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

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.

18 pages, 3 figure, orginally presented at Allerton 06

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