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Main Authors: Yang, Huiyuan, Shi, Yuxuan, Shao, Shuo, Yuan, Xiaojun
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.02501
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author Yang, Huiyuan
Shi, Yuxuan
Shao, Shuo
Yuan, Xiaojun
author_facet Yang, Huiyuan
Shi, Yuxuan
Shao, Shuo
Yuan, Xiaojun
contents This paper studies the joint data and semantics lossy compression problem, i.e., an extension of the hidden lossy source coding problem that entails recovering both the hidden and observable sources. We aim to study the nonasymptotic and second-order properties of this problem, especially the converse aspect. Specifically, we begin by deriving general nonasymptotic converse bounds valid for general sources and distortion measures, utilizing properties of distortion-tilted information. Subsequently, a second-order converse bound is derived under the standard block coding setting through asymptotic analysis of the nonasymptotic bounds. This bound is tight since it coincides with a known second-order achievability bound. We then examine the case of erased fair coin flips (EFCF), providing its specific nonasymptotic achievability and converse bounds. Numerical results under the EFCF case demonstrate that our second-order asymptotic approximation effectively approximates the optimum rate at given blocklengths.
format Preprint
id arxiv_https___arxiv_org_abs_2402_02501
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Joint Data and Semantics Lossy Compression: Nonasymptotic Converse Bounds and Second-Order Asymptotics
Yang, Huiyuan
Shi, Yuxuan
Shao, Shuo
Yuan, Xiaojun
Information Theory
This paper studies the joint data and semantics lossy compression problem, i.e., an extension of the hidden lossy source coding problem that entails recovering both the hidden and observable sources. We aim to study the nonasymptotic and second-order properties of this problem, especially the converse aspect. Specifically, we begin by deriving general nonasymptotic converse bounds valid for general sources and distortion measures, utilizing properties of distortion-tilted information. Subsequently, a second-order converse bound is derived under the standard block coding setting through asymptotic analysis of the nonasymptotic bounds. This bound is tight since it coincides with a known second-order achievability bound. We then examine the case of erased fair coin flips (EFCF), providing its specific nonasymptotic achievability and converse bounds. Numerical results under the EFCF case demonstrate that our second-order asymptotic approximation effectively approximates the optimum rate at given blocklengths.
title Joint Data and Semantics Lossy Compression: Nonasymptotic Converse Bounds and Second-Order Asymptotics
topic Information Theory
url https://arxiv.org/abs/2402.02501