列表可恢复码：好的、坏的和未知的（希望不是丑陋的）
List Recoverable Codes: The Good, the Bad, and the Unknown (hopefully not Ugly)
AI总结：
本文综述列表可恢复码的近期研究，分类介绍其存在性（好）、不可能性（坏）及未知结果，并阐述其在理论计算机科学中的广泛应用。
摘要：
列表恢复是纠错码的一项基本任务，极大地推广了针对最坏情况错误的唯一解码和列表解码。简而言之，给定以有界大小的输入列表 S_1,...,S_n 形式呈现的“软信息”，并论证没有太多码字与该软信息高度一致。这一通用问题以多种形式出现，既在编码理论内部，也在更广泛的理论计算机科学中。在本文中，我们综述了关于列表恢复码的近期结果，介绍了“好的”（即可能性结果，表明具有特定列表可恢复性的码存在）、“坏的”（不可能性结果）和“未知的”。我们进一步证明，尽管列表可恢复码最初是作为列表解码级联码的一个组成部分引入的，但此后它们在理论计算机科学的其他主题中找到了众多应用和联系。
英文摘要：
List recovery is a fundamental task for error-correcting codes, vastly generalizing unique decoding from worst-case errors and list decoding. Briefly, one is given ''soft information'' in the form of input lists S_1,...,S_n of bounded size, and one argues that there are not too many codewords that agree a lot with this soft information. This general problem appears in many guises, both within coding theory and in theoretical computer science more broadly. In this article we survey recent results on list recovery codes, introducing both the ''good'' (i.e., possibility results, showing that codes with certain list recoverability exist), the ''bad'' (impossibility results), and the ''unknown''. We additionally demonstrate that, while list recoverable codes were initially introduced as a component in list decoding concatenated codes, they have since found myriad applications to and connections with other topics in theoretical computer science.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
