偽逆矩陣的計算在許多通訊與訊號處理任務中扮演關鍵角色，尤其是在雜訊下的非同步隨機接取（IRSA）系統中使用的平行解碼策略。傳統方法如奇異值分解（SVD）對於大型稀疏矩陣而言計算量龐大，效率低下。為了解決此問題，我們提出一種基於動態規劃原則的創新訊息傳遞演算法，可有效地計算無環二分圖的偽逆矩陣，並保證獲得精確解。針對含有環的圖，我們進一步修改演算法，以處理非正交訊息交互的情形，並透過展平的有向無環圖（DAG）結構與阻尼技術來修正收斂準則，最終可取得準確近似解，甚至是精確解。數值實驗結果顯示，相較於高斯信念傳遞（GaBP）方法，本演算法在收斂速度與穩定性上表現更優，特別是在可使用SIC（連續干擾消除）解碼的含環圖中，展現其於大規模與分散式網路系統中的應用潛力。

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.