We study the adversarial torn-paper channel. This problem is motivated by applications in DNA data storage where the DNA strands that carry information may break into smaller pieces which are received out of order. Our model extends the previously researched probabilistic setting to the worst-case. We develop code constructions for any parameters of the channel for which non-vanishing asymptotic rate is possible and show our constructions achieve asymptotically optimal rate while allowing for efficient encoding and decoding. Finally, we extend our results to related settings included multi-strand storage, presence of substitution errors, or incomplete coverage.

翻译：我们研究对抗性撕纸信道。该问题源于DNA数据存储的应用场景，其中携带信息的DNA链可能断裂成更小的片段，且这些片段会以乱序方式被接收。我们的模型将先前研究的概率设置扩展至最坏情况。对于信道中任何允许非零渐进速率的参数，我们开发了编码构造方案，并证明这些方案在实现渐进最优速率的同时支持高效的编码与解码。最后，我们将结果推广至相关场景，包括多链存储、存在替换错误或不完全覆盖的情况。