论文标题
可回收系统
Recoverable Systems
论文作者
论文摘要
在既定的存储代码概念中的动机中，我们考虑了有限字母的无限序列集，使得连续条目的每一个$ k $ - 可以从序列中的$ l $ neimygorhood中独特地恢复。我们解决了找到集合的最大增长率的问题，我们将其定为容量，以及接近最佳速率的显式家庭的构造。我们采用的技术取决于该问题与受约束系统的联系。在本文的第二部分中，我们考虑对问题的修改，其中序列中的条目被视为随机变量在有限的字母上，遵循某个共同分布的有限字母，并且恢复条件要求$ k $ tuple的shannon熵在其$ l $ l-neighborhood的条件下以$ limienties的限制。 健康）状况。利用厄贡理论的工具，我们证明了熵最大化度量的某些特性。我们还建议从相应的确定性系统构建可构建$ε$的措施的过程。
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.
