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We study the image retrieval problem at the wireless edge, where an edge device captures an image, which is then used to retrieve similar images from an edge server. These can be images of the same person or a vehicle taken from other cameras at different times and locations. Our goal is to maximize the accuracy of the retrieval task under power and bandwidth constraints over the wireless link. Due to the stringent delay constraint of the underlying application, sending the whole image at a sufficient quality is not possible. We propose two alternative schemes based on digital and analog communications, respectively. In the digital approach, we first propose a deep neural network (DNN) aided retrieval-oriented image compression scheme, whose output bit sequence is transmitted over the channel using conventional channel codes. In the analog joint source and channel coding (JSCC) approach, the feature vectors are directly mapped into channel symbols. We evaluate both schemes on image based re-identification (re-ID) tasks under different channel conditions, including both static and fading channels. We show that the JSCC scheme significantly increases the end-to-end accuracy, speeds up the encoding process, and provides graceful degradation with channel conditions. The proposed architecture is evaluated through extensive simulations on different datasets and channel conditions, as well as through ablation studies.