Data-Driven Bee Identification for DNA Strands

We study a data-driven approach to the bee identification problem for DNA strands. The bee-identification problem, introduced by Tandon et al. (2019), requires one to identify M bees, each tagged by a unique barcode, via a set of M noisy measurements. Later, Chrisnata et al. (2022) extended the model to case where one observes N noisy measurements of each bee, and applied the model to address the unordered nature of DNA storage systems.In such systems, a unique address is typically prepended to each DNA data block to form a DNA strand, but the address may possibly be corrupted. While clustering is usually used to identify the address of a DNA strand, this requires ℳ
²
data comparisons (when ℳ is the number of reads). In contrast, the approach of Chrisnata et al. (2022) avoids data comparisons completely. In this work, we study an intermediate, data-driven approach to this identification task.For the binary erasure channel, we first show that we can almost surely correctly identify all DNA strands under certain mild assumptions. Then we propose a data-driven pruning procedure and demonstrate that on average the procedure uses only a fraction of ℳ
²
data comparisons. Specifically, for ℳ = 2
ⁿ
and erasure probability p, the expected number of data comparisons performed by the procedure is κℳ
²
, where ${\left( {\frac{{1 + 2p - {p^2}}}{2}} \right)^n} \leq \kappa \leq {\left( {\frac{{1 + p}}{2}} \right)^n}$.