Reliable provenance for LLM outputs requires multi-bit watermarks that remain robust under editing while maintaining low false-positive rates. Existing ECC-based LLM watermarks rely on hard-decision decoding, discarding token-level reliability information and limiting robustness under post-generation edits. We propose CORE-BREW, a COnstant-hit-Rate Embedding extension of BREW for multi-bit watermarking. CORE-BREW calibrates the watermark channel by targeting a fixed hit rate $p^\star$, yielding closed-form per-token log-likelihood ratios (LLRs) for soft-decision decoding. It incorporates entropy-aware erasures to limit perturbations in low-entropy contexts and combines likelihood-based scoring with soft-decision list decoding to exploit soft evidence. Experiments on open-source LLMs under token-level edits and paraphrasing demonstrate that CORE-BREW generally improves detection robustness and payload recovery over the BREW baseline while maintaining low observed false-positive rates. Despite higher conditional perplexity, BLEU and BERTScore remain close to those of unwatermarked text, indicating comparable reference-based translation quality.

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