Near Optimal Code Construction for the Adversarial Torn Paper Channel With Edit Errors

Abstract: Motivated by DNA storage systems and 3D fingerprinting, this work studies the adversarial torn paper channel with edit errors. This channel first applies at most $t_e$ edit errors (i.e., insertions, deletions, and substitutions) to the transmitted word and then breaks it into $t+1$ fragments at arbitrary positions. In this paper, we construct a near optimal error correcting code for this channel, which will be referred to as a $t$-breaks $t_e$-edit-errors resilient code. This code enables reconstructing the transmitted codeword from the $t+1$ noisy fragments. Moreover, we study list decoding of the torn paper channel by deriving bounds on the size of the list (of codewords) obtained from cutting a codeword of a $t$-breaks resilient code $t'$ times, where $t' > t$.