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 {0,1}^{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 + polylog(n-k).
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)
+ 5.