Non-Binary Codes for Correcting a Burst of at Most t Deletions

Shuche Wang, Yuanyuan Tang, Jin Sima, Ryan Gabrys, Farzad Farnoud

Abstract: The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at most $t$ deletions in non-binary sequences. When the alphabet size $q$ is even, we first propose a non-binary code correcting a burst of at most 2 deletions for $q$ -ary alphabets. Afterwards, we extend this result to the case where the length of the burst can be at most $t$ where $t$ is a constant. Finally, we consider the setup where the sequences that are transmitted are permutations. The proposed codes are the largest known for their respective parameter regimes.