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Reversible information-embedding (RIE) is a technique transforming host signals and the message into the stego-signals, and the stego-signals can be losslessly reversed to the host signals and the message. We consider the conditions: 1) the host signals are composed of gray-scale independent and identically distributed (i.i.d.) samples; 2) the mean squared error is adopted as the measure of distortion; and 3) the procedure is a scalar approach, i.e., the encoder only reads a host signal and then outputs the corresponding stego-signal in each iteration. In this paper, we propose an iterative algorithm to calculate the signal transition probabilities approximating the optimal rate-distortion bound. Then we propose an explicit implementation to embed a message in an i.i.d. host sequence. The experiments show that the proposed method closely approaches the expected rate-distortions in i.i.d. gray-scale signals. By the image prediction model, the proposed method can be applied to gray-scale images.