  In shotgun sequencing, the input string (typically, a long DNA sequence
composed of nucleotide bases) is sequenced as multiple overlapping fragments of
much shorter lengths (called \textit{reads}). Modelling the shotgun sequencing
pipeline as a communication channel for DNA data storage, the capacity of this
channel was identified in a recent work, assuming that the reads themselves are
noiseless substrings of the original sequence. Modern shotgun sequencers
however also output quality scores for each base read, indicating the
confidence in its identification. Bases with low quality scores can be
considered to be erased. Motivated by this, we consider the \textit{shotgun
sequencing channel with erasures}, where each symbol in any read can be
independently erased with some probability $\delta$. We identify achievable
rates for this channel, using a random code construction and a decoder that
uses typicality-like arguments to merge the reads.
