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In this study, the authors present a novel data hiding scheme using the minimum distortion look-up table (LUT) embedding that achieves good distortion-robustness performance. LUT-based data hiding is a simple and efficient way to embed information into multimedia content for various applications, such as transaction tracking and database annotation. The authors find it possible to optimally reduce the data hiding-introduced distortion by designing the LUT according to the distribution of the host at a given robustness level. The authors first analyse the distortion introduced by LUT embedding and formulate its relationship with run constraints of LUT to construct an optimal coding problem. Subsequently, a Viterbi algorithm is presented to find the minimum distortion LUT. Then a new practical data hiding scheme using the optimal LUT is applied in the wavelet domain. Theoretical analysis and numerical results show that the new LUT design achieves not only less distortion but also more robustness than the traditional LUT-based data embedding schemes under common attacks such as Gaussian noise and JPEG compression.