This study explores the self-synchronization problem in DNA coding, specifically addressing single-deletion errors without using delimiters between codewords. We aim to identify the beginning of each codeword without using delimiters, enhancing the transmission efficiency. The motivation arises from the inefficiency of adding meaningless symbols as delimiters, decreasing the information rate. In addition, the historical context in biology, specifically Francis Crick's proposal of ``codes without commas'' for DNA sequences, inspires this investigation. We introduce a novel approach for correcting single-deletion errors in continuous transmissions without delimiters, distinguishing the beginning and end of each codeword. This approach is based on the properties of {\it complementary information set codes}, which is used to present an algorithm for {\it single-deletion correcting codes} with self-synchronizing capability. Accordingly, we present encoding and decoding algorithms for self-synchronizing single-deletion correcting DNA codes with concrete examples.

翻译：本研究探讨DNA编码中的自同步问题，具体针对无需码字间分隔符的单删除错误。我们旨在无需分隔符即可识别每个码字的起始位置，从而提高传输效率。该研究的动机源于添加无意义符号作为分隔符会降低信息速率这一效率问题。此外，生物学的历史背景——特别是弗朗西斯·克里克提出的DNA序列“无逗号编码”——启发了本项研究。我们提出了一种新方法，用于在无分隔符的连续传输中校正单删除错误，并区分每个码字的起始与结束。该方法基于互补信息集码的性质，并据此提出了一种具有自同步能力的单删除校正码算法。最后，我们给出了自同步单删除校正DNA码的编码与解码算法，并附有具体示例。