The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as a collection of two-dimensional arrays. Motivated by error patterns observed in recent prototype architectures, our study focuses on correcting erasures in the last few symbols of each row, and also correcting arbitrary deletions across rows. We present code constructions and explicit encoders and decoders that are shown to be nearly optimal in many scenarios. We show that the new coding schemes are capable of effectively mitigating these errors, making these emerging storage platforms potentially promising solutions.

翻译：随着数据存储需求的不断增长，人们开始探索新的存储技术，其中分子数据存储是一种有前景的替代方案。本文针对一种可表示为二维数组集合的新型存储范式，设计了相应的编码方案。受近期原型架构中观测到的错误模式启发，本研究聚焦于纠正每行最后几个符号的擦除错误，同时纠正行间任意位置的删除错误。我们提出了码构造方案以及显式编码器和解码器，并在多种场景下证明其接近最优性能。研究结果表明，新型编码方案能够有效缓解这些错误，使这些新兴存储平台有望成为具有潜力的解决方案。