Robustness analysis of M-ary quantization based watermarking

This work addresses the issue on the robustness performance in M-ary quantization watermarking. If the encoded messages are arranged in the order of Gray Code such that adjacent messages differ at only one bit, this work demonstrates the robustness will be substantially improved in low DNR scenarios. Furthermore, the two-bit quantization watermarking can outperform the LUT approach which also provides the robustness improvement in the high-noisy environments.