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.

翻译：本文研究了在有损压缩中，当压缩器设计所假设的分布与实际（真实）信源分布失配时的最优解码策略。该问题在标准化通信系统中具有直接相关性，其中解码器获得了关于真实分布的边信息或先验知识，而这些信息对于固定的编码器是不可用的。我们正式定义了失配量化问题，证明了最优重建规则——称为生成式解压缩——与经典贝叶斯估计相一致，即在给定量化索引的条件下对真实分布取条件期望，并将其适配到固定编码器的约束中。该策略在解码端有效地执行了一种生成式贝叶斯校正，严格优于传统的质心规则。我们将此框架扩展到噪声信道传输，推导出一种鲁棒的软解码规则，该规则量化了标准模块化信源-信道分离架构在失配情况下的效率损失。此外，我们将该方法推广到面向任务的解码，表明最优策略从条件均值估计转变为最大后验概率检测。在高斯信源和基于深度学习的语义分类上的实验结果表明，生成式解压缩弥合了与理想联合优化基准之间绝大部分的性能差距，从而能够在无需修改编码器的情况下实现自适应的、高保真度的重建。