Coding into a source: a direct inverse Rate-Distortion theorem

TL;DR

This paper establishes a direct converse to Shannon's rate distortion theorem, proving that reliable transmission at rates below the rate distortion function guarantees the ability to transmit sources within the same distortion level.

Contribution

It provides a direct inverse rate-distortion theorem, filling a gap in the theoretical understanding of source transmission limits.

Findings

Proves the direct converse of the rate distortion theorem.

Shows reliable transmission at rates below R(D) implies source transmission within distortion D.

Enhances the theoretical foundation of information theory.

Abstract

Shannon proved that if we can transmit bits reliably at rates larger than the rate distortion function $R(D)$, then we can transmit this source to within a distortion $D$. We answer the converse question ``If we can transmit a source to within a distortion $D$, can we transmit bits reliably at rates less than the rate distortion function?'' in the affirmative. This can be viewed as a direct converse of the rate distortion theorem.