A Hyperbolic Bound for File Retrieval in DNA-Based Data Storage
Abstract
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.
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BibTeX
@misc{vlachos2026hyperbolic,
title = {{A Hyperbolic Bound for File Retrieval in DNA-Based Data Storage}},
author = {Constantinos Vasilios Argyris Vlachos and Daniella Bar-Lev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36067},
eprint = {2609.36067},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36067},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Hyperbolic Bound for File Retrieval in DNA-Based Data Storage
AU - Constantinos Vasilios Argyris Vlachos
AU - Daniella Bar-Lev
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36067
UR - https://arxiv.org/abs/2609.36067
AB - 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.
ER -