A Quaternary Code Correcting a Burst of at Most Two Deletion or Insertion Errors in DNA Storage

Abstract

Due to the properties of DNA data storage, the errors that occur in DNA strands make error correction an important and challenging task. In this paper, a new code design of quaternary code suitable for DNA storage is proposed to correct at most two consecutive deletion or insertion errors. The decoding algorithms of the proposed codes are also presented when one and two deletion or insertion errors occur, and it is proved that the proposed code can correct at most two consecutive errors. Moreover, the lower and upper bounds on the cardinality of the proposed quaternary codes are also evaluated, then the redundancy of the proposed code is provided as roughly 2log48n.

Novel q-ary Code Design for One Edit or Adjacent Transposition Error

“…If n = n − 1, inferring to Da scenario occurs, the deleted value a is determined as a = e . As mentioned in [15], decoding for deletion-correcting codes can not be always successful in determining the exact location of the deleted symbol. If a codeword with the large runs is sent and one deletion occurs in a large run, multiple candidates of the deleted position can be detected.…”