A Rigorous Revisit to the Partial Distortion Theorem in the Case of a Laplacian Source

This letter studies rigorously the partial distortion theorem in the case of a Laplacian probability density function and proves that, while essentially each cell of a minimum mean-square error nonuniform scalar quantizer contributes to distortion more or less the same as its neighbor, each outer cell contributes slightly more than its inner neighbor. Also it is proved that the outermost cell distortion cannot exceed asymptotically 1.914 times that of the innermost cell. Thus, this letter clarifies in the Laplacian case the meaning of approximate equidistortion stated in the partial distortion theorem.