AI 中文总结
本文提出因果条件感知下的序列有损压缩框架，针对马尔可夫和高斯-马尔可夫源建立率失真感知函数界，并证明高斯最优性及闭式解。
AI 中文摘要
本文研究了在因果条件感知准则下的序列有损压缩，该准则在给定相同重构历史的条件下比较源分布与重构分布。对于一阶马尔可夫源，我们构建了具有逐阶段约束的有限时域非预期率失真感知函数（NRDPF），并利用增强的强函数表示引理（SFRL）和公共随机性，建立了最小变长总速率的一次性下界和上界。对于在逐点均方误差（MSE）和条件平方Wasserstein-2保真度下的时变标量高斯-马尔可夫源，我们证明了高斯最优性，推导了对数方差表征，并获得了闭式解，该解在感知不受约束时恢复经典高斯非预期率失真函数（NRDF），在源平稳且无记忆时恢复经典高斯率失真感知函数（RDPF）。
英文摘要
In this paper, we study sequential lossy compression under a causal conditional perception criterion comparing source and reconstruction distributions given the same reconstruction history. For first-order Markov sources, we formulate the finite-horizon nonanticipative rate-distortion-perception function (NRDPF) with stagewise constraints and establish one-shot lower and upper bounds on the minimum variable-length sum rate using a strengthened strong functional-representation lemma (SFRL) and common randomness. For time-varying scalar Gauss--Markov sources under pointwise mean-squared error (MSE) and conditional squared Wasserstein-$2$ fidelity, we prove Gaussian optimality, derive a log-variance characterization, and obtain a closed-form solution that recovers the classical Gaussian nonanticipative rate-distortion function (NRDF) when perception is unconstrained and the classical Gaussian RDPF when the source is stationary and memoryless.
Comments6 pages, 1 figure, submitted paper
