Coded String Reconstruction from Erroneous Prefix-Suffix Compositions

The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all possible lengths of the string. In this work, we present binary codes of length $n$ in which every codeword can be efficiently reconstructed from its erroneous prefix-suffix compositions with at most $t$ composition errors, which include any combination of insertions, deletions and substitutions. All our constructions have decoding complexity polynomial in $n$.