LDPC Encoding and Decoding Algorithms Implementation

This article explores the complete implementation of LPDC encoding and decoding algorithms, detailing three distinct decoding approaches: the Belief Propagation (BP) algorithm, Log-Likelihood Ratio BP (LLR-BP) algorithm, and Min-Sum algorithm. These algorithms are implemented to handle communication over Additive White Gaussian Noise (AWGN) channels, with code examples demonstrating message passing mechanics and probability update rules. The implementation includes initialization functions for parity-check matrices and iterative decoding loops with early termination checks. We also provide background on LDPC code development and practical applications, discussing both the advantages and limitations of these algorithms in real-world scenarios. This resource aims to offer comprehensive insights for readers interested in LDPC coding techniques, featuring practical code structures that help bridge theoretical understanding with implementable solutions for modern error correction systems.