A Framework for Lossy Compression of Heavy-Tailed Sources

We study the rate-distortion problem for both scalar and vector memoryless heavy-tailed α-stable sources (0 < α < 2). Using a recently defined notion of “strength” as a power measure, we derive the rate-distortion function for α-stable sources subject to a constraint on the strength of the error and show it to be logarithmic in the strength-to-distortion ratio. We show how our framework paves the way for finding optimal quantizers for α- stable sources and other general heavy-tailed ones. In add