Compression of Samplable Sources

Luca Trevisan, Salil Vadhan, and David Zuckerman


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.


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