We investigate sequential decoding technqiues in a concatenated coding scheme for the insertion, deletion, and substitution channel 

The internship focuses on the analysis of code properties for burst insertion-deletion errors.

This work deals with the constuction and decoding of polar codes for the insertion, deletion, and substitution channel.

DNA is a promising data storing medium due to its longetivity and high storage density. However, due to its biological nature data errors can occur when storing or reading the DNA sequences. Moreover, not only substitution erros but also insertion and deletion errors occur frequently in the storage process. Therefore, it is important to tackle these kind of errors via coding. [1] presents methods how to correct a simplified model of deletion and insertion burst errors in DNA storage.

The student's task is to understand the coding scheme and error models discussed in [1], including the proposed proof method.

For an introduction, the references [2] and [3] may help.

References:

• [1] Lu, Ziyang, and Yiwei Zhang. "t-Deletion-1-Insertion-Burst Correcting Codes." arXiv preprint arXiv:2201.10259 (2022).

• [2] N. J. A. Sloane, “On Single-Deletion-Correcting Codes,” 2002.

• [3] V. I. Levenshtein, “Binary Codes Capable of Correcting Deletions, Insertions, and Reversals.” Soviet Physics-Doklady, Moscow, 1966.