Семинар Добрушинской математической лаборатории ИППИ РАН
22 марта, вторник, 16:00. Zoom-подключение см. на сайте семинара:
http://iitp.ru/ru/userpages/74/285.htm
Alexander Barg (ИППИ+Uni Maryland):
Recoverable systems (storage codes on graphs)
Abstract:
Consider a shift invariant measure $\mu$ on the set of infinite sequences
$X$
over a finite alphabet $Q$. Call $\mu$ epsilon-recoverable if the entropy of
$\xi$ conditional on its neighborhood is at most epsilon. What can be said
about the measure with maximum entropy $h(\mu)$? We establish
characterizations
of entropy maximizing recoverable measures. The deterministic version of
this problem is closely related to constrained systems, and we discuss
several results based on this link. Finally, we mention some capacity
results
for deterministic systems without assuming shift invariance, and also for
the version of this problem for finite graphs. The talk is based on several
recent papers with a number of coauthors including Ohad Elishco (Beer Sheva)
and Gilles Zemor (Bordeaux).
| 17.03.2022 | Комеч Сергей Александрович |