Universal finitary codes with exponential tails
概率论
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0502484,
title = {Universal finitary codes with exponential tails},
author = {Nate Harvey and Alexander E. Holroyd and Yuval Peres and Dan Romik},
journal= {arXiv preprint arXiv:math/0502484},
year = {2007}
}
备注
33 pages