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 $t' > t$.

翻译：受DNA存储系统和三维指纹识别技术的启发，本研究探讨了存在编辑错误的对抗性撕裂信道。该信道首先对传输码字施加最多$t_e$次编辑错误（即插入、删除和替换），随后在任意位置将其撕裂为$t+1$个片段。本文为该信道构造了一种近最优纠错码，称为$t$次撕裂$t_e$次编辑错误容忍码。该码能够从$t+1$个含噪片段中重构出传输的码字。此外，我们通过推导$t$次撕裂容忍码的码字被撕裂$t'$次（其中$t'>t$）时所得码字列表大小的界限，研究了撕裂信道的列表译码问题。