Motivated by applications in distributed storage, the notion of a locally recoverable code (LRC) was introduced a few years back. In an LRC, any coordinate of a codeword is recoverable by accessing only a small number of other coordinates. While different properties of LRCs have been well-studied, their performance on channels with random erasures or errors has been mostly unexplored. In this paper, we analyze the performance of LRCs over such stochastic channels. In particular, for input-symmetric discrete memoryless channels, we give a tight characterization of the gap to Shannon capacity when LRCs are used over the channel. Our results hold for a general notion of LRCs that correct multiple local erasures.

翻译：由分布式存储中的应用程序驱动,几年前就引入了本地可回收代码的概念。在 LRC 中,只要访问少数其他坐标,编码的任何协调都可以被恢复。虽然LRC的不同属性已得到很好地研究,但是在随机删除或错误的频道上的表现大多没有被探索。在本文中,我们分析了 LRC 在这种随机切换的频道上的性能。特别是,对于输入式对称离散的无记忆通道,我们给在频道上使用 LRC 时的香农能力给出了严格的空白描述。我们的结果为LRC 提供了一个普通概念,可以纠正多个本地断层。