The Noisy Drawing Channel: Reliable Data Storage in DNA Sequences

Motivated by recent advances in DNA-based data storage, we study a communication system, where information is conveyed over many sequences in parallel. In this system, the receiver cannot control the access to these sequences and can only draw from these sequences, unaware which sequence has been drawn. Further, the drawn sequences are susceptible to errors. In this paper, a suitable channel model that models this input-output relationship is analyzed and its information capacity is computed for a wide range of parameters and a general class of drawing distributions. This generalizes previous results for the noiseless case and specific drawing distributions. The analysis can guide future DNA-based data storage experiments by establishing theoretical limits on achievable information rates and by proposing decoding techniques that can be useful for practical implementations of decoders.