Capacity of the Shotgun Sequencing Channel

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