Universality of Logarithmic Loss in Successive Refinement

Abstract

We establish an universal property of logarithmic loss in the successive refinement problem. If the first decoder operates under logarithmic loss, we show that any discrete memoryless source is successively refinable under an arbitrary distortion criterion for the second decoder. Based on this result, we propose a low-complexity lossy compression algorithm for any discrete memoryless source.

Keywords

• logarithmic loss
• rate-distortion
• successive refinability