Recoverable Systems

Ohad Elishco, Alexander Barg

Research output: Contribution to journalArticlepeer-review


Motivated by the established notion of storage codes, we consider sets of infinite sequences over a finite alphabet such that every k-tuple of consecutive entries is uniquely recoverable from its l-neighborhood in the sequence. We address the problem of finding the maximum growth rate of the set, which we term capacity, as well as constructions of explicit families that approach the optimal rate. The techniques that we employ rely on the connection of this problem with constrained systems. In the second part of the paper we consider a modification of the problem wherein the entries in the sequence are viewed as random variables over a finite alphabet that follow some joint distribution, and the recovery condition requires that the Shannon entropy of the k-tuple conditioned on its l-neighborhood be bounded above by some ε > 0 .We study properties of measures on infinite sequences that maximize the metric entropy under the recoverability condition. Drawing on tools from ergodic theory, we prove some properties of entropy-maximizing measures. We also suggest a procedure of constructing an ε - recoverable measure from a corresponding deterministic system.

Original languageEnglish
Pages (from-to)3681-3699
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - 22 Feb 2022


  • Codes
  • Encoding
  • Entropy
  • Indexes
  • Markov processes
  • Probabilistic logic
  • Random variables

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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