DNA数据存储中文件检索的双曲界

中文摘要 AI 辅助

在基于DNA的存储系统中，数据通过从DNA池中采样分子进行测序来检索。我们研究了编码冗余在文件之间的共享方式如何影响其预期检索时间。我们关注的情况是两个文件由任意有限域上的系统线性码编码。我们考虑一个猜想：只要至少一个文件的维度大于1，每个文件维度除以其预期检索时间所得之和至多为1。为此，我们开发了检索过程的几何视角。随着分子的采样，我们跟踪生成矩阵对应列的生成跨度，并追踪该跨度中有多少来自每个文件。在扩大总跨度的样本中，这让我们能够比较那些在恢复两个文件方面取得进展的样本与那些在两个文件方面均未取得进展的样本。如果对应的编码符号结合了两个文件的信息，我们称该列为混合列。在这项工作中，我们强化了一个投影界，并用它来控制混合列的影响。当总信息维度至少是混合列数加二的两倍时，我们证明了该猜想。对于大小相等的文件，这允许混合列数比任一文件的维度少一列，并扩展了先前针对无混合列代码的结果。

英文摘要

In DNA-based storage systems, data are retrieved by sequencing molecules sampled from a DNA pool. We study how the way coding redundancy is shared between files affects their expected retrieval times. Our focus lies on the case of two files that are encoded by a systematic linear code over an arbitrary finite field. We consider the conjecture that the sum obtained by dividing each file dimension by its expected retrieval time is at most one whenever the dimension of at least one file is more than one. For this, we develop a geometric view of the retrieval process. As molecules are sampled, we follow the growing span of the corresponding columns of the generator matrix and track how much of this span comes from each file. Among the samples that enlarge the overall span, this lets us compare those that make progress toward recovering both files with those that make progress toward neither. We call a column mixed if the corresponding encoded symbol combines information from both files. In this work, we sharpen a projection bound and use it to control the effect of mixed columns. We prove the conjecture whenever the total information dimension is at least twice the number of mixed columns plus two. For equal-sized files, this allows up to one fewer mixed column than the dimension of either file and extends the previous result for codes with no mixed columns.

发表机构

• Universität Zürich（苏黎世大学）
• IBM Research Europe（IBM欧洲研究院）
• Technion—Israel Institute of Technology（以色列理工学院）

机构由 AI 辅助整理，请以论文原文为准。