Second-Order Image Characterization with Distortion and Secrecy
Cao Daming
原文摘要
Image characterization relates coding budgets to the probability carried by source cells and their output images. At second order, refining a cell can reveal unavailable information, while a change of reference measure can alter the relevant likelihood fluctuations. We establish image bounds that account for both effects. A finite-block partition theorem bounds the cost of merging component images by the joint conditional information spectrum of their label. It preserves continuous second-order profiles when that cost is negligible on the square-root blocklength scale. For reconstruction constraints, cell-dependent reference measures retain the actual distortion deficits in a single likelihood. A Gaussian evaluation gives matching second-order rates for Heegard--Berger coding with one uninformed decoder in the strict both-active regime, common reconstruction under a joint agreement and distortion criterion, and two-stage refinement with side information absent at the first decoder. A structured binary source illustrates partition stability even when its global density and conditional-divergence deficits are linear in blocklength. Posterior-mass images also sharpen extraction after a public refinement by charging its residual information rather than its alphabet size. These results preserve the joint constraints and the observations available for choosing the local coding experiment.
cs.IT