Iterative coding scheme satisfying GC balance and run-length constraints for DNA storage with robustness to error propagation

Abstract

In this paper, we propose a novel iterative encoding algorithm for DNA storage to satisfy both the GC balance and run-length constraints using a greedy algorithm. DNA strands with run-length more than three and the GC balance ratio far from 50% are known to be prone to errors. The proposed encoding algorithm stores data with high flexibility of run-length at most 𝑚 and GC balance between 0.5 ± 𝛼 for arbitrary 𝑚 and 𝛼. More importantly, we propose a novel mapping method to reduce the average bit error compared to the randomly generated mapping method. By using the proposed method, the average bit error caused by the one base error is 2.3455 bits, which is reduced by 20.5%, compared to the randomized mapping. Also, it is robust to error propagation since the input sequence is partitioned into small blocks during the mapping step. The proposed algorithm is implemented through iterative encoding, consisting of three main steps: randomization, M-ary mapping, and verification. It has an information density of 1.833 bits/nt in the case of 𝑚 = 3 and 𝛼 = 0.05.

Highly Robust DNA Data Storage Based on Controllable GC Content and homopolymer of 64-Element Coded Tables

“…For two DNA sequences, a and b, we use H(a, b) to denote the number of different bases at position i of the sequence (a, b) . The Hamming distance is calculated using the following formula[26]: …”

“…GC content refers to the ratio of the total number of G and C bases to the total number of bases in a DNA sequence, which is closely related to the stability of the DNA sequence and the melting point. The designed DNA sequence should be within the range of 40% ≤ GC(n) ≤ 60% to ensure that the constraints of GC content are met, and the formula of GC(n) is as follows[26]: where GC(n) denotes the GC content of the sequence, | G | and | C | represent the number of bases G and C, respectively, in the sequence n , and | n | denotes the total number of bases in the sequence.…”

“…For the codeword d(D 1 , D 2 , D 3 , …, D □), where D □ ∈ (A, T, G, C) , for any i , we have the following relation[26]: …”

“…GC content refers to the ratio of the total number of G and C bases to the total number of bases in a DNA sequence, which is closely related to the stability of the DNA sequence and the melting point. The designed DNA sequence should be within the range of 40% ≤ GC(n) ≤ 60% to ensure that the constraints of GC content are met, and the formula of GC(n) is as follows [26]:…”

“…During experiments, extreme GC content and longer homopolymer stretches (e.g., long homopolymer AAAAA) can lead to substitution errors during synthesis and sequencing. Literature [17] and literature [26] point out that the substitution error rate increases significantly, especially for homopolymer sequences of lengths more than six. In addition, DNA sequences with high GC content develop a highly variable state during PCR amplification.…”