Related papers: Reconstruction from Noisy Substrings
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
DNA, with remarkable properties of high density, durability, and replicability, is one of the most appealing storage media. Emerging DNA storage technologies use composite DNA letters, where information is represented by probability…
Life relies on the efficient performance of molecular codes, which relate symbols and meanings via error-prone molecular recognition. We describe how optimizing a code to withstand the impact of molecular recognition noise may be…
We consider the problem of reconstructing an undirected graph $G$ on $n$ vertices given multiple random noisy subgraphs or "traces". Specifically, a trace is generated by sampling each vertex with probability $p_v$, then taking the…
We investigate the problem of decoding a bar code from a signal measured with a hand-held laser-based scanner. Rather than formulating the inverse problem as one of binary image reconstruction, we instead incorporate the symbology of the…
This paper presents an explicit construction for an $((n,k,d=n-1), (\alpha,\beta))$ regenerating code over a field $\mathbb{F}_Q$ operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate $k/n$…
We provide an overview of current approaches to DNA-based storage system design and accompanying synthesis, sequencing and editing methods. We also introduce and analyze a suite of new constrained coding schemes for both archival and random…
This paper investigates adaptive streaming codes over a three-node relayed network. In this setting, a source transmits a sequence of message packets through a relay under a delay constraint of $T$ time slots per packet. The source-to-relay…
Distributed storage systems with replication are well known for storing large amount of data. A large number of replication is done in order to provide reliability. This makes the system expensive. Various methods have been proposed over…
We investigate the capacity of noisy frequency-based channels, motivated by DNA data storage in the short-molecule regime, where information is encoded in the frequency of items types rather than their order. The channel output is a…
This thesis consists of original contributions in the area of digital signal processing. The reconstruction of signals sparse (highly concentrated) in various transform domains is the primary problem analyzed in the thesis. The considered…
Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging…
In this paper we study the structure of specific linear codes called DNA codes. The first attempts on studying such codes have been proposed over four element rings which are naturally matched with DNA four letters. Later, double (pair) DNA…
The general trace reconstruction problem seeks to recover an original sequence from its noisy copies independently corrupted by deletions, insertions, and substitutions. This problem arises in applications such as DNA data storage, a…
The well-known trace reconstruction problem is the problem of inferring an unknown source string $x \in \{0,1\}^n$ from independent "traces", i.e. copies of $x$ that have been corrupted by a $\delta$-deletion channel which independently…
To increase the information capacity of DNA storage, composite DNA letters were introduced. We propose a novel channel model for composite DNA in which composite sequences are decomposed into ordered standard non-composite sequences. The…
We frame the task of predicting a semantic labeling as a sparse reconstruction procedure that applies a target-specific learned transfer function to a generic deep sparse code representation of an image. This strategy partitions training…