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When Does Error Correction Help? A Payload-Matched Study of Post-Hoc and End-to-End ECC in Neural Image Watermarking

Year: 2026
Type: preprint
Abstract: Error-correcting codes are routinely bolted onto neural image watermarking decoders, and increasingly integrated into training. Neither practice comes with a rule for when it helps, and comparisons rarely control for the payload the code itself consumes. Using MBRS as a fixed backbone under a single evaluation protocol, we show that the outcome is governed, to first order, by a single screening quantity: the code's normalized correction radius θ = t/n (with the miscorrection rate as a second, code-specific factor). The reason a threshold exists at all is that hard-decision decoding does not fail — it miscorrects. When a block has more errors than the code can fix, the decoder silently returns a different codeword, corrupting a roughly fixed fraction of that block's message bits. We measure that fraction at κ = 0.482 ± 0.029 (95% bootstrap CI [0.470, 0.497]) over two independently trained models and 15 attack–model pairs, with corrected BER linear in P_fail (R² = 0.997); κ is approximately stable across these attacks and models and shows no significant monotonic trend with raw BER. This yields a closed-form break-even of 18.8% raw BER for Hamming(7,4) (θ = 14.3%). The measured points nearest the crossing bracket it in [21.9%, 23.8%], though by margins within the evaluation's run-to-run variation, so we quote the closed form and treat the bracket as indicative. The empirical crossing sits above the closed form because real bit errors are mildly clustered. Matching the payload at first appears to reverse the ranking the literature implies. At equal 36-bit payload and with the same code, bolting BCH onto a trained model (no retraining) beats the published integrated model by 4.2× at JPEG Q50 (5.2% vs. 21.9%). But this gap is largely a property of the training mixture: the two models differ from the post-hoc arm in their Phase-3 noise pool, and retraining the integrated arm with the post-hoc arm's exact pool closes the gap to 5.4% vs. 5.2% (not significant) — and removes its +3.0 dB quality gain as well. In this retrain both of the published model's headline properties track the training mixture rather than whether ECC is integrated, though one retrain cannot separate the pool from training-to-training variance. With the mixture matched the two designs differ little at JPEG Q50 and trade off elsewhere: integration is better on salt-and-pepper and worse on additive Gaussian noise. The same break-even explains why the JPEG gap exists at all: the published model's raw channel at JPEG Q50 sits at the break-even (21.9%), so its parity buys almost nothing, whereas the post-hoc and pool-matched arms sit below it (≈ 8%) and correct to ≈ 5%. We further show that leaving BatchNorm in training mode at evaluation time inflates apparent robustness to additive noise by 2.4–6.7×.
DOI: 10.5281/zenodo.22970404
Author: Li, Yanze
Language: English
Open Access status: green
OpenAlex ID: W7214444606
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