Optimal Binary Coding for $q^+$ -state Data Embedding

In steganography, we always hope to maximize the embedding payload subject to an upper-bounded distortion. We need suitable distortion measurement to evaluate the embedding impact. However, different distortion functions exposes different levels of distortion evaluation, implying that we have different optimization distributions by applying different distortion functions. In applications, the embedding distortion is caused by a certain number of embedding operations. Instead of a predefined distortion, we actually utilize a number of modifications to embed as many message bits as possible as long as the modifications are acceptable. This paper focuses on the design of optimal binary codewords for data embedding with a limited number of modification candidates. We have proved the optimality of the designed codewords, and proposed the way to construct the optimal binary codewords. It is pointed out that the optimal binary code is not unique, and an optimal code can be computed within a low computational cost.