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In this letter, we investigate the power minimization problem while supporting the required reliability in wireless multi-hop relay networks. The novelty of the formulation is that it assumes a generalized relation between the power consumed in the transmitter and the packet reception rate in the receiver and, in addition, it takes into consideration the error detection capability of each relay node that can prevent unnecessary error propagation. We derive the optimality condition and provide a method that determines the optimal transmission power of each relay node sequentially. Numerical examples reveal that the optimal power allocation renders notable power saving effect while supporting the required level of reliability.