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Environmental perception in Automated Valet Parking (AVP) has been a challenging task due to severe occlusions in parking garages. Although Collaborative Perception (CP) can be applied to broaden the field of view of connected vehicles, the limited bandwidth of vehicular communications restricts its application. In this work, we propose a BEV feature-based CP network architecture for infrastructure-assisted AVP systems. The model takes the roadside camera and LiDAR as optional inputs and adaptively fuses them with onboard sensors in a unified BEV representation. Autoencoder and downsampling are applied for channel-wise and spatial-wise dimension reduction, while sparsification and quantization further compress the feature map with little loss in data precision. Combining these techniques, the size of a BEV feature map is effectively compressed to fit in the feasible data rate of the NR-V2X network. With the synthetic AVP dataset, we observe that CP can effectively increase perception performance, especially for pedestrians. Moreover, the advantage of infrastructure-assisted CP is demonstrated in two typical safety-critical scenarios in the AVP setting, increasing the maximum safe cruising speed by up to 3m/s in both scenarios., Comment: 7 pages, 7 figures, 4 tables, accepted by IEEE VTC2024-Spring