A Lower Bound on the Complexity of Approximating the Entropy of a Markov Source
Information Theory
2009-12-31 v1 math.IT
Abstract
Suppose that, for any (k \geq 1), (\epsilon > 0) and sufficiently large , we are given a black box that allows us to sample characters from a th-order Markov source over the alphabet (\{0, ..., \sigma - 1\}). Even if we know the source has entropy either 0 or at least (\log (\sigma - k)), there is still no algorithm that, with probability bounded away from (1 / 2), guesses the entropy correctly after sampling at most ((\sigma - k)^{k / 2 - \epsilon}) characters.
Keywords
Cite
@article{arxiv.0912.5079,
title = {A Lower Bound on the Complexity of Approximating the Entropy of a Markov Source},
author = {Travis Gagie},
journal= {arXiv preprint arXiv:0912.5079},
year = {2009}
}