The Shannon lower bound is one of the few lower bounds on the rate-distortionfunction that holds for a large class of sources. In this paper, it isdemonstrated that its gap to the rate-distortion function vanishes as theallowed distortion tends to zero for all sources having a finite differentialentropy and whose integer part is finite. Conversely, it is demonstrated thatif the integer part of the source has an infinite entropy, then itsrate-distortion function is infinite for every finite distortion. Consequently,the Shannon lower bound provides an asymptotically tight bound on therate-distortion function if, and only if, the integer part of the source has afinite entropy.
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