Embedded Codes for Reassembling Non-Overlapping Random DNA Fragments

We consider the problem of recovering the stored data from randomly broken Deoxyribonucleic Acid (DNA) fragments. More precisely, we assume a channel that breaks the DNA into a random number of non-overlapping fragments where the length of each fragment comes from a memoryless Geometric process. We devise an embedded code structure that enables reassembly of the DNA and analyze its error probability. We observe that the error decreases with DNA length for various breaking probabilities of the Geometric process. Our code is built upon Varshamov-Tenengolts (VT) codes, and enables a much more efficient recovery strategy compared to brute-force search among all permutations of the DNA fragments.