Generative Decompression: Optimal Lossy Decoding Against Distribution Mismatch
It addresses distribution mismatch in standardized communication systems, enabling adaptive, high-fidelity reconstruction without encoder modifications, though it is incremental as it builds on classical Bayesian estimation.
This paper tackles the problem of optimal decoding in lossy compression when the encoder's assumed source distribution mismatches the true distribution, showing that generative decompression, which uses Bayesian correction at the decoder, strictly outperforms conventional methods and closes a vast majority of the performance gap to ideal joint optimization.
This paper addresses optimal decoding strategies in lossy compression where the assumed distribution for compressor design mismatches the actual (true) distribution of the source. This problem has immediate relevance in standardized communication systems where the decoder acquires side information or priors about the true distribution that are unavailable to the fixed encoder. We formally define the mismatched quantization problem, demonstrating that the optimal reconstruction rule, termed generative decompression, aligns with classical Bayesian estimation by taking the conditional expectation under the true distribution given the quantization indices and adapting it to fixed-encoder constraints. This strategy effectively performs a generative Bayesian correction on the decoder side, strictly outperforming the conventional centroid rule. We extend this framework to transmission over noisy channels, deriving a robust soft-decoding rule that quantifies the inefficiency of standard modular source--channel separation architectures under mismatch. Furthermore, we generalize the approach to task-oriented decoding, showing that the optimal strategy shifts from conditional mean estimation to maximum a posteriori (MAP) detection. Experimental results on Gaussian sources and deep-learning-based semantic classification demonstrate that generative decompression closes a vast majority of the performance gap to the ideal joint-optimization benchmark, enabling adaptive, high-fidelity reconstruction without modifying the encoder.