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Pré-Publication, Document De Travail Année : 2024

Fixed-Length Lossy Compression with Distortion Risk Measure Constraints

Résumé

Storage or communication of data often requires lossy compression. As this data may be later utilized for decision making, compression introduces a source of uncertainty. In order to verify the quality of decisions, it is often desirable to quantify this uncertainty. This is often achieved via families of risk measures (such as distortion risk measures), rather than the mean. In this paper, we study fixed-length lossy compression subject to distortion risk measure constraints. We first establish conditions for the existence of a fixed-length lossy source code, which satisfies a distortion risk measure constraint. We then investigate the impact of quantifying uncertainty via a distortion risk measure, rather than standard expected distortion constraints. Finally, we quantify the impact of changing the source distribution on performance, measured in terms of a distortion risk measure.
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Dates et versions

hal-04582447 , version 1 (21-05-2024)

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  • HAL Id : hal-04582447 , version 1

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Malcolm Egan. Fixed-Length Lossy Compression with Distortion Risk Measure Constraints. 2024. ⟨hal-04582447⟩
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