  The problem of string reconstruction from substring information has found
many applications due to its relevance in DNA- and polymer-based data storage.
One practically important and challenging paradigm requires reconstructing
mixtures of strings based on the union of compositions of their prefixes and
suffixes, generated by mass spectrometry readouts. We describe new coding
methods that allow for unique joint reconstruction of subsets of strings
selected from a code and provide matching upper and lower bounds on the
asymptotic rate of the underlying codebooks. Under certain mild constraints on
the problem parameters, one can show that the largest possible rate of a
codebook that allows for all subcollections of $\leq h$ codestrings to be
uniquely reconstructable from the prefix-suffix information equals $1/h$.
