摘要
The computation of pseudoinverse matrices is critical in various communication and signal processing applications, especially in decoding schemes such as parallel decoding in Irregular Repetition Slotted ALOHA (IRSA) with noise. Traditional methods like singular value decomposition (SVD) are computationally intensive for large, sparse matrices. To address this issue, we propose a novel message-passing algorithm leveraging the dynamic programming principle to efficiently compute the pseudoinverse matrix of acyclic bipartite graphs, guaranteeing exact solutions. For cyclic graphs, we introduce modifications to handle non-orthogonal message propagation and implement a revised convergence criterion, resulting in accurate approximations or exact solutions upon convergence. Numerical results demonstrate that our algorithm converges faster and more reliably compared to Gaussian belief propagation (GaBP), particularly for cyclic SIC-decodable graphs, highlighting its potential in large-scale networked systems.