This paper introduces a new solution to DNA storage that integrates all three steps of retrieval, namely clustering, reconstruction, and error correction. DNA-correcting codes are presented as a unique solution to the problem of ensuring that the output of the storage system is unique for any valid set of input strands. To this end, we introduce a novel distance metric to capture the unique behavior of the DNA storage system and provide necessary and sufficient conditions for DNA-correcting codes. The paper also includes several bounds and constructions of DNA-correcting codes.

翻译：本文提出了一种DNA存储新方案，该方案整合了读取过程中的三个关键步骤：聚类、重建与纠错。DNA纠错码作为一种独特解决方案，旨在确保存储系统对任何有效输入链集合都能产生唯一输出。为此，我们引入了一种新颖的距离度量以刻画DNA存储系统的独特行为，并给出了DNA纠错码的充分必要条件。文中还提供了若干DNA纠错码的界值分析与构造方法。