全面覆盖：如何在DNA存储系统中最小化测序覆盖深度
Cover Your Bases: How to Minimize the Sequencing Coverage in DNA Storage Systems
AI总结：
本文研究DNA存储中的覆盖深度问题，通过分析纠错码与检索算法对所需读取次数的影响，证明均匀分布下MDS码最优，并构造出期望检索时间低于k的编码方案，以降低DNA存储的成本与延迟。
摘要：
尽管DNA测序的相关费用一直在迅速下降，但当前测序信息的成本仍约为每GB 120美元，这比从现有档案存储解决方案中读取要昂贵得多。在本工作中，我们旨在通过发起对DNA覆盖深度问题的研究，不仅降低DNA存储的成本，还降低其延迟；该问题旨在减少从存储系统中检索信息所需的读取次数。在此框架下，我们的主要目标是理解纠错码和检索算法对所需测序覆盖深度的影响。我们证明，当信道服从均匀分布时，信息检索所需的期望读取次数达到最小。我们还推导了该所需读取次数概率分布的上界和下界，并给出了其期望值的全面上界和下界。我们进一步证明，对于无噪声信道和均匀分布，MDS码在最小化期望读取次数方面是最优的。此外，我们研究了随机访问设置下的DNA覆盖深度问题，在该设置中，用户旨在仅从整个DNA存储系统中检索一个特定信息单元。我们证明，对于[n,k] MDS码以及其他码族，期望检索时间至少为k。更进一步，我们给出了能够实现期望检索时间低于k的显式编码构造，并通过解析方法和仿真评估其性能。最后，我们给出了最大期望检索时间的下界。我们的发现为降低DNA存储的成本和延迟提供了有价值的见解。
英文摘要：
Although the expenses associated with DNA sequencing have been rapidly decreasing, the current cost of sequencing information stands at roughly $120/GB, which is dramatically more expensive than reading from existing archival storage solutions today. In this work, we aim to reduce not only the cost but also the latency of DNA storage by initiating the study of the DNA coverage depth problem, which aims to reduce the required number of reads to retrieve information from the storage system. Under this framework, our main goal is to understand the effect of error-correcting codes and retrieval algorithms on the required sequencing coverage depth. We establish that the expected number of reads that are required for information retrieval is minimized when the channel follows a uniform distribution. We also derive upper and lower bounds on the probability distribution of this number of required reads and provide a comprehensive upper and lower bound on its expected value. We further prove that for a noiseless channel and uniform distribution, MDS codes are optimal in terms of minimizing the expected number of reads. Additionally, we study the DNA coverage depth problem under the random-access setup, in which the user aims to retrieve just a specific information unit from the entire DNA storage system. We prove that the expected retrieval time is at least k for [n,k] MDS codes as well as for other families of codes. Furthermore, we present explicit code constructions that achieve expected retrieval times below k and evaluate their performance through analytical methods and simulations. Lastly, we provide lower bounds on the maximum expected retrieval time. Our findings offer valuable insights for reducing the cost and latency of DNA storage.
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