1,355 research outputs found
Reconstruction Codes for DNA Sequences with Uniform Tandem-Duplication Errors
DNA as a data storage medium has several advantages, including far greater
data density compared to electronic media. We propose that schemes for data
storage in the DNA of living organisms may benefit from studying the
reconstruction problem, which is applicable whenever multiple reads of noisy
data are available. This strategy is uniquely suited to the medium, which
inherently replicates stored data in multiple distinct ways, caused by
mutations. We consider noise introduced solely by uniform tandem-duplication,
and utilize the relation to constant-weight integer codes in the Manhattan
metric. By bounding the intersection of the cross-polytope with hyperplanes, we
prove the existence of reconstruction codes with greater capacity than known
error-correcting codes, which we can determine analytically for any set of
parameters.Comment: 11 pages, 2 figures, Latex; version accepted for publicatio
The Capacity of Some P\'olya String Models
We study random string-duplication systems, which we call P\'olya string
models. These are motivated by DNA storage in living organisms, and certain
random mutation processes that affect their genome. Unlike previous works that
study the combinatorial capacity of string-duplication systems, or various
string statistics, this work provides exact capacity or bounds on it, for
several probabilistic models. In particular, we study the capacity of noisy
string-duplication systems, including the tandem-duplication, end-duplication,
and interspersed-duplication systems. Interesting connections are drawn between
some systems and the signature of random permutations, as well as to the beta
distribution common in population genetics
Low-redundancy codes for correcting multiple short-duplication and edit errors
Due to its higher data density, longevity, energy efficiency, and ease of
generating copies, DNA is considered a promising storage technology for
satisfying future needs. However, a diverse set of errors including deletions,
insertions, duplications, and substitutions may arise in DNA at different
stages of data storage and retrieval. The current paper constructs
error-correcting codes for simultaneously correcting short (tandem)
duplications and at most edits, where a short duplication generates a copy
of a substring with length and inserts the copy following the original
substring, and an edit is a substitution, deletion, or insertion. Compared to
the state-of-the-art codes for duplications only, the proposed codes correct up
to edits (in addition to duplications) at the additional cost of roughly
symbols of redundancy, thus achieving the same
asymptotic rate, where is the alphabet size and is a constant.
Furthermore, the time complexities of both the encoding and decoding processes
are polynomial when is a constant with respect to the code length.Comment: 21 pages. The paper has been submitted to IEEE Transaction on
Information Theory. Furthermore, the paper was presented in part at the
ISIT2021 and ISIT202
The capacity of some Pólya string models
We study random string-duplication systems, called Pólya string models, motivated by certain random mutation processes in the genome of living organisms. Unlike previous works that study the combinatorial capacity of string-duplication systems, or peripheral properties such as symbol frequency, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we give the exact capacity of the random tandem-duplication system, and the end-duplication system, and bound the capacity of the complement tandem-duplication system. Interesting connections are drawn between the former and the beta distribution common to population genetics, as well as between the latter system and signatures of random permutations
Coding for Optimized Writing Rate in DNA Storage
A method for encoding information in DNA sequences is described. The method is based on the precisionresolution framework, and is aimed to work in conjunction with a recently suggested terminator-free template independent DNA synthesis method. The suggested method optimizes the amount of information bits per synthesis time unit, namely, the writing rate. Additionally, the encoding scheme studied here takes into account the existence of multiple copies of the DNA sequence, which are independently distorted. Finally, quantizers for various run-length distributions are designed
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