  The DNA storage channel is considered, in which the $M$ Deoxyribonucleic acid
(DNA) molecules comprising each codeword are stored without order, sampled $N$
times with replacement, and then sequenced over a discrete memoryless channel.
For a constant coverage depth $M/N$ and molecule length scaling $\Theta(\log
M)$, lower (achievability) and upper (converse) bounds on the capacity of the
channel, as well as a lower (achievability) bound on the reliability function
of the channel are provided. Both the lower and upper bounds on the capacity
generalize a bound which was previously known to hold only for the binary
symmetric sequencing channel, and only under certain restrictions on the
molecule length scaling and the crossover probability parameters. When
specified to binary symmetric sequencing channel, these restrictions are
completely removed for the lower bound and are significantly relaxed for the
upper bound in the high-noise regime. The lower bound on the reliability
function is achieved under a universal decoder, and reveals that the dominant
error event is that of outage -- the event in which the capacity of the channel
induced by the DNA molecule sampling operation does not support the target
rate.
