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This paper presents a new model of the content reconstruction problem in self-embedding systems, based on an erasure communication channel. We explain why such a model is a good fit for this problem, and how it can be practically implemented with the use of digital fountain codes. The proposed method is based on an alternative approach to spreading the reference information over the whole image, which has recently been shown to be of critical importance in the application at hand. Our paper presents a theoretical analysis of the inherent restoration trade-offs. We analytically derive formulas for the reconstruction success bounds, and validate them experimentally with Monte Carlo simulations and a reference image authentication system. We perform an exhaustive reconstruction quality assessment, where the presented reference scheme is compared to five state-of-the-art alternatives in a common evaluation scenario. Our paper leads to important insights on how self-embedding schemes should be constructed to achieve optimal performance. The reference authentication system designed according to the presented principles allows for high-quality reconstruction, regardless of the amount of the tampered content. The average reconstruction quality, measured on 10000 natural images is 37 dB, and is achievable even when 50% of the image area becomes tampered.