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Recent work has shown that 3D Gaussian-based SLAM enables high-quality reconstruction, accurate pose estimation, and real-time rendering of scenes. However, these approaches are built on a tremendous number of redundant 3D Gaussian ellipsoids, leading to high memory and storage costs, and slow training speed. To address the limitation, we propose a compact 3D Gaussian Splatting SLAM system that reduces the number and the parameter size of Gaussian ellipsoids. A sliding window-based masking strategy is first proposed to reduce the redundant ellipsoids. Then we observe that the covariance matrix (geometry) of most 3D Gaussian ellipsoids are extremely similar, which motivates a novel geometry codebook to compress 3D Gaussian geometric attributes, i.e., the parameters. Robust and accurate pose estimation is achieved by a global bundle adjustment method with reprojection loss. Extensive experiments demonstrate that our method achieves faster training and rendering speed while maintaining the state-of-the-art (SOTA) quality of the scene representation.