An invariant of finitary codes with finite expected square root coding length

Details An invariant of finitary codes with finite expected square root coding length An invariant of finitary codes with finite expected square root coding length

2003-09-08

arxiv.org/abs/math/0309120v1

Mathematics

Probability

18 pages

Scientific paper

Let $p$ and $q$ be probability vectors with the same entropy $h$. Denote by $B(p)$ the Bernoulli shift indexed by $\Z$ with marginal distribution $p$. Suppose that $\phi$ is a measure preserving homomorphism from $B(p)$ to $B(q)$. We prove that if the coding length of $\phi$ has a finite 1/2 moment, then $\sigma_p^2=\sigma_q^2$, where $\sigma_p^2=\sum_i p_i(-\log p_i-h)^2$ is the {\dof informational variance} of $p$. In this result, which sharpens a theorem of Parry (1979), the 1/2 moment cannot be replaced by a lower moment. On the other hand, for any $\theta<1$, we exhibit probability vectors $p$ and $q$ that are not permutations of each other, such that there exists a finitary isomorphism $\Phi$ from $B(p)$ to $B(q)$ where the coding lengths of $\Phi$ and of its inverse have a finite $\theta$ moment. We also present an extension to ergodic Markov chains.

Affiliated with

Also associated with

No associations

Rating

An invariant of finitary codes with finite expected square root coding length does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An invariant of finitary codes with finite expected square root coding length, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An invariant of finitary codes with finite expected square root coding length will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-47769