A novel approach to CSS syndrome decoding has been formulated using factor graphs, enabling the integration of joint belief propagation (joint BP) and four-state BP. This method leverages the binary parity-check constraints imposed by the two check matrices on the Pauli error components, resulting in a binary factor graph with two coupled Tanner graphs. The joint BP algorithm, also known as the sum-product algorithm, is applied to this factorization, allowing for the retention of local channel correlation. This development has significant implications for quantum computing and cryptography, as it challenges existing assumptions about computation and error correction1. The use of factor graphs and joint BP enables a more efficient and accurate decoding process, which is crucial for the development of reliable quantum computing systems. So what matters to practitioners is that this advancement could lead to breakthroughs in quantum error correction, ultimately enhancing the security and reliability of quantum computing systems.