2005/02/23 by Nate Harvey, Harvey, Nate, Alexander E. Holroyd +5
Mathematics · #28D20 #37A50 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:28D20 #msc:37A50
paper · pdf · doi:10.48550/arxiv.math/0502484
33 pages
arxiv created 2005/02/23 · arxiv updated 2009/12/01
In 1977, Keane and Smorodinsky showed that there exists a finitary homomorphism from any finite-alphabet Bernoulli process to any other finite-alphabet Bernoulli process of strictly lower entropy. In 1996, Serafin proved the existence of a finitary homomorphism with finite expected coding length. In this paper, we construct such a homomorphism in which the coding length has exponential tails. Our construction is source-universal, in the sense that it does not use any information on the source distribution other than the alphabet size and a bound on the entropy gap between the source and target distributions. We also indicate how our methods can be extended to prove a source-specific version of the result for Markov chains.