Sequential Lossy Compression With Causal Conditional Perception

2026-09-08

AI Summary

本文研究了在因果条件感知准则下的序列有损压缩问题，通过使用强化的强函数表示引理等方法为马尔可夫源建立了最小变长总码率的一次性上下界。

Abstract

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.

Problem

• sequential lossy compression
• causal conditional perception
• Markov sources

Innovation

• Causal Conditional Perception
• Nonanticipative Rate-Distortion-Perception Function (NRDPF)
• Strengthened Strong Functional-Representation Lemma (SFRL)
• Gaussian Optimality
• Closed-Form Solution