Subset-Universal Lossy Compression

A lossy source code $\mathcal{C}$ with rate $R$ for a discrete memoryless source $S$ is called subset-universal if for every $0<R^{\mathrm{\prime }}<R$, almost every subset of $2^{n{R}^{\mathrm{\prime }}}$ of its codewords achieves average distortion close to the source’s distortion-rate function $D(R^{\mathrm{\prime }})$. 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.