Sparse Vector Coding (SVC) has long been considered an encoding method that meets the URLLC QOS requirements. This encoding method has been widely studied and applied due to its low encoding and decoding complexity, no pilot transmission, resistance to inter-carrier interference, and low power consumption. However, due to the use of position indexing, the encoding essentially reduces the signal-to-noise ratio requirements by increasing the communication bandwidth, which also leads to low encoding efficiency and strong rigidity in decoding. Based on the sparse representation characteristics of SVC, we propose a joint sparse representation encoding, namely Sparse Matrix Coding (SMC). This encoding method utilizes multi-user information joint encoding, and the sparsity and sparse locations between users are shared.