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Although the semantic communications have exhibited satisfactory performance in a large number of tasks, the impact of semantic noise and the robustness of the systems have not been well investigated. Semantic noise is a particular kind of noise in semantic communication systems, which refers to the misleading between the intended semantic symbols and received ones. In this paper, we first propose a framework for the robust end-to-end semantic communication systems to combat the semantic noise. Particularly, we analyze the causes of semantic noise and propose a practical method to generate it. To remove the effect of semantic noise, adversarial training is proposed to incorporate the samples with semantic noise in the training dataset. Then, the masked autoencoder (MAE) is designed as the architecture of a robust semantic communication system, where a portion of the input is masked. To further improve the robustness of semantic communication systems, we firstly employ the vector quantization-variational autoencoder (VQ-VAE) to design a discrete codebook shared by the transmitter and the receiver for encoded feature representation. Thus, the transmitter simply needs to transmit the indices of these features in the codebook. Simulation results show that our proposed method significantly improves the robustness of semantic communication systems against semantic noise with significant reduction on the transmission overhead.