Provably optimal DFT modification rule for Tab-Drw

Determine whether a provably optimal strategy exists for modifying the discrete Fourier transform (DFT) components in Tab-Drw—specifically, adjusting the imaginary parts of selected frequency-domain entries—to maximize watermark detectability while minimizing distortion of tabular data, and precisely characterize the sense of optimality (for example, optimal trade-off under a distortion budget or optimal statistical power for detection).

Background

Tab-Drw is a post-editing watermarking scheme for tabular data that embeds signals by modifying the imaginary components of the row-wise DFT representation to align with pseudorandom bits. A soft variant controls distortion via hyperparameters that limit which entries are modified and how strongly they are altered, and the paper provides theoretical bounds on distortion and robustness. Despite these results, the authors note that selecting the modification rule to achieve the best possible detectability–fidelity trade-off remains unresolved.

Identifying a provably optimal DFT modification rule would formalize the trade-off between watermark detectability and data fidelity, potentially yielding principled embedding policies or performance guarantees beyond heuristic tuning of soft parameters. This would strengthen both the theoretical foundation and practical deployment of Tab-Drw.