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

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