance. Through meticulous debugging and optimization, this implementation achieves balanced computational efficiency and decoding accuracy. Key MATLAB functions include sparse matrix operations for parity-check matrix handling, LU factorization using built-in decomposition functions, and optimized message-passing loops for BP decoding. The code has been rigorously validated to ensure reliability for various communication applications requiring robust data transmission capabilities.