12,709 research outputs found
On Codes for the Noisy Substring Channel
We consider the problem of coding for the substring channel, in which
information strings are observed only through their (multisets of) substrings.
Because of applications to DNA-based data storage, due to DNA sequencing
techniques, interest in this channel has renewed in recent years. In contrast
to existing literature, we consider a noisy channel model, where information is
subject to noise \emph{before} its substrings are sampled, motivated by in-vivo
storage.
We study two separate noise models, substitutions or deletions. In both
cases, we examine families of codes which may be utilized for error-correction
and present combinatorial bounds. Through a generalization of the concept of
repeat-free strings, we show that the added required redundancy due to this
imperfect observation assumption is sublinear, either when the fraction of
errors in the observed substring length is sufficiently small, or when that
length is sufficiently long. This suggests that no asymptotic cost in rate is
incurred by this channel model in these cases.Comment: ISIT 2021 version (including all proofs
On Coding over Sliced Information
The interest in channel models in which the data is sent as an unordered set
of binary strings has increased lately, due to emerging applications in DNA
storage, among others. In this paper we analyze the minimal redundancy of
binary codes for this channel under substitution errors, and provide several
constructions, some of which are shown to be asymptotically optimal up to
constants. The surprising result in this paper is that while the information
vector is sliced into a set of unordered strings, the amount of redundant bits
that are required to correct errors is order-wise equivalent to the amount
required in the classical error correcting paradigm
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
Rates of DNA Sequence Profiles for Practical Values of Read Lengths
A recent study by one of the authors has demonstrated the importance of
profile vectors in DNA-based data storage. We provide exact values and lower
bounds on the number of profile vectors for finite values of alphabet size ,
read length , and word length .Consequently, we demonstrate that for
and , the number of profile vectors is at least
with very close to one.In addition to enumeration
results, we provide a set of efficient encoding and decoding algorithms for
each of two particular families of profile vectors
- …