  Data storage in DNA is developing as a possible solution for archival digital
data. Recently, to further increase the potential capacity of DNA-based data
storage systems, the combinatorial composite DNA synthesis method was
suggested. This approach extends the DNA alphabet by harnessing short DNA
fragment reagents, known as shortmers. The shortmers are building blocks of the
alphabet symbols, consisting of a fixed number of shortmers. Thus, when
information is read, it is possible that one of the shortmers that forms part
of the composition of a symbol is missing and therefore the symbol cannot be
determined. In this paper, we model this type of error as a type of asymmetric
error and propose code constructions that can correct such errors in this
setup. We also provide a lower bound on the redundancy of such error-correcting
codes and give an explicit encoder and decoder pair for our construction. Our
suggested error model is also supported by an analysis of data from actual
experiments that produced DNA according to the combinatorial scheme. Lastly, we
also provide a statistical evaluation of the probability of observing such
error events, as a function of read depth.
