Rank-Modulation Codes for DNA Storage With Shotgun Sequencing

Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to maintain reliability in reading and writing, new coding schemes must be developed. In a reading technique called shotgun sequencing, a long DNA string is read in a sliding window fashion, and a profile vector is produced. It was recently suggested by Kiah et al. that such a vector can represent the permutation which is induced by its entries, and hence a rank-modulation scheme arises. Although this interpretation suggests high error tolerance, it is unclear which permutations are feasible and how to produce a DNA string whose profile vector induces a given permutation. In this paper, by observing some necessary conditions, an upper bound for the number of feasible permutations is given. Furthermore, a technique for deciding the feasibility of a permutation is devised. By using insights from this technique, an algorithm for producing a considerable number of feasible permutations is given, which applies to any alphabet size and any window length

Rank-Modulation Codes for DNA Storage With Shotgun Sequencing

Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to maintain reliability in reading and writing, new coding schemes must be developed. In a reading technique called shotgun sequencing, a long DNA string is read in a sliding window fashion, and a profile vector is produced. It was recently suggested by Kiah et al. that such a vector can represent the permutation which is induced by its entries, and hence a rank-modulation scheme arises. Although this interpretation suggests high error tolerance, it is unclear which permutations are feasible and how to produce a DNA string whose profile vector induces a given permutation. In this paper, by observing some necessary conditions, an upper bound for the number of feasible permutations is given. Furthermore, a technique for deciding the feasibility of a permutation is devised. By using insights from this technique, an algorithm for producing a considerable number of feasible permutations is given, which applies to any alphabet size and any window length

Homomorphisms and automorphisms of 2-D de Bruijn-Good graphs

AbstractIn the paper all homomorphisms of a 2-D de Bruijn-Good graph with order (m+1,n) over an arbitrary set to a 2-D de Bruijn-Good Graph with order (m,n) are given, the automorphism group of a 2-D de Bruijn-Good Graph is determined and it is shown that there are exactly six 2n to 1 homomorphisms of a 2-D de Bruijn-Good Graph with order (m+1,n) over the finite field F2 to a 2-D de Bruijn-Good Graph with order (itm,n)