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We investigate power allocation methods over AWGN channels in order to maximize the lower bound of the achievable rate, which is a more practical measure than channel capacity in the finite block length regime. Since the objective function of the optimization problem to solve is not concave, a part of the objective function is relaxed into a Taylor series expansion. Using the modified objective function, we propose a modified water-filling scheme to maximize the lower bound of the achievable rate with given power constraints, and verify the convergence of the proposed method. Numerical results show that the proposed scheme outperforms the conventional water-filling method in the finite block length regime.