AI 中文总结
本文提出二阶图像刻画方法，统一处理失真与保密约束，给出多输出联合波动下的速率界，并应用于多源辅助、高斯描述及隐私放大等场景。
AI 中文摘要
图像大小刻画将编码约束与信源单元及其输出图像所携带的概率联系起来。在二阶意义上，这种联系必须保留所有有效约束的联合波动，并区分编码器可观测的信源变化与不可观测的信道噪声。我们将单输出后验刻画扩展为同时的后验与条件组合图像界。这些界保留了多个输出的实际耦合，量化了不规则单元的条件似然损失，并允许实际失真标记。另外两个扩展将不相交计数替换为加权重构策略图像，并将输出基数替换为用于保密的后验质量约束。直接应用为兼容的多信源辅助交集、一个有损重构伴随多个知情无损重构、高斯公共/私有描述以及从规定条件类型进行隐私放大，生成了匹配的二阶区域。高斯描述结果还给出了联合速率-失真偏移。对于一般辅助部分、真正有损的知情重构、高斯Wyner-Ziv编码以及协调后提取，相同的图像方法给出了显式速率界，并识别了其剩余损失。由此产生的速率修正既反映了图像约束，也反映了每个终端可用的观测。
英文摘要
Image-size characterization connects coding constraints to the probability carried by source cells and their output images. At second order, this connection must retain the joint fluctuations of all active constraints and distinguish encoder-observable source variation from unobserved channel noise. We extend the single-output posterior characterization to simultaneous posterior and conditional-composition image bounds. The bounds preserve the actual coupling of multiple outputs, quantify conditional likelihood losses for irregular cells, and admit actual-distortion marks. Two further extensions replace disjoint counting by weighted reconstruction-policy images and replace output cardinality by posterior-mass constraints for secrecy. Direct applications yield matching second-order regions for compatible multi-source helper intersections, one lossy reconstruction with several informed lossless reconstructions, Gaussian common/private descriptions, and privacy amplification from a prescribed conditional type. The Gaussian description result also gives joint rate--distortion offsets. For general helper sections, genuinely lossy informed reconstruction, Gaussian Wyner--Ziv coding, and reconciliation followed by extraction, the same image methods give explicit rate bounds with their remaining losses identified. The resulting rate corrections reflect both the image constraints and the observations available to each terminal.
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