Sequential data compression improves quality by matching future context
Sequential Lossy Compression With Causal Conditional Perception
Information Theory
Summary
Compressing data usually means making it smaller by removing some details, but it's important that the compressed version still feels right compared to the original. This paper looks at compressing sequences of data while ensuring the compressed version looks similar when considering past outputs. The researchers focus on a type of source where each item depends only on the previous one, and they develop mathematical tools to find the best way to compress it with minimal size and distortion. They also study specific kinds of data called Gauss-Markov sources and find exact solutions that match existing known results when special conditions apply.
lossy compressionsequential compressionrate-distortion theoryMarkov sourcesrate-distortion-perception functionmean-squared errorWasserstein distanceGaussian sourcesfunctional representation lemmanonanticipative coding
Authors
Photios A. Stavrou, Zixuan He
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.