Strong Successive Refinability: Sufficient Conditions

We investigate the second order asymptotics (source dispersion) of the successive refinement problem. Similarly to the classical definition of a successively refinable source, we say that a source is strongly successively refinable if successive refinement coding can achieve the second order optimum rate (including the dispersion terms) at both receivers. We propose a sufficient condition for strong successive refinability. As a corollary, we show that any discrete source with Hamming distortion is strongly successively refinable. For a Gaussian source with quadratic distortion, we show directly that the source is strongly successively refinable.