Covert Multi-bit LLM Watermarking: An Information Theory and Coding Approach
It provides an information-theoretic framework and practical algorithm for embedding multiple bits covertly in LLM outputs, addressing the need for robust and efficient watermarking.
The paper introduces a multi-bit watermarking method for LLMs, achieving a bit-error rate below 10% at 0.375 bits/token with negligible perplexity degradation.
We study the problem of multi-bit watermarking for large language models (LLMs). We introduce a block-autoregressive model inspired by multi-token prediction, in which the encoder has limited non-causal access to token distributions within each block. This formulation enables an information-theoretic characterization of multi-bit watermarking capacity, by which the knowledge of LLM cover statistics is leveraged to enable a multi-bit covert embedding. We study the information-theoretic limits of the model by combining Gelfand-Pinsker and channel synthesis coding techniques and obtain an exact characterization of the capacity. The embedding strategy is further optimized across blocks using a constrained Markov decision process (CMDP) and we develop an explicit algorithm based on polar codes following the information-theoretic principles. Our algorithm achieves a bit-error rate below 10 percent with a rate of 0.375 bits/token over short token lengths with negligible perplexity and distortion degradation.