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One-to-one device-to-device (D2D) communications are expected to play a major role in future releases of LTE-A, as well as in future 5G networks. Despite the abundance of works on resource allocation for D2D communications, few works, if any, discuss how D2D should be realized within the LTE-A protocol stack. While it is generally understood that D2D endpoints should be able to communicate both on the direct path or sidelink (SL) and on the relayed path (RP) through the eNB, little has been said on how this can be achieved in practice. In this paper we present a comprehensive proposal for a data-plane architecture for D2D communication: we define how communications should occur on the SL and the RP, and propose a solution for the challenges associated with mode switching between the SL and the RP. In particular, we argue that two different communication modes on the RP are required to allow D2D connections to be kept alive across cell borders in a multicell environment. Our proposal is scalable, since it does not require any signaling, and is guaranteed to not introduce losses. We evaluate our proposal through detailed system-level simulations, also focusing on its interplay with transport-layer protocols.