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Diversity is an effective technique to enhance link quality and increasing network capacity. In this paper, we propose a generalized distributed turbo codes (DTC)-based coded cooperation protocol for two-hop relay networks with an arbitrary number of relays. This scheme aims at achieving improved diversity over the classical coded cooperation method in Rayleigh fading channels. We develop a closed-form expression for the pairwise error probability (PEP) and a tight upper bound for the bit error rate (BER) using DTC. The results demonstrate the merits of DTC-based coded cooperation with multiple relays, under various relay and uplink channel conditions. Moreover, the analytical upper bounds are validated with simulation results.