computational complexity

, Volume 14, Issue 3, pp 186–227

Compression of Samplable Sources

Authors

    • Computer Science DivisionU.C. Berkeley
  • Salil Vadhan
    • Division of Engineering and Applied SciencesHarvard University
  • David Zuckerman
    • Department of Computer ScienceUniversity of Texas
Open AccessOriginal Paper

DOI: 10.1007/s00037-005-0198-6

Cite this article as:
Trevisan, L., Vadhan, S. & Zuckerman, D. comput. complex. (2005) 14: 186. doi:10.1007/s00037-005-0198-6

Abstract.

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. 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.
  1. 2.

    If H(X) ≤ k =  n − O(log n), we show how to compress to expected length k + polylog(nk).

     
  2. 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.

     

Keywords.

Expander graphs arithmetic coding randomized logspace pseudorandom generators approximate counting

Subject classification.

68P30

Copyright information

© Birkhäuser Verlag, Basel 2005