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Results tagged with it.information-theory
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user 20062
Theoretical and experimental aspects of information theory and coding theory. This tag covers but is not limited to following branches: information theory, information geometry, optimal transportation theory, coding theory.
12
votes
2
answers
2k
views
Proving a messy inequality
EDIT:
After much work I was able to reduce the inequality to a single variable function which I need to show is non-positive. That function is (for $0\leq p\leq\frac{1}{2}$)
$$\frac{p^2(\log(p))^2 - ( …
- 1,034
9
votes
2
answers
461
views
Entropy conjecture for distributions over $\mathbb{Z}_n$
Suppose we have two independent random variables $X$ (with distribution $p_X$) and $Y$ (with distribution $p_Y$) which take values in the cyclic group $\mathbb{Z}_n$. Let $Z = X +Y$, where the additio …
- 1,034
5
votes
Accepted
Proving a messy inequality
I think I managed to prove the entire inequality analytically. The whole proof is a bit long to post here (about 7 pages) and involves ugly looking expressions. I'll outline the general strategy I use …
- 1,034
2
votes
Accepted
Entropy conjecture for distributions over $\mathbb{Z}_n$
The conjecture is wrong! It wasn't as complicated as I thought it was.
A simple counter example is over $\mathbb{Z}_6$. Consider $H(X) = 1$ and $H(y) = 1 +\epsilon$ where $\epsilon$ is very small. …
- 1,034