DNA-Correcting Codes: End-to-End Correction in DNA Storage Systems

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. We also establish bounds and constructions for these codes, including an exploration of the $\ell _{\infty } $ distance applied to permutations. Here, instead of interpreting permutation elements as numerical values and assessing absolute differences, we treat them as vectors and consider the Hamming distance to better model the DNA Storage System.