On Lossy Compression of Generalized Gaussian Sources

摘要

This paper considers a problem of lossy compression of generalized Gaussian (GG) sources (i.e., sources with the probability density functions proportional to exp(-|x|^{s/2) ,s > 0) with an l_r, r > 0, distortion measure. It is shown that an optimal reconstruction distribution always exists and properties of this distribution are studied. In particular, it is shown that if s ≤ r - 1 then an optimal reconstruction must have unbounded support and for s > r an optimal reconstruction must have bounded support. Further, it is shown that Shannon's lower bound is achievable if and only if r = s ∈ (0, 1] ∪ {2}, or in other words when the GG distribution is self-decomposable. Finally, conditions are shown under which an optimal reconstruction is discrete with finitely many mass points.}