  Synthetic polymer-based storage seems to be a particularly promising
candidate that could help to cope with the ever-increasing demand for archival
storage requirements. It involves designing molecules of distinct masses to
represent the respective bits $\{0,1\}$, followed by the synthesis of a polymer
of molecular units that reflects the order of bits in the information string.
Reading out the stored data requires the use of a tandem mass spectrometer,
that fragments the polymer into shorter substrings and provides their
corresponding masses, from which the \emph{composition}, i.e. the number of
$1$s and $0$s in the concerned substring can be inferred. Prior works have
dealt with the problem of unique string reconstruction from the set of all
possible compositions, called \emph{composition multiset}. This was
accomplished either by determining which string lengths always allow unique
reconstruction, or by formulating coding constraints to facilitate the same for
all string lengths. Additionally, error-correcting schemes to deal with
substitution errors caused by imprecise fragmentation during the readout
process, have also been suggested. This work builds on this research by
generalizing previously considered error models, mainly confined to
substitution of compositions. To this end, we define new error models that
consider insertions of spurious compositions and deletions of existing ones,
thereby corrupting the composition multiset. We analyze if the reconstruction
codebook proposed by Pattabiraman \emph{et al.} is indeed robust to such
errors, and if not, propose new coding constraints to remedy this.
