Related papers: Sequence Reconstruction for Limited-Magnitude Erro…
We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
Channels with synchronization errors, exhibiting deletion and insertion errors, find practical applications in DNA storage, data reconstruction, and various other domains. Presence of insertions and deletions render the channel with memory,…
Let $\mathcal{B}(\cdot)$ be an error ball function. A set of $q$-ary sequences of length $n$ is referred to as an \emph{$(n,q,N;\mathcal{B})$-reconstruction code} if each sequence $\boldsymbol{x}$ within this set can be uniquely…
We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the…
Given a set of samples, a few of them being possibly saturated, we propose an efficient algorithm in order to cancel saturation while reconstructing band-limited signals. Our method satisfies a minimum-loss constraint and relies on…
In modern practical data centers, storage nodes are usually organized into equally sized groups, which is called racks. The cost of cross-rack communication is much more expensive compared with the intra-rack communication cost. The codes…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that are built into the existing redundancy of the system, we propose a…
In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…
Artificial synthesis of DNA molecules is an essential part of the study of biological mechanisms. The design of a synthetic DNA molecule usually involves many objectives. One of the important objectives is to eliminate short sequence…
DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
Motivated by DNA-based data storage, we investigate a system where digital information is stored in an unordered set of several vectors over a finite alphabet. Each vector begins with a unique index that represents its position in the whole…
The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems.…
Regenerating codes for distributed storage have attracted much research interest in the past decade. Such codes trade the bandwidth needed to repair a failed node with the overall amount of data stored in the network. Minimum storage…
In this review paper, we delve into the nascent field of molecular data storage, focusing on system implementations and code constructions. We start by providing an overview of basic concepts in synthetic and computational biology.…
A method to construct and count all the linear codes (of arbitrary length) in $\mathbb{F}_{4}$ that are invariant under reverse permutation and that contain the repetition code is presented. These codes are suitable for constructing DNA…
Efficient arithmetic circuit design for resourceconstrained hardware involves challenging combinatorial optimization problems, among which Multiple Constant Multiplication (MCM) is a prominent example. MCM aims at implementing…
Recent medical image reconstruction techniques focus on generating high-quality medical images suitable for clinical use at the lowest possible cost and with the fewest possible adverse effects on patients. Recent works have shown…