Capacity-Achieving Constrained Codes with GC-Content and Runlength Limits for DNA Storage

GC-content and homopolymer run are two constraints of interest in DNA storage systems. Extensive experiments showed that if GC-content is too high (low), or homopolymer run exceeds six in a DNA sequence, there will give rise to dramatical increase of insertion, deletion and substitution errors. Committing to study the DNA sequences with both constraints, a recent work (Nguyen et al. 2020) proposed a class of (ϵ, ℓ)-constrained codes that can only asymptotically approach the capacity, but may have reasonable loss for finite code lengths.In this paper, we design the first (ϵ, ℓ)-constrained codes based on the enumeration coding technique which can always achieve capacity regardless of code lengths. In addition, motivated by the influence of local GC-content, we consider a nontrivial case that the prefixes of a DNA sequence also hold GC-content constraint for the first time, called (δ,ℓ)-prefix constrained codes.