The Shannon Lower Bound is Asymptotically Tight
Abstract
The Shannon lower bound is one of the few lower bounds on the rate-distortion function that holds for a large class of sources. In this paper, it is demonstrated that its gap to the rate-distortion function vanishes as the allowed distortion tends to zero for all sources having a finite differential entropy and whose integer part is finite. Conversely, it is demonstrated that if the integer part of the source has an infinite entropy, then its rate-distortion function is infinite for every finite distortion. Consequently, the Shannon lower bound provides an asymptotically tight bound on the rate-distortion function if, and only if, the integer part of the source has a finite entropy.
Cite
@article{arxiv.1504.08245,
title = {The Shannon Lower Bound is Asymptotically Tight},
author = {Tobias Koch},
journal= {arXiv preprint arXiv:1504.08245},
year = {2016}
}
Comments
13 pages, no figures. Replaced with version that has been submitted to IEEE Transactions on Information Theory. Lemma 1 has been generalized