Subset-universal lossy compression

A lossy source code C with rate R for a discrete memoryless source S is called subset-universal if for every 0 <; R´ <; R, almost every subset of 2^nR´ of its codewords achieves average distortion close to the source´s distortion-rate function D(R´). In this paper we prove the asymptotic existence of such codes. Moreover, we show the asymptotic existence of a code that is subset-universal with respect to all sources with the same alphabet.