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Transmit power allocation between source and relays is a critical design issue in a cooperative relaying system where source and relays are powered by batteries. In this paper, a low-complexity power allocation method is proposed for a 3-node cooperative bit-interleaved coded modulation system with adaptive decode-and-forward relaying, aiming to minimize the bit-error-rate at the destination. The key novelty of the method lies in transforming the power allocation into a max-min optimization problem which can be solved in a first-order equation with very low-complexity. Computer simulations show that the proposed method outperforms the equal gain power allocation with large margins in different channel conditions.