  Due to the redundant nature of DNA synthesis and sequencing technologies, a
basic model for a DNA storage system is a multi-draw "shuffling-sampling"
channel. In this model, a random number of noisy copies of each sequence is
observed at the channel output. Recent works have characterized the capacity of
such a DNA storage channel under different noise and sequencing models, relying
on sophisticated typicality-based approaches for the achievability. Here, we
consider a multi-draw DNA storage channel in the setting of noise corruption by
a binary erasure channel. We show that, in this setting, the capacity is
achieved by linear coding schemes. This leads to a considerably simpler
derivation of the capacity expression of a multi-draw DNA storage channel than
existing results in the literature.
