Fundamental Trade-Offs in Multi-Bit Watermarking of Stochastic Processes
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918492413886464 |
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| author | He, Haiyun Liu, Yepeng Shen, Zhuoer Wang, Ziqiao Mao, Yongyi Bu, Yuheng |
| author_facet | He, Haiyun Liu, Yepeng Shen, Zhuoer Wang, Ziqiao Mao, Yongyi Bu, Yuheng |
| contents | We study multi-bit watermarking for data generated by stochastic processes, where a hidden message is embedded during sampling and must be decodable by an authorized detector that possesses side information unavailable to unauthorized observers. In high-stakes deployments, a practical watermark must simultaneously control false alarms, preserve generation quality without distorting the output distribution, and support reliable multi-bit decoding. Satisfying all three goals at once inevitably creates fundamental trade-offs. We formulate watermark embedding as a distributional information-embedding problem and watermark detection as a multiple-hypothesis testing problem under distortion and rate constraints, leading to four fundamental metrics: false-alarm probability, detection error probability, distortion, and information rate. Within this information-theoretic framework, we derive matched converse and achievability bounds that characterize the optimal trade-offs and provide scheme-agnostic benchmarks for any watermarking method. For stationary ergodic stochastic processes, we further obtain matched asymptotic limits and connect them to the finite-sample regime. Finally, we present a reference watermarking construction satisfying our assumptions and empirically illustrating the predicted trade-offs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_08826 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fundamental Trade-Offs in Multi-Bit Watermarking of Stochastic Processes He, Haiyun Liu, Yepeng Shen, Zhuoer Wang, Ziqiao Mao, Yongyi Bu, Yuheng Information Theory We study multi-bit watermarking for data generated by stochastic processes, where a hidden message is embedded during sampling and must be decodable by an authorized detector that possesses side information unavailable to unauthorized observers. In high-stakes deployments, a practical watermark must simultaneously control false alarms, preserve generation quality without distorting the output distribution, and support reliable multi-bit decoding. Satisfying all three goals at once inevitably creates fundamental trade-offs. We formulate watermark embedding as a distributional information-embedding problem and watermark detection as a multiple-hypothesis testing problem under distortion and rate constraints, leading to four fundamental metrics: false-alarm probability, detection error probability, distortion, and information rate. Within this information-theoretic framework, we derive matched converse and achievability bounds that characterize the optimal trade-offs and provide scheme-agnostic benchmarks for any watermarking method. For stationary ergodic stochastic processes, we further obtain matched asymptotic limits and connect them to the finite-sample regime. Finally, we present a reference watermarking construction satisfying our assumptions and empirically illustrating the predicted trade-offs. |
| title | Fundamental Trade-Offs in Multi-Bit Watermarking of Stochastic Processes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.08826 |