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

Abstract

Error-correcting codes are routinely bolted onto neural image watermarkingdecoders, and increasingly integrated into training. Neither practice comes with arule for when it helps, and comparisons rarely control for the payload the codeitself consumes. Using MBRS as a fixed backbone under a single evaluation protocol,we show that one quantity governs the outcome: the code's correctable fractiontheta = t/n. The reason a threshold exists at all is that hard-decision decodingdoes not fail -- it miscorrects. When a block has more errors than the code can fix,the decoder silently returns a different codeword, corrupting a fixed fraction ofthat block's message bits. We measure that fraction at kappa = 0.482 +/- 0.029 overtwo independently trained models and 15 attack-model pairs; crucially, it does nottrack the channel. This yields a closed-form break-even, located empirically at 22%raw BER for Hamming(7,4) (theta = 14.3%). Matching the payload reverses the ranking the literature currently implies. At equal36-bit payload, identical weights and identical code, bolting BCH onto a trainedmodel beats integrating it into training by 4.2x at JPEG Q50 (5.2% vs. 21.9%), andintegration is significantly worse on 6 of 17 attacks and better on 1. Integrationstill buys +3.0 dB PSNR -- real, but a third less than earlier reports -- because itdegrades the raw channel past the break-even, so its own parity bits buy nothing andthe two penalties compound instead of cancelling. We further show that leavingBatchNorm in training mode at evaluation time inflates apparent robustness toadditive noise by 2.4-6.7x.