Coded Shotgun Sequencing

Most DNA sequencing technologies are based on the shotgun paradigm: many short reads obtained from random unknown locations in sequence. A fundamental question, Motahari et al. , (2013), is what read length and coverage depth (i.e., total number of reads) needed to guarantee reliable sequence reconstruction. Motivated by DNA-based storage, we study coded version this problem; i.e., scenario where molecule being sequenced a codeword predefined codebook. Our main result an exact characterization capacity resulting xmlns:xlink="http://www.w3.org/1999/xlink">shotgun channel as function depth. In particular, our results imply that, while uncoded case, $O(n)$ greater than notation="LaTeX">$2 \log n$ for reconstruction length- notation="LaTeX">$n$ binary sequence, only notation="LaTeX">$O(n/\log n)$ notation="LaTeX">$\log be arbitrarily close 1.