### Abstract

When the information source is a continuous distribution and the rate-distortion function is strictly larger than the Shannon lower bound, the explicit evaluation of the rate-distortion function is not straightforward. We evaluate the rate-distortion function for an independent identically distributed gamma source with respect to the absolute-log distortion measure. The logarithmic transformation reduces this rate-distortion problem to that under the absolute distortion measure. Extending the explicit evaluation of the rate-distortion function for the Gaussian sources, we obtain the parametric form of the rate-distortion function. We show that the optimal distribution of reconstruction consists of a continuous component enclosed by left and right discrete components, and the left discrete component vanishes when the acceptable distortion is small. We further extend the result for a wider class of source distributions.

Publication

*IEEE Transactions on Information Theory*