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 \(\{0, 1\}^n\)).

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 \(\mathbf{P}\).
2. If \(H(X) ≤ k = n−O(\log n)\), we show how to compress to expected length \(k + \mathrm{polylog}(n − k)\).
3. If the support of \(X\) is the witness set for a self-reducible \(\mathbf{NP}\) relation, then we show how to compress to expected length \(H(X)+ 5\).