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The ongoing densification in cellular networks has turned interference into a serious problem in future cellular networks. Since the interference experienced by close-by users in a cellular network is usually correlated, it can be cooperatively suppressed to improve user experience. In this article, we introduce the idea of cooperative interference cancellation (CIC) between close-by users using device-to-device (D2D) communications for the example of the upcoming 3rd Generation Partnership Program (3GPP) Long Term Evolution (LTE) Rel-12 D2D technology. We understand CIC as a new network interference management tool, capable of exploiting interference correlation to improve downlink throughput. We discuss possible deployment scenarios as well as theoretical and practical challenges. To each challenge we provide some possible solutions. Finally, a first feasibility analysis using numerical simulations is presented that demonstrates the potential gains of CIC.