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

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.