To improve the accuracy and efficiency of 3D LiDAR mapping, real-time cooperative SLAM has been considered to explore large and complex areas. To merge the individual maps from multiple robots, it is crucial to identify the common areas and obtain alternative matches between them. However, data transmission, especially in sparse networks with narrow bandwidth and limited range, is a challenging issue for the above problem. Since the distribution manner is suitable for limited communication, we proposed a common framework of 3D real-time distributed cooperative SLAM to fill the community gap. Assuming that each robot can communicate with others, the presented framework consists of four key modules: place recognition, relative pose estimation, distributed graph optimization, and communication. Meanwhile, we developed a complete real-time distributed cooperative SLAM system, called RDC-SLAM, by integrating state-of-the-art components into the framework. For computation and data transmission efficiency, descriptor-based registration is used instead of the conventional point cloud matching. An intensity-based descriptor is developed to perform the place recognition and obtain the alternative matches, while an eigenvalue-based segment descriptor is applied to further refine the relative pose estimations between these alternative matches. A distributed graph optimization method is utilized to obtain the maximum likelihood of multi-trajectory estimation. A communication protocol is also designed to associate data among robots that are easy to deploy and have low network requirements. The RDC-SLAM is validated by real-world experiments and exhibits superior performance concerning accuracy, computation efficiency, and data efficiency.