In the realm of reconfigurable intelligent surface (RIS)-assisted wireless communications, efficient channel state information (CSI) feedback is paramount. This paper introduces RIS-CoCsiNet, a novel deep learning-based framework designed to greatly enhance feedback efficiency. By leveraging the inherent correlation among proximate user equipments (UEs), our approach strategically categorizes RIS-UE CSI into shared and unique data sets. This nuanced understanding allows for significant reductions in feedback overhead, as the shared data is no longer redundantly relayed. Setting RIS-CoCsiNet apart from traditional autoencoder systems, we incorporate an additional decoder and a combination neural network at the base station. These enhancements are tasked with the precise retrieval and fusion of shared and individual data. And notably, all these innovations are achieved without modifying the UEs. For those UEs boasting multiple antennas, our design seamlessly integrates long short-term memory modules, capturing the intricate correlations between antennas. With a recognition of the non-sparse nature of the RIS-UE CSI phase, we pioneer two magnitude-dependent phase feedback strategies. These strategies adeptly weave in both statistical and real-time CSI magnitude data. The potency of RIS-CoCsiNet is further solidified through compelling simulation results drawn from two diverse channel datasets.

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