A new paper from the group has been accepted for publication
The paper “The Shannon lower bound is asymptotically tight” by T. Koch has been accepted for publication in the IEEE Transactions on Information Theory.
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.