相关论文: Multi-strand Reconstruction from Substrings

Although deep learning (DL) methods are powerful for solving inverse problems, their reliance on high-quality training data is a major hurdle. This is significant in high-dimensional (dynamic/volumetric) magnetic resonance imaging (MRI),…

The high-throughput short-reads RNA-seq protocols often produce paired-end reads, with the middle portion of the fragments being unsequenced. We explore if the full-length fragments can be computationally reconstructed from the sequenced…

We argue that the behavior of string theory at high temperature and high longitudinal boosts, combined with the emergence of p-branes as necessary ingredients in various string dualities, point to a possible reformulation of strings, as…

The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication setting in which a sender transmits a codeword and the receiver observes K independent noisy versions of this codeword. In this work, we study…

We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is…

In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many,…

As the global need for large-scale data storage is rising exponentially, existing storage technologies are approaching their theoretical and functional limits in terms of density and energy consumption, making DNA based storage a potential…

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a…

The coded trace reconstruction problem asks to construct a code $C\subset \{0,1\}^n$ such that any $x\in C$ is recoverable from independent outputs ("traces") of $x$ from a binary deletion channel (BDC). We present binary codes of rate…

Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization…

Determining whether an unordered collection of overlapping substrings (called shingles) can be uniquely decoded into a consistent string is a problem that lies within the foundation of a broad assortment of disciplines ranging from…

Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol…

Dynamic Magnetic Resonance Imaging (dMRI) is widely used to assess various cardiac conditions such as cardiac motion and blood flow. To accelerate MR acquisition, techniques such as undersampling and Simultaneous Multi-Slice (SMS) are often…

We introduce a new variant of the $k$-deck problem, which in its traditional formulation asks for determining the smallest $k$ that allows one to reconstruct any binary sequence of length $n$ from the multiset of its $k$-length…

We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such,…

Recent advances in optical systems make them ideal for undersampling multiband signals that have high bandwidths. In this paper we propose a new scheme for reconstructing multiband sparse signals using a small number of sampling channels.…

Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm…

This paper studies the sequence reconstruction problem for a channel inspired by protein identification. We introduce a coloring channel, where a sequence is transmitted through a channel that deletes all symbols not belonging to a fixed…

DNA codes have many applications, such as in data storage, DNA computing, etc. Good DNA codes have large sizes and satisfy some certain constraints. In this paper, we present a new construction method for reversible DNA codes. We show that…

The $k$-deck problem is concerned with finding the smallest positive integer $S(k)$ such that there exist at least two strings of length $S(k)$ that share the same $k$-deck, i.e., the multiset of subsequences of length $k$. We introduce the…