Comparative Analysis of Various LDPC Decoding Algorithms

In this paper, we conduct a comprehensive comparison of various decoding algorithms for LDPC codes, focusing on Belief Propagation (BP), Min-Sum algorithm, and Brute-Force (BF) approach. LDPC (Low-Density Parity-Check) codes represent an error correction technique that enhances error-correcting capability by introducing sparsity during encoding. Although LDPC codes have been widely adopted in communication systems, the choice of decoding algorithm significantly impacts practical performance. The implementation of BP algorithm typically involves iterative message passing between variable nodes and check nodes using Tanner graphs, where probability updates are calculated through sum-product operations. The Min-Sum algorithm serves as a simplified approximation of BP, replacing probabilistic multiplications with minimum operations to reduce computational complexity while maintaining reasonable performance. Brute-Force method, though computationally intensive, provides a baseline by exhaustively testing all possible codeword combinations. This study details the fundamental principles, advantages, and limitations of each decoding algorithm, supported by experimental results and performance analysis. We examine key implementation aspects such as iteration control, convergence criteria, and computational complexity metrics. The comparative evaluation covers error rate performance, convergence speed, and hardware implementation feasibility across different signal-to-noise ratio conditions. This analysis aims to provide valuable insights for researchers and engineers in selecting appropriate decoding strategies for specific LDPC applications, facilitating better understanding of algorithm trade-offs and optimal deployment scenarios in modern communication systems.