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Future wireless networks are expected to support diverse mobile services, including artificial intelligence (AI) services and ubiquitous data transmissions. Federated learning (FL), as a revolutionary learning approach, enables collaborative AI model training across distributed mobile edge devices. By exploiting the superposition property of multiple-access channels, over-the-air computation allows concurrent model uploading from massive devices over the same radio resources, and thus significantly reduces the communication cost of FL. In this paper, we study the coexistence of over-the-air FL and traditional information transfer (IT) in a mobile edge network. We propose a coexisting federated learning and information transfer (CFLIT) communication framework, where the FL and IT devices share the wireless spectrum in an OFDM system. Under this framework, we aim to maximize the IT data rate and guarantee a given FL convergence performance by optimizing the long-term radio resource allocation. A key challenge that limits the spectrum efficiency of the coexisting system lies in the large overhead incurred by frequent communication between the server and edge devices for FL model aggregation. To address the challenge, we rigorously analyze the impact of the computation-to-communication ratio on the convergence of over-the-air FL in wireless fading channels. The analysis reveals the existence of an optimal computation-to-communication ratio that minimizes the amount of radio resources needed for over-the-air FL to converge to a given error tolerance. Based on the analysis, we propose a low-complexity online algorithm to jointly optimize the radio resource allocation for both the FL devices and IT devices. Extensive numerical simulations verify the superior performance of the proposed design for the coexistence of FL and IT devices in wireless cellular systems.