Sequential Lossy Compression With Causal Conditional Perception
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.
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BibTeX
@misc{stavrou2026sequential,
title = {{Sequential Lossy Compression With Causal Conditional Perception}},
author = {Photios A. Stavrou and Zixuan He},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08611},
eprint = {2609.08611},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08611},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sequential Lossy Compression With Causal Conditional Perception
AU - Photios A. Stavrou
AU - Zixuan He
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08611
UR - https://arxiv.org/abs/2609.08611
AB - 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.
ER -