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arXiv:2610.09472 · v3

Second-Order Image Characterization with Distortion and Secrecy

Cao Daming
cs.IT
首次提交 2026-10-07 13:31
版本更新 2026-11-04 20:52
雷达观测 2026-11-05 11:10
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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.

作者备注：Draft manuscript

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Image-size characterization relates coding budgets to the probability carried by source cells and their output images. At second order, thisrefining relationa mustcell preservecan thereveal jointunavailable fluctuationsinformation, ofwhile activea constraintschange andof thereference informationmeasure availablecan foralter choosingthe anrelevant auxiliarylikelihood descriptionfluctuations. We developestablish simultaneousimage posteriorbounds andthat conditionalaccount for both effects. A finite-compositionblock imagepartition theorem bounds, togetherthe withcost cell-dependentof referencemerging measurescomponent forimages reconstructionby constraints.the Thejoint referenceconditional measuresinformation retainspectrum bothof distortiontheir deficitslabel. inIt onepreserves likelihoodcontinuous andsecond-order permitprofiles when that cost is negligible on the samesquare-root analyticalblocklength descriptionscale. costFor toreconstruction cancelconstraints, betweencell-dependent tworeference imagemeasures comparisonsretain 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, its common-reconstruction counterpart, and the corresponding two-stage refinement corner. The frameworkreconstruction alsounder givesa compatiblejoint helper-imageagreement intersections,and reconstruction-celldistortion boundscriterion, and conditionaltwo-type privacy amplification. Anstage agreed-reproductionrefinement imagewith explainsside wheninformation aabsent scalarat Gaussianthe coefficientfirst replacesdecoder. anA optimizedstructured information--distortionbinary profile.source Gaussianillustrates Wyner--Zivpartition andstability Gray--Wynereven characterizationswhen provideits attributedglobal benchmarksdensity and complementaryconditional-divergence evaluationsdeficits ofare thelinear imagein constraintsblocklength. For arbitraryPosterior-mass helperimages sections,also generalsharpen reconstructionextraction policies,after anda reliable-keypublic generation,refinement theby finite-blockcharging boundsits identifyresidual theinformation remainingrather likelihoodthan orits partitionalphabet constraintsize. The rateThese applicationsresults usepreserve the same observationjoint patternconstraints and jointthe performanceobservations eventavailable infor choosing the converselocal andcoding constructionexperiment.

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相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。

v3 · 2026-11-04 20:52 · 最新观测版本

Second-Order Image Characterization with Distortion and Secrecy

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.

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v2 · 2026-11-03 14:58

Second-Order Image Characterization with Distortion and Secrecy

Image-size characterization relates coding budgets to the probability carried by source cells and their output images. At second order, this relation must preserve the joint fluctuations of active constraints and the information available for choosing an auxiliary description. We develop simultaneous posterior and conditional-composition image bounds, together with cell-dependent reference measures for reconstruction constraints. The reference measures retain both distortion deficits in one likelihood and permit the same analytical description cost to cancel between two image comparisons. A Gaussian evaluation gives matching second-order rates for Heegard--Berger coding with one uninformed decoder in the strict both-active regime, its common-reconstruction counterpart, and the corresponding two-stage refinement corner. The framework also gives compatible helper-image intersections, reconstruction-cell bounds, and conditional-type privacy amplification. An agreed-reproduction image explains when a scalar Gaussian coefficient replaces an optimized information--distortion profile. Gaussian Wyner--Ziv and Gray--Wyner characterizations provide attributed benchmarks and complementary evaluations of the image constraints. For arbitrary helper sections, general reconstruction policies, and reliable-key generation, the finite-block bounds identify the remaining likelihood or partition constraint. The rate applications use the same observation pattern and joint performance event in the converse and construction.

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