MATLAB Implementation of LDPC Encoding, Hard/Soft Decoding, and Performance Simulation

This article provides a detailed exploration of LDPC encoding concepts, principles, and practical applications. We begin by explaining the fundamental principles of LDPC encoding, including the construction of parity-check matrices and generation methods for parity bits, with MATLAB implementation examples demonstrating sparse matrix generation using functions like sprand or gallery. Next, we examine both hard-decision and soft-decision decoding algorithms for LDPC codes. The hard-decision decoding typically employs bit-flipping algorithms implemented through iterative parity-check validation, while soft-decision decoding uses belief propagation (sum-product algorithm) that processes log-likelihood ratios (LLRs) with message-passing between variable and check nodes. We compare their performance differences in terms of computational complexity and error correction capability. Finally, we conduct comprehensive performance simulation experiments to evaluate LDPC code performance under various channel conditions. The simulations include AWGN channel modeling with different SNR values, BER calculation through Monte Carlo methods, and visualization of performance curves using MATLAB's plotting functions. Through this article, you will gain a thorough understanding of LDPC coding and its practical implementation in modern communication systems, with ready-to-use MATLAB code frameworks for each component.