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Improving the reliability and spectral efficiency of wireless systems is a key goal in wireless systems. However, most efforts have been devoted to improving data channel capacity, whereas control-plane capacity bottlenecks are often neglected. In this paper, we propose a means of improving the control-plane capacity and reliability by shrinking the bit size of a key signaling message - the 5G Downlink Control Information (DCI). In particular, a transformer model is studied as a probability distribution estimator for Arithmetic coding to achieve lossless compression. Feature engineering, neural model design, and training technique are comprehensively discussed in this paper. Both temporal and spatial correlations among DCI messages are explored by the transformer model to achieve reasonable lossless compression performance. Numerical results show that the proposed method achieves 21.7% higher compression ratio than Huffman coding in DCI compression for a single-cell scheduling scenario.