Recommendation systems have become a key technology in mitigating information overload in the era of big data, with widespread applications in E-commerce and other fields. However, traditional centralized data collection methods expose significant risks of user privacy leakage. Federated learning enables collaborative model training across multiple data holders without the need to share raw user data, thus protecting privacy. Federated recommendation systems have gained considerable attention from both academia and industry. Existing federated recommendation algorithms place the model training process in a distributed environment, effectively avoiding the centralized storage of sensitive user data on a single server. However, these approaches still face challenges related to privacy leakage and high communication costs. To address these issues, this study proposes a communication-efficient federated recommendation algorithm based on differential privacy. The algorithm introduces a general sub-model selection strategy that strengthens privacy protection of user interaction data on the client side through a randomized response mechanism. On the server side, it employs maximum likelihood estimation to infer the true interaction frequencies of items and optimize the sub-model selection process. This strategy achieves an effective balance between privacy protection and model utility. The proposed algorithm is applicable not only to matrix factorization-based recommendation models but also to deep learning-based models, demonstrating high flexibility and adaptability across various recommendation scenarios. Furthermore, to reduce communication overhead, a global model partitioning strategy is proposed to address the complex structures and large parameter sizes of deep learning models. Differentiated optimization strategies are applied to shallow and deep networks to effectively mitigate communication costs. Theoretical analysis shows that the method satisfies differential privacy, while experimental results on real-world datasets demonstrate that the proposed approach preserves user data privacy without significantly compromising model utility, while substantially improving communication efficiency in federated recommendation systems.