Computer Science – Information Theory
Scientific paper
2007-04-06
Computer Science
Information Theory
Submitted to IEEE Transactions on Information Theory
Scientific paper
We study universal compression of sequences generated by monotonic distributions. We show that for a monotonic distribution over an alphabet of size $k$, each probability parameter costs essentially $0.5 \log (n/k^3)$ bits, where $n$ is the coded sequence length, as long as $k = o(n^{1/3})$. Otherwise, for $k = O(n)$, the total average sequence redundancy is $O(n^{1/3+\epsilon})$ bits overall. We then show that there exists a sub-class of monotonic distributions over infinite alphabets for which redundancy of $O(n^{1/3+\epsilon})$ bits overall is still achievable. This class contains fast decaying distributions, including many distributions over the integers and geometric distributions. For some slower decays, including other distributions over the integers, redundancy of $o(n)$ bits overall is achievable, where a method to compute specific redundancy rates for such distributions is derived. The results are specifically true for finite entropy monotonic distributions. Finally, we study individual sequence redundancy behavior assuming a sequence is governed by a monotonic distribution. We show that for sequences whose empirical distributions are monotonic, individual redundancy bounds similar to those in the average case can be obtained. However, even if the monotonicity in the empirical distribution is violated, diminishing per symbol individual sequence redundancies with respect to the monotonic maximum likelihood description length may still be achievable.
No associations
LandOfFree
Universal Source Coding for Monotonic and Fast Decaying Monotonic Distributions 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 Universal Source Coding for Monotonic and Fast Decaying Monotonic Distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universal Source Coding for Monotonic and Fast Decaying Monotonic Distributions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-699577