Compression of samplable sources

We study the compression of polynomially samplable sources. In particular, we give efficient prefix-free compression and decompression algorithms for three classes of such sources (whose support is a subset of {0, l}ⁿ). 1) We show how to compress sources X samplable by logspace machines to expected length H(X) + O(1). Our next results concern flat sources whose support is in P. 2) If H(X) ≤ k = n - O(log n), we show how to compress to length k + δ· (n - k) for any constant δ > 0; in quasi-polynomial time we show how to compress to length k + O(polylog log (n - k)) even if k = n -polylog(n). 3) If the support of X is the witness set for a self-reducible NP relation, then we show how to compress to expected length H(X) + 4.