Algorithms of self-synchronizing single-deletion-correcting codes
For DNA storage and communication systems, this work provides a method to improve transmission efficiency by eliminating the need for delimiters, though it is an incremental contribution building on existing code concepts.
This paper addresses the problem of self-synchronization in DNA coding without delimiters, proposing algorithms for single-deletion-correcting codes that can identify codeword boundaries. The approach uses complementary information set codes to achieve self-synchronization and correct single-deletion errors.
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.