Recoverable systems (storage codes on graphs)

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).
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