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

Reconstructing Mixtures of Coded Strings from Prefix and Suffix Compositions