Capacity-Approaching Constrained Codes with Error Correction for DNA-Based Data Storage

We propose coding techniques that limit the length of homopolymers runs, ensure the GC-content constraint, and are capable of correcting a single edit error in strands of nucleotides in DNA-based data storage systems. In particular, for given $\ell, ε > 0$, we propose simple and efficient encoders/decoders that transform binary sequences into DNA base sequences (codewords), namely sequences of the symbols A, T, C and G, that satisfy the following properties: (i) Runlength constraint: the maximum homopolymer run in each codeword is at most $\ell$, (ii) GC-content constraint: the GC-content of each codeword is within $[0.5-ε, 0.5+ε]$, (iii) Error-correction: each codeword is capable of correcting a single deletion, or single insertion, or single substitution error. For practical values of $\ell$ and $ε$, we show that our encoders achieve much higher rates than existing results in the literature and approach the capacity. Our methods have low encoding/decoding complexity and limited error propagation.

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