Error Exponents for DNA Storage Codes with a Variable Number of Reads

In this paper, we study error exponents for a concatataned coding based class of DNA storage codes in which the number of reads performed can be variable. That is, the decoder can sequentially perform reads and choose whether to output the final decision or take more reads, and we are interested in minimizing the average number of reads performed rather than a fixed pre-specified value. We show that this flexibility leads to a considerable reduction in the error probability compared to a fixed number of reads, not only in terms of constants in the error exponent but also in the scaling laws. This is shown via an achievability result for a suitably-designed protocol, and in certain parameter regimes we additionally establish a matching converse that holds for all protocols within a broader concatenated coding based class.