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Design of Nonbinary Error Correction Codes With a Maximum Run-Length Constraint to Correct a Single Insertion or Deletion Error for DNA Storage

Abstract
Due to the advantages of high information densities and longevity, DNA storage systems have begun to attract a lot of attention. However, common obstacles to DNA storage are caused by insertion, deletion, and substitution errors occurring in DNA synthesis and sequencing. In this paper, we first explain a method to convert binary data into general maximum run-length r sequences with specific length construction, which can be used as the message sequence of our proposed code. Then, we propose a new single insertion/deletion nonbinary systematic error correction code and its corresponding encoding algorithm. For the proposed code, we design the fixed maximum run-length r in the parity sequence of the proposed code to be three. Additionally, the last parity symbol and the first message symbol are always different. Hence, the overall maximum run-length r of the output codeword is guaranteed to be three when the maximum run-length of the message sequence is three. Finally, we determine the feasibility of the proposed encoding algorithm, verify successful decoding when a single insertion/deletion error occurs in the codeword, and present the comparison results with relevant works.

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